A Faster Algorithm for Quasi-convex Integer Polynomial Optimization
Hildebrand, Robert
2010-01-01
We present a faster exponential-time algorithm for integer optimization over quasi-convex polynomials. We study the minimization of a quasi-convex polynomial subject to s quasi-convex polynomial constraints and integrality constraints for all variables. The new algorithm is an improvement upon the best known algorithm due to Heinz (Journal of Complexity, 2005). A lower time complexity is reached through applying a stronger ellipsoid rounding method and applying a recent advancement in the shortest vector problem to give a smaller exponential-time complexity of a Lenstra-type algorithm. For the bounded case, our algorithm attains a time-complexity of s (r l M d)^{O(1)} 2^{2n\\log_2(n) + O(n)} when M is a bound on the number of monomials in each polynomial and r is the binary encoding length of a bound on the feasible region. In the general case, s l^{O(1)} d^{O(n)} 2^{2n\\log_2(n)}. In each we assume d>=2 is a bound on the total degree of the polynomials and l bounds the maximum binary encoding size of the input...
A Convex Optimization Model and Algorithm for Retinex
Directory of Open Access Journals (Sweden)
Qing-Nan Zhao
2017-01-01
Full Text Available Retinex is a theory on simulating and explaining how human visual system perceives colors under different illumination conditions. The main contribution of this paper is to put forward a new convex optimization model for Retinex. Different from existing methods, the main idea is to rewrite a multiplicative form such that the illumination variable and the reflection variable are decoupled in spatial domain. The resulting objective function involves three terms including the Tikhonov regularization of the illumination component, the total variation regularization of the reciprocal of the reflection component, and the data-fitting term among the input image, the illumination component, and the reciprocal of the reflection component. We develop an alternating direction method of multipliers (ADMM to solve the convex optimization model. Numerical experiments demonstrate the advantages of the proposed model which can decompose an image into the illumination and the reflection components.
DEFF Research Database (Denmark)
Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan
2012-01-01
for the purpose of designing iterative image reconstruction algorithms for CT. The primal–dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application......The primal–dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1–26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems...
Convex Optimization without Projection Steps
Jaggi, Martin
2011-01-01
We study the general problem of minimizing a convex function over a compact convex domain. We will investigate a simple iterative approximation algorithm that does not need projection steps in order to stay inside the optimization domain. Instead of a projection step, the linearized problem defined by a current subgradient is solved, which gives a step direction that will naturally stay in the domain. The approach generalizes the sparse greedy algorithm of Clarkson (and the low-rank SDP solver by Hazan) to arbitrary convex domains, and to using subgradients for the case of non-differentiable convex functions. Analogously, we give a convergence proof guaranteeing {\\epsilon}-small duality gap after O(1/{\\epsilon}) iterations. The framework allows us understand the sparsity of approximate solutions for any l1-regularized convex optimization problem, expressed as a function of the approximation quality. We obtain matching upper and lower bounds of {\\Theta}(1/{\\epsilon}) for the sparsity for l1-problems. The same ...
An Inner Convex Approximation Algorithm for BMI Optimization and Applications in Control
Dinh, Quoc Tran; Diehl, Moritz
2012-01-01
In this work, we propose a new local optimization method to solve a class of nonconvex semidefinite programming (SDP) problems. The basic idea is to approximate the feasible set of the nonconvex SDP problem by inner positive semidefinite convex approximations via a parameterization technique. This leads to an iterative procedure to search a local optimum of the nonconvex problem. The convergence of the algorithm is analyzed under mild assumptions. Applications in static output feedback control are benchmarked and numerical tests are implemented based on the data from the COMPLeib library.
Quantum information and convex optimization
Energy Technology Data Exchange (ETDEWEB)
Reimpell, Michael
2008-07-01
This thesis is concerned with convex optimization problems in quantum information theory. It features an iterative algorithm for optimal quantum error correcting codes, a postprocessing method for incomplete tomography data, a method to estimate the amount of entanglement in witness experiments, and it gives necessary and sufficient criteria for the existence of retrodiction strategies for a generalized mean king problem. (orig.)
Directory of Open Access Journals (Sweden)
Akemi Gálvez
2013-01-01
Full Text Available Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor’s method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.
Non-convex multi-objective optimization
Pardalos, Panos M; Žilinskas, Julius
2017-01-01
Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in...
A simple convex optimization problem with many applications
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1994-01-01
This paper presents an algorithm for the solution of a simple convex optimization problem. This problem is a generalization of several other optimization problems which have applications to resource allocation, optimal capacity expansion, and vehicle scheduling. The algorithm is based...
Reverse convex problems: an approach based on optimality conditions
Directory of Open Access Journals (Sweden)
Ider Tseveendorj
2006-01-01
Full Text Available We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.
Reverse convex problems: an approach based on optimality conditions
Ider Tseveendorj
2006-01-01
We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.
A Mean Point Based Convex Hull Computation Algorithm
Directory of Open Access Journals (Sweden)
Digvijay Singh
2016-11-01
Full Text Available The optimal solution of a Linear Programming problem (LPP is a basic feasible solution and all basic feasible solutions are extreme or boundary points of a convex region formed by the constraint functions of the LPP. In fact, the feasible solution space is not always a convex set so the verification of extreme points for optimality is quite difficult. In order to cover the non-convex feasible points within a convex set, a convex hull is imagined so that the extreme or boundary points may be checked for evaluation of the optimum solution in the decision-making process. In this article a computer assisted convex hull computation algorithm using the Mean Point and Python code verified results of the designed algorithm are discussed.
Conference on Convex Analysis and Global Optimization
Pardalos, Panos
2001-01-01
There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by th...
A Convex Optimization Approach to pMRI Reconstruction
Zhang, Cishen
2013-01-01
In parallel magnetic resonance imaging (pMRI) reconstruction without using estimation of coil sensitivity functions, one group of algorithms reconstruct sensitivity encoded images of the coils first followed by the magnitude only image reconstruction, e.g. GRAPPA, and another group of algorithms jointly compute the image and sensitivity functions by regularized optimization which is a non-convex problem with local only solutions. For the magnitude only image reconstruction, this paper derives a reconstruction formulation, which is linear in the magnitude image, and an associated convex hull in the solution space of the formulated equation containing the magnitude of the image. As a result, the magnitude only image reconstruction for pMRI is formulated into a two-step convex optimization problem, which has a globally optimal solution. An algorithm based on split-bregman and nuclear norm regularized optimizations is proposed to implement the two-step convex optimization and its applications to phantom and in-vi...
Convex analysis and global optimization
Tuy, Hoang
2016-01-01
This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students (also in applied mathematics), and practitioners in various fields of engineering. The second edition has been brought up to date and continues to develop a coherent and rigorous theory of deterministic global optimization, highlighting the essential role of convex analysis. The text has been revised and expanded to meet the needs of research, education, and applications for many years to come. Updates for this new edition include: · Discussion of modern approaches to minimax, fixed point, and equilibrium theorems, and to nonconvex optimization; · Increased focus on dealing more efficiently with ill-posed problems of global optimization, particularly those with hard constraints;
Finite dimensional convexity and optimization
Florenzano, Monique
2001-01-01
The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.
Convex functions and optimization methods on Riemannian manifolds
Udrişte, Constantin
1994-01-01
This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...
Convex analysis and optimization in Hadamard spaces
Bacak, Miroslav
2014-01-01
This book gives a first systematic account on the subject of convex analysis and optimization in Hadamard spaces. It is primarily aimed at both graduate students and researchers in analysis and optimization.
Global optimization over linear constraint non-convex programming problem
Institute of Scientific and Technical Information of China (English)
ZHANG Gui-Jun; WU Ti-Huan; YE Rong; YANG Hai-qing
2005-01-01
A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programmin g problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.
Institute of Scientific and Technical Information of China (English)
张忠武; 周宇; 孟祥华; 肖永
2015-01-01
First improve the Quadrilateral method fast convex hull algorithm to adapt it to the Pyramid convex hull algorithm, and then put forward the Initial approximate convex hull algorithm.Next to the working principle of the Initial approximate convex hull algorithm is expounded, and the concrete steps of implementing description.At last, through a large number of Experimental data to analyze the acceleration of the approximate convex hull efficiency and coarse convex hull the best choice of the number of edges.%首先改进四边形法快速凸壳算法使其适应金字塔凸壳算法,进而提出初始近似凸壳算法.其次对初始近似凸壳算法的工作原理进行阐述,并其具体的实现步骤描述.最后通过大量实验数据分析近似凸壳的加速效率以及粗凸壳边数的最佳选择方案.
Directional Convexity and Finite Optimality Conditions.
1984-03-01
system, Necessary Conditions for optimality. Work Unit Number 5 (Optimization and Large Scale Systems) *Istituto di Matematica Applicata, Universita...that R(T) is convex would then imply x(u,T) e int R(T). Cletituto di Matematica Applicata, Universita di Padova, 35100 ITALY. Sponsored by the United
Optimal convex shapes for concave functionals
Bucur, Dorin; Lamboley, Jimmy
2011-01-01
Motivated by a long-standing conjecture of Polya and Szeg\\"o about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application to isoperimetriclike inequalities. As a byproduct of this approach we also obtain a quantitative version of the Kneser-S\\"uss inequality. Finally, for a large class of functionals involving Dirichlet energies and the surface measure, we perform a local analysis of strictly convex portions of the boundary via second order shape derivatives. This allows in particular to exclude the presence of smooth regions with positive Gauss curvature in an optimal shape for Polya-Szeg\\"o problem.
A New Representation and Algorithm for Constructing Convex Hulls in Higher Dimensional Spaces
Institute of Scientific and Technical Information of China (English)
吕伟; 梁友栋
1992-01-01
This paper presents a new and simple scheme to describe the convex hull in Rd,which only uses three kinds of the faces of the convex hull.i.e.,the d-1-faces,d-2-faces and 0-faces.Thus,we develop and efficient new algorithm for constructing the convex hull of a finite set of points incrementally.This algorithm employs much less storage and time than that of the previously-existing approaches.The analysis of the runniing time as well as the storage for the new algorithm is also theoretically made.The algorithm is optimal in the worst case for even d.
Convergence of Algorithms for Reconstructing Convex Bodies and Directional Measures
DEFF Research Database (Denmark)
Gardner, Richard; Kiderlen, Markus; Milanfar, Peyman
2006-01-01
We investigate algorithms for reconstructing a convex body K in Rn from noisy measurements of its support function or its brightness function in k directions u1, . . . , uk. The key idea of these algorithms is to construct a convex polytope Pk whose support function (or brightness function) best ...
DEFF Research Database (Denmark)
Lauritzen, Niels
-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point...
Non-convex polygons clustering algorithm
Directory of Open Access Journals (Sweden)
Kruglikov Alexey
2016-01-01
Full Text Available A clustering algorithm is proposed, to be used as a preliminary step in motion planning. It is tightly coupled to the applied problem statement, i.e. uses parameters meaningful only with respect to it. Use of geometrical properties for polygons clustering allows for a better calculation time as opposed to general-purpose algorithms. A special form of map optimized for quick motion planning is constructed as a result.
Skala, Vaclav
2016-06-01
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees, octrees, kd-trees, bounding volume hierarchies etc. However in some applications a non-orthogonal space subdivision can offer new ways for actual speed up. In the case of convex polygon in E2 a simple Point-in-Polygon test is of the O(N) complexity and the optimal algorithm is of O(log N) computational complexity. In the E3 case, the complexity is O(N) even for the convex polyhedron as no ordering is defined. New Point-in-Convex Polygon and Point-in-Convex Polyhedron algorithms are presented based on space subdivision in the preprocessing stage resulting to O(1) run-time complexity. The presented approach is simple to implement. Due to the principle of duality, dual problems, e.g. line-convex polygon, line clipping, can be solved in a similarly.
First-order convex feasibility algorithms for x-ray CT
DEFF Research Database (Denmark)
Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan
2013-01-01
Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times......, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems....... In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution—thereby facilitating...
Identification of community structure in networks with convex optimization
Hildebrand, Roland
2008-01-01
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous one. A semidefinite relaxation of this conic program then allows to compute upper bounds on the maximum modularity of the network. Based on the solution of the corresponding semidefinite program, we design a randomized algorithm generating partitions of the network with suboptimal modularities. We apply this algorithm to several benchmark networks, demonstrating that it is competitive in accuracy with the best algorithms previously known. We use our method to provide the first proof of optimality of a partition for a real-world network.
Institute of Scientific and Technical Information of China (English)
Qin Ni; Ch. Zillober; K. Schittkowski
2005-01-01
In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming (SCP). A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.
Convex hull ranking algorithm for multi-objective evolutionary algorithms
Davoodi Monfrared, M.; Mohades, A.; Rezaei, J.
2012-01-01
Due to many applications of multi-objective evolutionary algorithms in real world optimization problems, several studies have been done to improve these algorithms in recent years. Since most multi-objective evolutionary algorithms are based on the non-dominated principle, and their complexity depen
Sidky, Emil Y; Pan, Xiaochuan
2012-01-01
Iterative image reconstruction (IIR) algorithms in Computed Tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this article, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for efficient algorithms for their solution -- thereby facilitating the IIR algorithm design process. An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex fea...
Institute of Scientific and Technical Information of China (English)
胡图; 景志宏; 张磊; 张秋林
2012-01-01
Aimed at the characteristics of cognitive Ad hoc network, a corresponding network model is established and a distributed power control algorithm based on convex optimization theory is proposed. Based on the analysis of system interference, by taking the network utility maximization as the target and transmit power of cognitive user as the solution object, a general math optimized model is formulated. Under the guidance of convex optimization theory , the model is transformed into a convex optimized model by introducing auxiliary variable and substituting variables. Lagrangian dual decomposition technique is used to solve the convex optimized model and the distributed power iterative algorithm is obtained. The simulation shows that under the premise of meeting the system constraints, the use of the proposed algorithm can obtain better system performances than that of other algorithms.%针对认知Ad hoc网络的特点,构建了相应的网络模型,提出了一种基于凸优化理论的分布式功率控制算法.在分析系统内部干扰的基础上,以最大化网络效用值为目标,以认知用户的发射功率为求解对象,建立了一个通用的数学优化模型.在凸优化理论的指导下,通过引入辅助变量和变量的对数变换,将该模型转变为等价的凸优化模型,采用拉格朗日对偶法对该模型进行求解,得到了分布式的功率迭代算法.仿真实验表明:与其他算法相比,该算法在满足系统约束条件的前提下,取得更好的系统性能.
Statistical Mechanics of Optimal Convex Inference in High Dimensions
Advani, Madhu; Ganguli, Surya
2016-07-01
A fundamental problem in modern high-dimensional data analysis involves efficiently inferring a set of P unknown model parameters governing the relationship between the inputs and outputs of N noisy measurements. Various methods have been proposed to regress the outputs against the inputs to recover the P parameters. What are fundamental limits on the accuracy of regression, given finite signal-to-noise ratios, limited measurements, prior information, and computational tractability requirements? How can we optimally combine prior information with measurements to achieve these limits? Classical statistics gives incisive answers to these questions as the measurement density α =(N /P )→∞ . However, these classical results are not relevant to modern high-dimensional inference problems, which instead occur at finite α . We employ replica theory to answer these questions for a class of inference algorithms, known in the statistics literature as M-estimators. These algorithms attempt to recover the P model parameters by solving an optimization problem involving minimizing the sum of a loss function that penalizes deviations between the data and model predictions, and a regularizer that leverages prior information about model parameters. Widely cherished algorithms like maximum likelihood (ML) and maximum-a posteriori (MAP) inference arise as special cases of M-estimators. Our analysis uncovers fundamental limits on the inference accuracy of a subclass of M-estimators corresponding to computationally tractable convex optimization problems. These limits generalize classical statistical theorems like the Cramer-Rao bound to the high-dimensional setting with prior information. We further discover the optimal M-estimator for log-concave signal and noise distributions; we demonstrate that it can achieve our high-dimensional limits on inference accuracy, while ML and MAP cannot. Intriguingly, in high dimensions, these optimal algorithms become computationally simpler than
A New Hybrid Shuffled Frog Leaping Algorithm to Solve Non-convex Economic Load Dispatch Problem
Directory of Open Access Journals (Sweden)
Ehsan Bijami
2011-11-01
Full Text Available This paper presents a New Hybrid Shuffled Frog Leaping (NHSFL algorithm applied to solve Economic Load Dispatch (ELD problem. Practical ELD has non-convex cost function and various equality and inequality constraints that convert the ELD problem as a nonlinear, non-convex and non-smooth optimization problem. In this paper, a new frog leaping rule is proposed to improve the local exploration and the performance of the conventional SFL algorithm. Also a genetic mutation operator is used for the creation of new frogs instead of random frog creation that improves the convergence. To show the efficiency of the proposed approach, the non-convex ELD problem is solved using conventional SFL and an improved SFL method proposed by other researchers. Then the results of SFL methods are compared to the results obtained by the proposed NHSFL algorithm. Simulation studies show that the results obtained by NHSFL are more effective and better compared with these algorithms.
A capacity scaling algorithm for convex cost submodular flows
Energy Technology Data Exchange (ETDEWEB)
Iwata, Satoru [Kyoto Univ. (Japan)
1996-12-31
This paper presents a scaling scheme for submodular functions. A small but strictly submodular function is added before scaling so that the resulting functions should be submodular. This scaling scheme leads to a weakly polynomial algorithm to solve minimum cost integral submodular flow problems with separable convex cost functions, provided that an oracle for exchange capacities are available.
A New Subspace Correction Method for Nonlinear Unconstrained Convex Optimization Problems
Institute of Scientific and Technical Information of China (English)
Rong-liang CHEN; Jin-ping ZENG
2012-01-01
This paper gives a new subspace correction algorithm for nonlinear unconstrained convex optimization problems based on the multigrid approach proposed by S.Nash in 2000 and the subspace correction algorithm proposed by X.Tai and J.Xu in 2001.Under some reasonable assumptions,we obtain the convergence as well as a convergence rate estimate for the algorithm.Numerical results show that the algorithm is effective.
Institute of Scientific and Technical Information of China (English)
邵言剑; 陶卿; 姜纪远; 周柏
2014-01-01
Stochastic gradient descent (SGD) is one of the efficient methods for dealing with large-scale data. Recent research shows that the black-box SGD method can reach an O(1/T) convergence rate for strongly-convex problems. However, for solving the regularized problem with L1 plus L2 terms, the convergence rate of the structural optimization method such as COMID (composite objective mirror descent) can only attain O(lnT/T). In this paper, a weighted algorithm based on COMID is presented, to keep the sparsity imposed by the L1 regularization term. A prove is provided to show that it achieves an O(1/T) convergence rate. Furthermore, the proposed scheme takes the advantage of computation on-the-fly so that the computational costs are reduced. The experimental results demonstrate the correctness of theoretic analysis and effectiveness of the proposed algorithm.%随机梯度下降(SGD)算法是处理大规模数据的有效方法之一。黑箱方法SGD在强凸条件下能达到最优的O(1/T)收敛速率，但对于求解L1+L2正则化学习问题的结构优化算法，如COMID(composite objective mirror descent)仅具有O(lnT/T)的收敛速率。提出一种能够保证稀疏性基于COMID的加权算法，证明了其不仅具有O(1/T)的收敛速率，还具有on-the-fly计算的优点，从而减少了计算代价。实验结果表明了理论分析的正确性和所提算法的有效性。
Exploiting Symmetry in Integer Convex Optimization using Core Points
Herr, Katrin; Schürmann, Achill
2012-01-01
We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. We define a core point of such a symmetry group as an integral point for which the convex hull of its orbit does not contain integral points other than the orbit points themselves. These core points allow us to decompose symmetric integer convex programming problems. Especially for symmetric integer linear programs we describe two algorithms based on this decomposition. Using a characterization of core points for direct products of symmetric groups, we show that prototype implementations can compete with state-of-the art commercial solvers and solve an open MIPLIB problem.
Global Optimization Approach to Non-convex Problems
Institute of Scientific and Technical Information of China (English)
LU Zi-fang; ZHENG Hui-li
2004-01-01
A new approach to find the global optimal solution of the special non-convex problems is proposed in this paper. The non-convex objective problem is first decomposed into two convex sub-problems. Then a generalized gradient is introduced to determine a search direction and the evolution equation is built to obtain a global minimum point. By the approach, we can prevent the search process from some local minima and search a global minimum point. Two numerical examples are given to prove the approach to be effective.
Closedness type regularity conditions in convex optimization and beyond
Directory of Open Access Journals (Sweden)
Sorin-Mihai Grad
2016-09-01
Full Text Available The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we de- and reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively, for general optimization problems in order to stress that they arise naturally when dealing with such problems. The results are then specialized for constrained and unconstrained convex optimization problems. We also hint towards other classes of optimization problems where closedness type regularity conditions were successfully employed and discuss other possible applications of them.
Gradient of the Value Function in Parametric Convex Optimization Problems
Baotić, Mato
2016-01-01
We investigate the computation of the gradient of the value function in parametric convex optimization problems. We derive general expression for the gradient of the value function in terms of the cost function, constraints and Lagrange multipliers. In particular, we show that for the strictly convex parametric quadratic program the value function is continuously differentiable at every point in the interior of feasible space for which the Linear Independent Constraint Qualification holds.
Implementation of an optimal first-order method for strongly convex total variation regularization
DEFF Research Database (Denmark)
Jensen, Tobias Lindstrøm; Jørgensen, Jakob Heide; Hansen, Per Christian;
2012-01-01
We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to μ-strongly convex objective functions with L-Lipschitz continuous gradient...
Optimal Energy Consumption in Refrigeration Systems - Modelling and Non-Convex Optimisation
DEFF Research Database (Denmark)
Hovgaard, Tobias Gybel; Larsen, Lars F. S.; Skovrup, Morten J.
2012-01-01
that is somewhat more efficient than general purpose optimisation algorithms for NMPC and still near to optimal. Since the non-convex cost function has multiple extrema, standard methods for optimisation cannot be directly applied. A qualitative analysis of the system's constraints is presented and a unique...
Derivative-free generation and interpolation of convex Pareto optimal IMRT plans.
Hoffmann, Aswin L; Siem, Alex Y D; den Hertog, Dick; Kaanders, Johannes H A M; Huizenga, Henk
2006-12-21
In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.
Memoryless Routing in Convex Subdivisions: Random Walks are Optimal
Chen, Dan; Dujmovic, Vida; Morin, Pat
2009-01-01
A memoryless routing algorithm is one in which the decision about the next edge on the route to a vertex t for a packet currently located at vertex v is made based only on the coordinates of v, t, and the neighbourhood, N(v), of v. The current paper explores the limitations of such algorithms by showing that, for any (randomized) memoryless routing algorithm A, there exists a convex subdivision on which A takes Omega(n^2) expected time to route a message between some pair of vertices. Since this lower bound is matched by a random walk, this result implies that the geometric information available in convex subdivisions is not helpful for this class of routing algorithms. The current paper also shows the existence of triangulations for which the Random-Compass algorithm proposed by Bose etal (2002,2004) requires 2^{\\Omega(n)} time to route between some pair of vertices.
AN EFFICIENT ALGORITHM FOR THE CONVEX HULL OF PLANAR SCATTERED POINT SET
Directory of Open Access Journals (Sweden)
Z. Fu
2012-07-01
Full Text Available Computing the convex hull of a point set is requirement in the GIS applications. This paper studies on the problem of minimum convex hull and presents an improved algorithm for the minimum convex hull of planar scattered point set. It adopts approach that dividing the point set into several sub regions to get an initial convex hull boundary firstly. Then the points on the boundary, which cannot be vertices of the minimum convex hull, are removed one by one. Finally the concave points on the boundary, which cannot be vertices of the minimum convex hull, are withdrew. Experimental analysis shows the efficiency of the algorithm compared with other methods.
Greedy vs. L1 convex optimization in sparse coding
DEFF Research Database (Denmark)
Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor;
2015-01-01
, such as face and action recognition, a comparative study of codes in abnormal event detection is less studied and hence no conclusion is gained on the effect of codes in detecting abnormalities. We constrict our comparison in two types of the above L0-norm solutions: greedy algorithms and convex L1-norm...
Asynchronous Code-Division Random Access Using Convex Optimization
Applebaum, Lorne; Duarte, Marco F; Calderbank, Robert
2011-01-01
Many applications in cellular systems and sensor networks involve a random subset of a large number of users asynchronously reporting activity to a base station. This paper examines the problem of multiuser detection (MUD) in random access channels for such applications. Traditional orthogonal signaling ignores the random nature of user activity in this problem and limits the total number of users to be on the order of the number of signal space dimensions. Contention-based schemes, on the other hand, suffer from delays caused by colliding transmissions and the hidden node problem. In contrast, this paper presents a novel asynchronous (non-orthogonal) code-division random access scheme along with a convex optimization-based MUD algorithm that overcomes the issues associated with orthogonal signaling and contention-based methods. Two key distinguishing features of the proposed algorithm are that it does not require knowledge of the delay or channel state information of every user and it has polynomial-time com...
Trading Regret for Efficiency: Online Convex Optimization with Long Term Constraints
Mahdavi, Mehrdad; Yang, Tianbao
2011-01-01
In this paper we propose a framework for solving constrained online convex optimization problem. Our motivation stems from the observation that most algorithms proposed for online convex optimization require a projection onto the convex set $\\mathcal{K}$ from which the decisions are made. While for simple shapes (e.g. Euclidean ball) the projection is straightforward, for arbitrary complex sets this is the main computational challenge and may be inefficient in practice. In this paper, we consider an alternative online convex optimization problem. Instead of requiring decisions belong to $\\mathcal{K}$ for all rounds, we only require that the constraints which define the set $\\mathcal{K}$ be satisfied in the long run. We show that our framework can be utilized to solve a relaxed version of online learning with side constraints addressed in \\cite{DBLP:conf/colt/MannorT06} and \\cite{DBLP:conf/aaai/KvetonYTM08}. By turning the problem into an online convex-concave optimization problem, we propose an efficient algo...
Pinson, Robin Marie
Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed
Visualizing Data as Objects by DC (Difference of Convex) Optimization
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
2017-01-01
In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization prob...
Bot, Radu Ioan
2012-01-01
The aim of this paper is to develop an efficient algorithm for solving a class of unconstrained nondifferentiable convex optimization problems in finite dimensional spaces. To this end we formulate first its Fenchel dual problem and regularize it in two steps into a differentiable strongly convex one with Lipschitz continuous gradient. The doubly regularized dual problem is then solved via a fast gradient method with the aim of accelerating the resulting convergence scheme. The theoretical results are finally applied to an l1 regularization problem arising in image processing.
Triangulation Algorithm Based on Empty Convex Set Condition
Directory of Open Access Journals (Sweden)
Klyachin Vladimir Aleksandrovich
2015-11-01
Full Text Available The article is devoted to generalization of Delaunay triangulation. We suggest to consider empty condition for special convex sets. For given finite set P ⊂ Rn we shall say that empty condition for convex set B ⊂ Rn is fullfiled if P ∩ B = P ∩ ∂B. Let Φ = Φα, α ∈ A be a family of compact convex sets with non empty inner. Consider some nondegenerate simplex S ⊂ Rn with vertexes p0,...,pn. We define the girth set B(S ∈ Φ if qi ∈ ∂B(S, i = 0, 1, ..., n. We suppose that the family Φ has the property: for arbitrary nondegenerate simplex S there is only one the girth set B(S. We prove the following main result. Theorem 1. If the family Φ = Φα, α ∈ A of convex sets have the pointed above property then for the girth sets it is true: 1. The set B(S is uniquely determined by any simplex with vertexes on ∂B(S. 2. Let S1, S2 be two nondegenerate simplexes such that B(S1 ≠ B(S2. If the intersection B(S1 ∩ B(S2 is not empty, then the intersection of boundaries B(S1, B(S2 is (n − 2-dimensional convex surface, lying in some hyperplane. 3. If two simplexes S1 and S2 don’t intersect by inner points and have common (n − 1-dimensional face G and A, B are vertexes don’t belong to face G and vertex B of simplex B(S2 such that B ∉ B(S1 then B(S2 does not contain the vertex A of simplex S1. These statements allow us to define Φ-triangulation correctly by the following way. The given triangulation T of finite set P ⊂ Rn is called Φ-triangulation if for all simlex S ∈ T the girth set B(S ∈ Φ is empty. In the paper we give algorithm for construct Φ-triangulation arbitrary finite set P ⊂ Rn. Besides we describe examples of families Φ for which we prove the existence and uniqueness of girth set B(S for arbitrary nondegenerate simplex S.
A new algorithm for computing the convex hull of a planar point set
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
When the edges of a convex polygon are traversed along one direction, the interior of the convex polygon is always on the same side of the edges. Based on this characteristic of convex polygons, a new algorithm for computing the convex hull of a simple polygon is proposed in this paper, which is then extended to a new algorithm for computing the convex hull of a planar point set. First, the extreme points of the planar point set are found, and the subsets of point candidate for vertex of the convex hull between extreme points are obtained. Then, the ordered convex hull point sequences between extreme points are constructed separately and concatenated by removing redundant extreme points to get the convex hull. The time complexity of the new planar convex hull algorithm is O(nlogh), which is equal to the time complexity of the best output-sensitive planar convex hull algorithms.Compared with the algorithm having the same complexity, the new algorithm is much faster.
Nonlinear Non-convex Optimization of Hydraulic Networks
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Kallesøe, Carsten; Leth, John-Josef
2013-01-01
Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption...... in pumps and also to regulate the pressure at the end-user valves to a desired value. The optimization problem which is solved is a nonlinear and non-convex optimization. The barrier method is used to solve this problem. The modeling framework and the optimization technique which are used are general...
Robust Quantum Error Correction via Convex Optimization
Kosut, R L; Lidar, D A
2007-01-01
Quantum error correction procedures have traditionally been developed for specific error models, and are not robust against uncertainty in the errors. Using a semidefinite program optimization approach we find high fidelity quantum error correction procedures which present robust encoding and recovery effective against significant uncertainty in the error system. We present numerical examples for 3, 5, and 7-qubit codes. Our approach requires as input a description of the error channel, which can be provided via quantum process tomography.
Non-convex onion peeling using a shape hull algorithm
Fadili, Jalal M.; Melkemi, Mahmoud; Elmoataz, Abderrahim
2004-01-01
International audience; The convex onion-peeling of a set of points is the organization of these points into a sequence of interpolating convex polygons. This method is adequate to detect the shape of the “center” of a set of points when this shape is convex. However it reveals inadequate to detect non-convex shapes. Alternatively, we propose an extension of the convex onion-peeling method. It consists in representing a set of points with a sequence of non-convex polylines which are computed ...
Institute of Scientific and Technical Information of China (English)
ZHU Detong
2000-01-01
This paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems.The mixed strategy is adopted which switches to back tracking steps when a trial projected gradient step produced by the trust region subproblem is unacceptable. A nonmonotone criterion is used to speed up the convergence progress in some curves with large curvature.A theoretical analysis is given which proves that the proposed algorithms are globally convergent and have local superlinear convergence rate under some reasonable conditions.The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.
Vector optimization and monotone operators via convex duality recent advances
Grad, Sorin-Mihai
2014-01-01
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
A toolbox for robust PID controller tuning using convex optimization
Sadeghpour, Mehdi; de Oliveira, Vinicius; Karimi, Alireza
2012-01-01
A robust PID controller design toolbox for Matlab is presented in this paper. The design is based on linearizing or convexifying the conventional non-convex constraints on the classical robustness margins or H∞ constraints. Then the existing optimization solvers can be used to compute the controller parameters. The software can be used in a wide range of controller design problems, including multi-model systems and gain-scheduled controllers. The models can be parametric or non-parametric whi...
M. Dyer; R. Kannan; L. Stougie (Leen)
2014-01-01
htmlabstractWe consider maximising a concave function over a convex set by a simplerandomised algorithm. The strength of the algorithm is that it requires only approximatefunction evaluations for the concave function and a weak membership oraclefor the convex set. Under smoothness conditions on the
Optimal placement of convex polygons to maximize point containment
Energy Technology Data Exchange (ETDEWEB)
Dickerson, M. [Middlebury College, VT (United States); Scharstein, D. [Cornell Univ., Ithaca, NY (United States)
1996-12-31
Given a convex polygon P with m vertices and a set S of n points in the plane, we consider the problem of finding a placement of P that contains the maximum number of points in S. We allow both translation and rotation. Our algorithm is self-contained and utilizes the geometric properties of the containing regions in the parameter space of transformations. The algorithm requires O(nk{sup 2} m{sup 2} log(mk)) time and O(n + m) space, where k is the maximum number of points contained. This provides a linear improvement over the best previously known algorithm when k is large ({Theta}(n)) and a cubic improvement when k is small. We also show that the algorithm can be extended to solve bichromatic and general weighted variants of the problem.
Optimal convex correcting procedures in problems of high dimension
Dokukin, A. A.; Senko, O. V.
2011-09-01
The properties of convex correcting procedures (CCPs) over sets of predictors are examined. It is shown that the minimization of the generalized error in a CCP is reduced to a quadratic programming problem. The conditions are studied under which a set of predictors cannot be reduced without degrading the accuracy of the corresponding optimal CCP. Experimental studies of the prognostic properties of CCPs for samples of one-dimensional linear regressions showed that CCP optimization can be an effective tool for regression variable selection.
Nonlinear Non-convex Optimization of Hydraulic Networks
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Kallesøe, Carsten; Leth, John-Josef
2013-01-01
Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption...... in pumps and also to regulate the pressure at the end-user valves to a desired value. The optimization problem which is solved is a nonlinear and non-convex optimization. The barrier method is used to solve this problem. The modeling framework and the optimization technique which are used are general....... They can be used for a general hydraulic networks to optimize the leakage and energy consumption and to satisfy the demands at the end-users. The results in this paper show that the power consumption of the pumps is reduced....
Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging
Girard, Julien N; Starck, Jean Luc; Corbel, Stéphane; Woiselle, Arnaud; Tasse, Cyril; McKean, John P; Bobin, Jérôme
2015-01-01
Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we expose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ~2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emissions as compared to CLEAN. With the advent of large radiotel...
A convex programming framework for optimal and bounded suboptimal well field management
DEFF Research Database (Denmark)
Dorini, Gianluca Fabio; Thordarson, Fannar Ørn; Bauer-Gottwein, Peter
2012-01-01
are often convex, hence global optimality can be attained by a wealth of algorithms. Among these, the Interior Point methods are extensively employed for practical applications, as they are capable of efficiently solving large-scale problems. Despite this, management models explicitly embedding both systems....... The objective of the management is to minimize the total cost of pump operations over a multistep time horizon, while fulfilling a set of time-varying management constraints. Optimization in groundwater management and pressurized WDNs have been widely investigated in the literature. Problem formulations...
A New Interpolation Approach for Linearly Constrained Convex Optimization
Espinoza, Francisco
2012-08-01
In this thesis we propose a new class of Linearly Constrained Convex Optimization methods based on the use of a generalization of Shepard\\'s interpolation formula. We prove the properties of the surface such as the interpolation property at the boundary of the feasible region and the convergence of the gradient to the null space of the constraints at the boundary. We explore several descent techniques such as steepest descent, two quasi-Newton methods and the Newton\\'s method. Moreover, we implement in the Matlab language several versions of the method, particularly for the case of Quadratic Programming with bounded variables. Finally, we carry out performance tests against Matab Optimization Toolbox methods for convex optimization and implementations of the standard log-barrier and active-set methods. We conclude that the steepest descent technique seems to be the best choice so far for our method and that it is competitive with other standard methods both in performance and empirical growth order.
An Optimal Online Algorithm for Halfplane Intersection
Institute of Scientific and Technical Information of China (English)
WU Jigang; JI Yongchang; CHEN Guoliang
2000-01-01
The intersection of N halfplanes is a basic problem in computational geometry and computer graphics. The optimal offiine algorithm for this problem runs in time O(N log N). In this paper, an optimal online algorithm which runs also in time O(N log N) for this problem is presented. The main idea of the algorithm is to give a new definition for the left side of a given line, to assign the order for the points of a convex polygon, and then to use binary search method in an ordered vertex set. The data structure used in the algorithm is no more complex than array.
Greedy vs. L1 Convex Optimization in Sparse Coding
DEFF Research Database (Denmark)
Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor
Sparse representation has been applied successfully in many image analysis applications, including abnormal event detection, in which a baseline is to learn a dictionary from the training data and detect anomalies from its sparse codes. During this procedure, sparse codes which can be achieved...... and action recognition, a comparative study of codes in abnormal event detection is less studied and hence no conclusion is gained on the effect of codes in detecting abnormalities. We constrict our comparison in two types of the above L0-norm solutions: greedy algorithms and convex L1-norm solutions....... Considering the property of abnormal event detection, i.e., only normal videos are used as training data due to practical reasons, effective codes in classification application may not perform well in abnormality detection. Therefore, we compare the sparse codes and comprehensively evaluate their performance...
Optimal Orthogonal Graph Drawing with Convex Bend Costs
Bläsius, Thomas; Wagner, Dorothea
2012-01-01
Traditionally, the quality of orthogonal planar drawings is quantified by either the total number of bends, or the maximum number of bends per edge. However, this neglects that in typical applications, edges have varying importance. Moreover, as bend minimization over all planar embeddings is NP-hard, most approaches focus on a fixed planar embedding. We consider the problem OptimalFlexDraw that is defined as follows. Given a planar graph G on n vertices with maximum degree 4 and for each edge e a cost function cost_e : N_0 --> R defining costs depending on the number of bends on e, compute an orthogonal drawing of G of minimum cost. Note that this optimizes over all planar embeddings of the input graphs, and the cost functions allow fine-grained control on the bends of edges. In this generality OptimalFlexDraw is NP-hard. We show that it can be solved efficiently if 1) the cost function of each edge is convex and 2) the first bend on each edge does not cause any cost (which is a condition similar to the posi...
Optimization-based mesh correction with volume and convexity constraints
D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; Bochev, Pavel; Shashkov, Mikhail
2016-05-01
We consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.
Group Leaders Optimization Algorithm
Daskin, Anmer
2010-01-01
Complexity of global optimization algorithms makes implementation of the algorithms difficult and leads the algorithms to require more computer resources for the optimization process. The ability to explore the whole solution space without increasing the complexity of algorithms has a great importance to not only get reliable results but so also make the implementation of these algorithms more convenient for higher dimensional and complex-real world problems in science and engineering. In this paper, we present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique that is designed into a group architecture similar to the architecture of Cooperative Coevolutionary Algorithms. Therefore, we present the implementation method and the experimental results for the single and multidimensional optimization test problems and a scientific real world problem, the energies and the geometric structures of Lennard-Jones clusters.
Optimization algorithms and applications
Arora, Rajesh Kumar
2015-01-01
Choose the Correct Solution Method for Your Optimization ProblemOptimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs. The book covers both gradient and stochastic methods as solution techniques for unconstrained and constrained optimization problems. It discusses the conjugate gradient method, Broyden-Fletcher-Goldfarb-Shanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible direc
Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces
Directory of Open Access Journals (Sweden)
Kim JongKyu
2010-01-01
Full Text Available The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi- -asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.
Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces
Directory of Open Access Journals (Sweden)
Shih-sen Chang
2010-01-01
Full Text Available The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi-ϕ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.
A Localization Method for Multistatic SAR Based on Convex Optimization.
Directory of Open Access Journals (Sweden)
Xuqi Zhong
Full Text Available In traditional localization methods for Synthetic Aperture Radar (SAR, the bistatic range sum (BRS estimation and Doppler centroid estimation (DCE are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.
A Localization Method for Multistatic SAR Based on Convex Optimization.
Zhong, Xuqi; Wu, Junjie; Yang, Jianyu; Sun, Zhichao; Huang, Yuling; Li, Zhongyu
2015-01-01
In traditional localization methods for Synthetic Aperture Radar (SAR), the bistatic range sum (BRS) estimation and Doppler centroid estimation (DCE) are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R) pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.
First-order Convex Optimization Methods for Signal and Image Processing
DEFF Research Database (Denmark)
Jensen, Tobias Lindstrøm
2012-01-01
In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can...... be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple......-description problem. We finally present the contributions of the thesis. The remaining parts of the thesis consist of five research papers. The first paper addresses non-smooth first-order convex optimization and the trade-off between accuracy and smoothness of the approximating smooth function. The second and third...
SOLVING CONVEX QUADRATIC PROGRAMMING BY POTENTIAL-REDUCTION INTERIOR-POINT ALGORITHM
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The solution of quadratic programming problems is an importantissue in the field of mathematical programming and industrial applications. In this paper, we solve convex quadratic programming by a potential-reduction interior-point algorithm. It is proved that the potential-reduction interior-point algorithm is globally convergent. Some numerical experiments were made.
A DEEP CUT ELLIPSOID ALGORITHM FOR CONVEX-PROGRAMMING - THEORY AND APPLICATIONS
FRENK, JBG; GROMICHO, J; ZHANG, S
1994-01-01
This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent s
Lateral ventricle segmentation of 3D pre-term neonates US using convex optimization.
Qiu, Wu; Yuan, Jing; Kishimoto, Jessica; Ukwatta, Eranga; Fenster, Aaron
2013-01-01
Intraventricular hemorrhage (IVH) is a common disease among preterm infants with an occurrence of 12-20% in those born at less than 35 weeks gestational age. Neonates at risk of IVH are monitored by conventional 2D ultrasound (US) for hemorrhage and potential ventricular dilation. Compared to 2D US relying on linear measurements from a single slice and visually estimates to determine ventricular dilation, 3D US can provide volumetric ventricle measurements, more sensitive to longitudinal changes in ventricular volume. In this work, we propose a global optimization-based surface evolution approach to the segmentation of the lateral ventricles in preterm neonates with IVH. The proposed segmentation approach makes use of convex optimization technique in combination with a subject-specific shape model. We show that the introduced challenging combinatorial optimization problem can be solved globally by means of convex relaxation. In this regard, we propose a coupled continuous max-flow model, which derives a new and efficient dual based algorithm, that can be implemented on GPUs to achieve a high-performance in numerics. Experiments demonstrate the advantages of our approach in both accuracy and efficiency. To the best of our knowledge, this paper reports the first study on semi-automatic segmentation of lateral ventricles in neonates with IVH from 3D US images.
Energy Technology Data Exchange (ETDEWEB)
Cho, Tae Min; Lee, Byung Chai [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of)
2010-01-15
In this study, an effective method for reliability-based design optimization (RBDO) is proposed enhancing sequential optimization and reliability assessment (SORA) method by convex approximations. In SORA, reliability estimation and deterministic optimization are performed sequentially. The sensitivity and function value of probabilistic constraint at the most probable point (MPP) are obtained in the reliability analysis loop. In this study, the convex approximations for probabilistic constraint are constructed by utilizing the sensitivity and function value of the probabilistic constraint at the MPP. Hence, the proposed method requires much less function evaluations of probabilistic constraints in the deterministic optimization than the original SORA method. The efficiency and accuracy of the proposed method were verified through numerical examples
An uncertain multidisciplinary design optimization method using interval convex models
Li, Fangyi; Luo, Zhen; Sun, Guangyong; Zhang, Nong
2013-06-01
This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss-Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.
libCreme: An optimization library for evaluating convex-roof entanglement measures
Röthlisberger, Beat; Loss, Daniel
2011-01-01
We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the Matlab programming language, but is fully compatible to the free and open-source Octave platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focussing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems.
Higher-order principal component pursuit via tensor approximation and convex optimization
Institute of Scientific and Technical Information of China (English)
Sijia Cai; Ping Wang; Linhao Li; Chuhan Zhang
2014-01-01
Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit (PCP). This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit (HOPCP), since it is critical in multi-way data analysis. Unlike the convexification (nuclear norm) for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme: the augmented Lagrangian alternating di-rection method (ALADM) and its truncated higher-order singular value decomposition (ALADM-THOSVD) version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computational y intractable problems. Experimental re-sults on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.
A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Yu Qian; Huang Chongchao; Jiang Yan
2006-01-01
This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step,where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O(√nL) iteration complexity which is the best result for convex quadratic programming so far.
Vegh, Laszlo A.
2011-01-01
A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\\sum_{ij\\in E} C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function. We give a strongly polynomial algorithm for the case when all $C_{ij}$'s are convex quadratic functions, settling an open problem raised e.g. by Hochbaum [1994]. We also give strongly polynomial algorithms for computing market equilibria in Fisher markets with linear util...
An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations
Guermond, Jean-Luc
2009-01-01
We describe an algorithm for solving steady one-dimensional convex-like Hamilton-Jacobi equations using a L1-minimization technique on piecewise linear approximations. For a large class of convex Hamiltonians, the algorithm is proven to be convergent and of optimal complexity whenever the viscosity solution is q-semiconcave. Numerical results are presented to illustrate the performance of the method.
Nature-inspired optimization algorithms
Yang, Xin-She
2014-01-01
Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical background and practical implementation, complements extensive literature with well-chosen case studies to illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms, simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search, algorithm analysis, constraint handling, hybrid methods, parameter tuning
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui;
2016-01-01
This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed...... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...... solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui
2016-01-01
This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed...... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...... solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....
An algorithm for the construction of convex hulls in simple integer recourse programming
Klein Haneveld, W.K.; Stougie, L.; van der Vlerk, M.H.
1996-01-01
We consider the objective function of a simple integer recourse problem with fixed technology matrix and discretely distributed right-hand sides. Exploiting the special structure of this problem, we devise an algorithm that determines the convex hull of this function efficiently. The results are imp
Reconstruction of the early Universe as a convex optimization problem
Brenier, Y.; Frisch, U.; Hénon, M.; Loeper, G.; Matarrese, S.; Mohayaee, R.; Sobolevskiĭ, A.
2003-12-01
We show that the deterministic past history of the Universe can be uniquely reconstructed from knowledge of the present mass density field, the latter being inferred from the three-dimensional distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales - a few Mpc - where multistreaming becomes significant. Above 6 h-1 Mpc we propose and implement an effective Monge-Ampère-Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge. After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than O(N3) time complexity and reasonable CPU time requirements. Testing against N-body cosmological simulations gives over 60 per cent of exactly reconstructed points. We apply several interrelated tools from optimization theory that were not used in cosmological reconstruction before, such as the Monge-Ampère equation, its relation to the mass transportation problem, the Kantorovich duality and the auction algorithm for optimal assignment. A self-contained discussion of relevant notions and techniques is provided.
Wei, W. B.; Tan, L.; Jia, M. Q.; Pan, Z. K.
2017-01-01
The variational level set method is one of the main methods of image segmentation. Due to signed distance functions as level sets have to keep the nature of the functions through numerical remedy or additional technology in an evolutionary process, it is not very efficient. In this paper, a normal vector projection method for image segmentation using Chan-Vese model is proposed. An equivalent formulation of Chan-Vese model is used by taking advantage of property of binary level set functions and combining with the concept of convex relaxation. Threshold method and projection formula are applied in the implementation. It can avoid the above problems and obtain a global optimal solution. Experimental results on both synthetic and real images validate the effects of the proposed normal vector projection method, and show advantages over traditional algorithms in terms of computational efficiency.
Networked and Distributed Convex Optimization for Design, Estimation, and Verification
2009-10-01
IEEE Transactions on Automatic Control . 3...to appear in IEEE Transactions on Automatic Control , October 2009. 7. S. Joshi and S. Boyd, “Subspaces that Minimize the Condition Number of a Matrix...Jitter,” IEEE Transactions on Automatic Control , 54(3):652-657, March 2009. 16. A. Magnani and S. Boyd, “Convex Piecewise-Linear
A proximal point method for nonsmooth convex optimization problems in Banach spaces
Directory of Open Access Journals (Sweden)
Y. I. Alber
1997-01-01
Full Text Available In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.
Fast Bundle-Level Type Methods for Unconstrained and Ball-Constrained Convex Optimization
2014-12-01
of half- spaces , hence it is convex and closed. Therefore, the subproblem (3.4) always has a unique solution as long as Qk is non-empty. To finish the...pixels in the image. The ‖u‖TV is convex and non-smooth. Table 5.1 Uniformly distributed QP instances A : n = 4000,m = 3000, L = 2.0e6, e0 = 2.89e4 Alg...generation. Mathematical pro- gramming, 118(1):177–206, 2009. [14] G. Lan. Bundle-level type methods uniformly optimal for smooth and non-smooth convex
Rotationally resliced 3D prostate TRUS segmentation using convex optimization with shape priors.
Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Fenster, Aaron
2015-02-01
Efficient and accurate segmentations of 3D end-firing transrectal ultrasound (TRUS) images play an important role in planning of 3D TRUS guided prostate biopsy. However, poor image quality of the input 3D TRUS images, such as strong imaging artifacts and speckles, often makes it a challenging task to extract the prostate boundaries accurately and efficiently. In this paper, the authors propose a novel convex optimization-based approach to delineate the prostate surface from a given 3D TRUS image, which reduces the original 3D segmentation problem to a sequence of simple 2D segmentation subproblems over the rotational reslices of the 3D TRUS volume. Essentially, the authors introduce a novel convex relaxation-based contour evolution approach to each 2D slicewise image segmentation with the joint optimization of shape information, where the learned 2D nonlinear statistical shape prior is incorporated to segment the initial slice, its result is propagated as a shape constraint to the segmentation of the following slices. In practice, the proposed segmentation algorithm is implemented on a GPU to achieve the high computational performance. Experimental results using 30 patient 3D TRUS images show that the proposed method can achieve a mean Dice similarity coefficient of 93.4% ± 2.2% in 20 s for one 3D image, outperforming the existing local-optimization-based methods, e.g., level-set and active-contour, in terms of accuracy and efficiency. In addition, inter- and intraobserver variability experiments show its good reproducibility. A semiautomatic segmentation approach is proposed and evaluated to extract the prostate boundary from 3D TRUS images acquired by a 3D end-firing TRUS guided prostate biopsy system. Experimental results suggest that it may be suitable for the clinical use involving the image guided prostate biopsy procedures.
High-Dimensional Analysis of Convex Optimization-Based Massive MIMO Decoders
Ben Atitallah, Ismail
2017-04-01
A wide range of modern large-scale systems relies on recovering a signal from noisy linear measurements. In many applications, the useful signal has inherent properties, such as sparsity, low-rankness, or boundedness, and making use of these properties and structures allow a more efficient recovery. Hence, a significant amount of work has been dedicated to developing and analyzing algorithms that can take advantage of the signal structure. Especially, since the advent of Compressed Sensing (CS) there has been significant progress towards this direction. Generally speaking, the signal structure can be harnessed by solving an appropriate regularized or constrained M-estimator. In modern Multi-input Multi-output (MIMO) communication systems, all transmitted signals are drawn from finite constellations and are thus bounded. Besides, most recent modulation schemes such as Generalized Space Shift Keying (GSSK) or Generalized Spatial Modulation (GSM) yield signals that are inherently sparse. In the recovery procedure, boundedness and sparsity can be promoted by using the ℓ1 norm regularization and by imposing an ℓ∞ norm constraint respectively. In this thesis, we propose novel optimization algorithms to recover certain classes of structured signals with emphasis on MIMO communication systems. The exact analysis permits a clear characterization of how well these systems perform. Also, it allows an automatic tuning of the parameters. In each context, we define the appropriate performance metrics and we analyze them exactly in the High Dimentional Regime (HDR). The framework we use for the analysis is based on Gaussian process inequalities; in particular, on a new strong and tight version of a classical comparison inequality (due to Gordon, 1988) in the presence of additional convexity assumptions. The new framework that emerged from this inequality is coined as Convex Gaussian Min-max Theorem (CGMT).
Institute of Scientific and Technical Information of China (English)
田朝薇; 宋海洲
2011-01-01
针对非凸二次约束二次规划(QCQP)问题,将问题中二次函数的凸函数部分保留,达到所得松弛规划的可行域更加紧致的目的,得到原问题更好的下界.利用正交变换的方法得到原问题的一个凸规划松弛模型,再利用分支定界算法求其全局最优解.根据问题的最优性和可行性原则,提出一种能整体删除或缩小算法迭代过程中产生的分割子区域的区域删减策略.数值算例表明,算法及区域删减策略均是有效的.%In this paper, we obtain a sharper low bound by reserving the part of the convex function of the quadratic function for a non-convex quadratic programming with non-convex quadratic constraints (QCQP). The QCQP problem is first transformed into a convex quadratic programming with linear constraints by employing the orthogonal transformation and then the latter is solved by the branch-bound method. In order to improve the convergence of the proposed algorithm, two region-prunning techniques are given to delete or contract the sub-regions in which does not contain the optimal solutions of QCQP according to the optimality and feasibility of the problem. The numerical results show that the proposed algorithm and the prunning techniques are effective.
A recurrent neural network for solving a class of generalized convex optimization problems.
Hosseini, Alireza; Wang, Jun; Hosseini, S Mohammad
2013-08-01
In this paper, we propose a penalty-based recurrent neural network for solving a class of constrained optimization problems with generalized convex objective functions. The model has a simple structure described by using a differential inclusion. It is also applicable for any nonsmooth optimization problem with affine equality and convex inequality constraints, provided that the objective function is regular and pseudoconvex on feasible region of the problem. It is proven herein that the state vector of the proposed neural network globally converges to and stays thereafter in the feasible region in finite time, and converges to the optimal solution set of the problem.
Directory of Open Access Journals (Sweden)
Bruno H. Dias
2010-01-01
Full Text Available This paper presents a new approach for the expected cost-to-go functions modeling used in the stochastic dynamic programming (SDP algorithm. The SDP technique is applied to the long-term operation planning of electrical power systems. Using state space discretization, the Convex Hull algorithm is used for constructing a series of hyperplanes that composes a convex set. These planes represent a piecewise linear approximation for the expected cost-to-go functions. The mean operational costs for using the proposed methodology were compared with those from the deterministic dual dynamic problem in a case study, considering a single inflow scenario. This sensitivity analysis shows the convergence of both methods and is used to determine the minimum discretization level. Additionally, the applicability of the proposed methodology for two hydroplants in a cascade is demonstrated. With proper adaptations, this work can be extended to a complete hydrothermal system.
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui;
2016-01-01
solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....
Distributed Algorithms for Optimal Power Flow Problem
Lam, Albert Y S; Tse, David
2011-01-01
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real time. With some special network structure, e.g. trees, the problem has been shown to have a zero duality gap and the convex dual problem yields the optimal solution. In this paper, we propose a primal and a dual algorithm to coordinate the smaller subproblems decomposed from the convexified OPF. We can arrange the subproblems to be solved sequentially and cumulatively in a central node or solved in parallel in distributed nodes. We test the algorithms on IEEE radial distribution test feeders, some random tree-structured networks, and the IEEE transmission system benchmarks. Simulation results show that the computation time can be improved dramatically with our algorithms over the centralized approach of solving the problem without decomposition, especially in tree-structured...
Quoc, Tran Dinh; Diehl, Moritz
2011-01-01
A new algorithm for solving large-scale separable convex optimization problems is proposed. The basic idea is to combine three techniques including Lagrangian dual decomposition, excessive gap and smoothing techniques. The main advantage of this algorithm is to dynamically update the smoothness parameters which leads to a numerically stable performance ability. The convergence of the algorithm is proved under weak conditions imposed on the original problem. The worst-case complexity is estimated which is $O(1/k)$, where $k$ is the iteration counter. Then, the algorithm is coupled with a dual scheme to construct a switching variant of the dual decomposition. Discussion on the implementation issues is presented and theoretical comparison is analyzed. Numerical results are implemented to confirm the theoretical development.
Convex and Network Flow Optimization for Structured Sparsity
Mairal, Julien; Obozinski, Guillaume; Bach, Francis
2011-01-01
We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2 or l_infinity norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of l_infinity norms can be computed exactly in polynomial time by solving a quadratic minimum cost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with non-overlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such a...
Reconstruction of the early Universe as a convex optimization problem
Brenier, Y; Hénon, M; Loeper, G; Matarrese, S; Mohayaee, R; Sobolevskii, A
2003-01-01
We show that the deterministic past history of the Universe can be uniquely reconstructed from the knowledge of the present mass density field, the latter being inferred from the 3D distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales -- a few Mpc -- where multi-streaming becomes significant. Above 6 Mpc/h we propose and implement an effective Monge-Ampere-Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge (1781). After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than cubic time complexity in N and reasonable CPU time requirements. Testing against N-body cosmological simulations gives over 60% of exactly reconstructed points. We apply several interrelated tools f...
An Optimal Algorithm for Linear Bandits
Cesa-Bianchi, Nicolò
2011-01-01
We provide the first algorithm for online bandit linear optimization whose regret after T rounds is of order sqrt{Td ln N} on any finite class X of N actions in d dimensions, and of order d*sqrt{T} (up to log factors) when X is infinite. These bounds are not improvable in general. The basic idea utilizes tools from convex geometry to construct what is essentially an optimal exploration basis. We also present an application to a model of linear bandits with expert advice. Interestingly, these results show that bandit linear optimization with expert advice in d dimensions is no more difficult (in terms of the achievable regret) than the online d-armed bandit problem with expert advice (where EXP4 is optimal).
QR Code Image Correction based on Corner Detection and Convex Hull Algorithm
Directory of Open Access Journals (Sweden)
Suran Kong
2013-12-01
Full Text Available Since the angular deviation produced when shooting a QR code image by a camera would cause geometric distortion of the QR code image, the traditional algorithm of QR code image correction would produce distortion. Therefore this paper puts forward the algorithm which combines corner detection with convex hull algorithm. Firstly, binaryzation of the collected QR code image with uneven light is obtained by the methods of local threshold and mathematical morphology. Next, the outline of the QR code and the dots on it are found and the distorted image is recovered by perspective collineation, according to the algorithm raised by this paper. Finally, experimental verification is made that the algorithm raised by this paper can correctly find the four apexes of QR code and achieves good effects of geometric correction. It will also significantly increase the recognition rate of seriously distorted QR code images
Convex optimization approach to the fusion of identity information
Li, Lingjie; Luo, Zhi-Quan; Wong, Kon M.; Bosse, Eloi
1999-03-01
We consider the problem of identity fusion for a multi- sensor target tracking system whereby sensors generate reports on the target identities. Since the sensor reports are typically fuzzy, 'incomplete' and inconsistent, the fusion approach based on the minimization of inconsistencies between the sensor reports by using a convex Quadratic Programming (QP) and linear programming (LP) formulation. In contrast to the Dempster-Shafer's evidential reasoning approach which suffers from exponentially growing completely, our approach is highly efficient. Moreover, our approach is capable of fusing 'ratio type' sensor reports, thus it is more general than the evidential reasoning theory. When the sensor reports are consistent, the solution generated by the new fusion method can be shown to converge to the true probability distribution. Simulation work shows that our method generates reasonable fusion results, and when only 'Subset type' sensor reports are presented, it produces fusion results similar to that obtained via the evidential reasoning theory.
Craft, David
2010-10-01
A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets.
An Effective Branch-and-Bound Algorithm for Convex Quadratic Integer Programming
Buchheim, Christoph; Caprara, Alberto; Lodi, Andrea
We present a branch-and-bound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints. In a given node of the enumeration tree, corresponding to the fixing of a subset of the variables, a lower bound is given by the continuous minimum of the restricted objective function. We improve this bound by exploiting the integrality of the variables using suitably-defined lattice-free ellipsoids. Experiments show that our approach is very fast on both unconstrained problems and problems with box constraints. The main reason is that all expensive calculations can be done in a preprocessing phase, while a single node in the enumeration tree can be processed in linear time in the problem dimension.
Huang, Wenxuan; Dacek, Stephen; Rong, Ziqin; Urban, Alexander; Cao, Shan; Luo, Chuan; Ceder, Gerbrand
2016-01-01
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, and fluid mechanics, among others. However, the problem of finding the true global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved, with only a limited number of results for highly simplified systems known. In this article, we present the first general algorithm to find the exact ground states of complex lattice models and to prove their global optimality, resolving this fundamental problem in condensed matter and materials theory. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and non-smooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy respectively. By systematically converging th...
A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions
Fowkes, Jaroslav M.
2012-06-21
We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other branch and bound algorithms, lower bounds are obtained via nonconvex underestimators of the function. For a numerical example, we apply the proposed branch and bound algorithm to radial basis function approximations. © 2012 Springer Science+Business Media, LLC.
Microgenetic optimization algorithm for optimal wavefront shaping
Anderson, Benjamin R; Gunawidjaja, Ray; Eilers, Hergen
2015-01-01
One of the main limitations of utilizing optimal wavefront shaping in imaging and authentication applications is the slow speed of the optimization algorithms currently being used. To address this problem we develop a micro-genetic optimization algorithm ($\\mu$GA) for optimal wavefront shaping. We test the abilities of the $\\mu$GA and make comparisons to previous algorithms (iterative and simple-genetic) by using each algorithm to optimize transmission through an opaque medium. From our experiments we find that the $\\mu$GA is faster than both the iterative and simple-genetic algorithms and that both genetic algorithms are more resistant to noise and sample decoherence than the iterative algorithm.
Reduction of shock induced noise in imperfectly expanded supersonic jets using convex optimization
Adhikari, Sam
2007-11-01
Imperfectly expanded jets generate screech noise. The imbalance between the backpressure and the exit pressure of the imperfectly expanded jets produce shock cells and expansion or compression waves from the nozzle. The instability waves and the shock cells interact to generate the screech sound. The mathematical model consists of cylindrical coordinate based full Navier-Stokes equations and large-eddy-simulation turbulence modeling. Analytical and computational analysis of the three-dimensional helical effects provide a model that relates several parameters with shock cell patterns, screech frequency and distribution of shock generation locations. Convex optimization techniques minimize the shock cell patterns and the instability waves. The objective functions are (convex) quadratic and the constraint functions are affine. In the quadratic optimization programs, minimization of the quadratic functions over a set of polyhedrons provides the optimal result. Various industry standard methods like regression analysis, distance between polyhedra, bounding variance, Markowitz optimization, and second order cone programming is used for Quadratic Optimization.
Poker, Gilad; Zarai, Yoram; Margaliot, Michael; Tuller, Tamir
2014-11-06
Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation-elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n. Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics.
Robust Nearfield Wideband Beamforming Design Based on Adaptive-Weighted Convex Optimization
Directory of Open Access Journals (Sweden)
Guo Ye-Cai
2017-01-01
Full Text Available Nearfield wideband beamformers for microphone arrays have wide applications in multichannel speech enhancement. The nearfield wideband beamformer design based on convex optimization is one of the typical representatives of robust approaches. However, in this approach, the coefficient of convex optimization is a constant, which has not used all the freedom provided by the weighting coefficient efficiently. Therefore, it is still necessary to further improve the performance. To solve this problem, we developed a robust nearfield wideband beamformer design approach based on adaptive-weighted convex optimization. The proposed approach defines an adaptive-weighted function by the adaptive array signal processing theory and adjusts its value flexibly, which has improved the beamforming performance. During each process of the adaptive updating of the weighting function, the convex optimization problem can be formulated as a SOCP (Second-Order Cone Program problem, which could be solved efficiently using the well-established interior-point methods. This method is suitable for the case where the sound source is in the nearfield range, can work well in the presence of microphone mismatches, and is applicable to arbitrary array geometries. Several design examples are presented to verify the effectiveness of the proposed approach and the correctness of the theoretical analysis.
Convex Array Vector Velocity Imaging Using Transverse Oscillation and Its Optimization
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Brandt, Andreas Hjelm; Bachmann Nielsen, Michael
2015-01-01
A method for obtaining vector flow images using the transverse oscillation (TO) approach on a convex array is presented. The paper presents optimization schemes for TO fields and evaluates their performance using simulations and measurements with an experimental scanner. A 3-MHz 192-element conve...
New Optimization Algorithms in Physics
Hartmann, Alexander K
2004-01-01
Many physicists are not aware of the fact that they can solve their problems by applying optimization algorithms. Since the number of such algorithms is steadily increasing, many new algorithms have not been presented comprehensively until now. This presentation of recently developed algorithms applied in physics, including demonstrations of how they work and related results, aims to encourage their application, and as such the algorithms selected cover concepts and methods from statistical physics to optimization problems emerging in theoretical computer science.
Antenna optimization using Particle Swarm Optimization algorithm
Directory of Open Access Journals (Sweden)
Golubović Ružica M.
2006-01-01
Full Text Available We present the results for two different antenna optimization problems that are found using the Particle Swarm Optimization (PSO algorithm. The first problem is finding the maximal forward gain of a Yagi antenna. The second problem is finding the optimal feeding of a broadside antenna array. The optimization problems have 6 and 20 optimization variables, respectively. The preferred values of the parameters of the PSO algorithm are found for presented problems. The results show that the preferred parameters of PSO are somewhat different for optimization problems with different number of dimensions of the optimization space. The results that are found using the PSO algorithm are compared with the results that are found using other optimization algorithms, in order to estimate the efficiency of the PSO.
Efficient convex optimization approach to 3D non-rigid MR-TRUS registration.
Sun, Yue; Yuan, Jing; Rajchl, Martin; Qiu, Wu; Romagnoli, Cesare; Fenster, Aaron
2013-01-01
In this study, we propose an efficient non-rigid MR-TRUS deformable registration method to improve the accuracy of targeting suspicious locations during a 3D ultrasound (US) guided prostate biopsy. The proposed deformable registration approach employs the multi-channel modality independent neighbourhood descriptor (MIND) as the local similarity feature across the two modalities of MR and TRUS, and a novel and efficient duality-based convex optimization based algorithmic scheme is introduced to extract the deformations which align the two MIND descriptors. The registration accuracy was evaluated using 10 patient images by measuring the TRE of manually identified corresponding intrinsic fiducials in the whole gland and peripheral zone, and performance metrics (DSC, MAD and MAXD) for the apex, mid-gland and base of the prostate were also calculated by comparing two manually segmented prostate surfaces in the registered 3D MR and TRUS images. Experimental results show that the proposed method yielded an overall mean TRE of 1.74 mm, which is favorably comparable to a clinical requirement for an error of less than 2.5 mm.
Convex relaxation of Optimal Power Flow in Distribution Feeders with embedded solar power
DEFF Research Database (Denmark)
Hermann, Alexander Niels August; Wu, Qiuwei; Huang, Shaojun
2016-01-01
panels with uncontrolled inverters, the upper limit of installable capacity is quickly reached in many of today’s distribution feeders. This problem can often be mitigated by optimally controlling the voltage angles of inverters. However, the optimal power flow problem in its standard form is a large......There is an increasing interest in using Distributed Energy Resources (DER) directly coupled to end user distribution feeders. This poses an array of challenges because most of today’s distribution feeders are designed for unidirectional power flow. Therefore when installing DERs such as solar...... scale non-convex optimization problem, and thus can’t be solved precisely and also is computationally heavy and intractable for large systems. This paper examines the use of a convex relaxation using Semi-definite programming to optimally control solar power inverters in a distribution grid in order...
A PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING
Institute of Scientific and Technical Information of China (English)
梁昔明; 钱积新
2002-01-01
The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.
Convex set of quantum states with positive partial transpose analysed by hit and run algorithm
Szymański, Konrad; Collins, Benot; Szarek, Tomasz; Życzkowski, Karol
2017-06-01
The convex set of quantum states of a composite K × K system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an estimation for the convergence speed of the algorithm is derived. For K≥slant 3 this algorithm works faster than sampling over the entire set of states and verifying whether the partial transpose is positive. The level density of the PPT states is shown to differ from the Marchenko-Pastur distribution, supported in [0, 4] and corresponding asymptotically to the entire set of quantum states. Based on the shifted semi-circle law, describing asymptotic level density of partially transposed states, and on the level density for the Gaussian unitary ensemble with constraints for the spectrum we find an explicit form of the probability distribution supported in [0, 3], which describes well the level density obtained numerically for PPT states.
Online algorithms for optimal energy distribution in microgrids
Wang, Yu; Nelms, R Mark
2015-01-01
Presenting an optimal energy distribution strategy for microgrids in a smart grid environment, and featuring a detailed analysis of the mathematical techniques of convex optimization and online algorithms, this book provides readers with essential content on how to achieve multi-objective optimization that takes into consideration power subscribers, energy providers and grid smoothing in microgrids. Featuring detailed theoretical proofs and simulation results that demonstrate and evaluate the correctness and effectiveness of the algorithm, this text explains step-by-step how the problem can b
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2013-01-01
Full Text Available We introduce composite implicit and explicit iterative algorithms for solving a general system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in a real smooth and uniformly convex Banach space. These composite iterative algorithms are based on Korpelevich's extragradient method and viscosity approximation method. We first consider and analyze a composite implicit iterative algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another composite explicit iterative algorithm in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm. Under suitable assumptions, we derive some strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literatures.
Visualizing Data as Objects by DC (Difference of Convex) Optimization
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective...
Visualizing Data as Objects by DC (Difference of Convex) Optimization
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective...
Convex Optimization methods for computing the Lyapunov Exponent of matrices
Protasov, Vladimir Yu
2012-01-01
We introduce a new approach to evaluate the largest Lyapunov exponent of a family of nonnegative matrices. The method is based on using special positive homogeneous functionals on $R^{d}_+,$ which gives iterative lower and upper bounds for the Lyapunov exponent. They improve previously known bounds and converge to the real value. The rate of convergence is estimated and the efficiency of the algorithm is demonstrated on several problems from applications (in functional analysis, combinatorics, and lan- guage theory) and on numerical examples with randomly generated matrices. The method computes the Lyapunov exponent with a prescribed accuracy in relatively high dimensions (up to 60). We generalize this approach to all matrices, not necessar- ily nonnegative, derive a new universal upper bound for the Lyapunov exponent, and show that such a lower bound, in general, does not exist.
Exact Convex Relaxation of Optimal Power Flow in Radial Networks
Energy Technology Data Exchange (ETDEWEB)
Gan, LW; Li, N; Topcu, U; Low, SH
2015-01-01
The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.
On the acceleration of the double smoothing technique for unconstrained convex optimization problems
Bot, Radu Ioan
2012-01-01
In this article we investigate the possibilities of accelerating the double smoothing technique when solving unconstrained nondifferentiable convex optimization problems. This approach relies on the regularization in two steps of the Fenchel dual problem associated to the problem to be solved into an optimization problem having a differentiable strongly convex objective function with Lipschitz continuous gradient. The doubly regularized dual problem is then solved via a fast gradient method. The aim of this paper is to show how do the properties of the functions in the objective of the primal problem influence the implementation of the double smoothing approach and its rate of convergence. The theoretical results are applied to linear inverse problems by making use of different regularization functionals.
Acho, Sussan Nkwenti; Rae, William Ian Duncombe
2016-10-01
A convex active contour model requires a predefined threshold value to determine the global solution for the best contour to use when doing mass segmentation. Fixed thresholds or manual tuning of threshold values for optimum mass boundary delineation are impracticable. A proposed method is presented to determine an optimized mass-specific threshold value for the convex active contour derived from the probability matrix of the mass with the particle swarm optimization method. We compared our results with the Chan-Vese segmentation and a published global segmentation model on masses detected on direct digital mammograms. The regional term of the convex active contour model maximizes the posterior partitioning probability for binary segmentation. Suppose the probability matrix is binary thresholded using the particle swarm optimization to obtain a value T1, we define the optimal threshold value for the global minimizer of the convex active contour as the mean intensity of all pixels whose probabilities are greater than T1. The mean Jaccard similarity indices were 0.89±0.07 for the proposed/Chan-Vese method and 0.88±0.06 for the proposed/published segmentation model. The mean Euclidean distance between Fourier descriptors of the segmented areas was 0.05±0.03 for the proposed/Chan-Vese method and 0.06±0.04 for the proposed/published segmentation model. This efficient method avoids problems of initial level set contour placement and contour re-initialization. Moreover, optimum segmentation results are realized for all masses improving on the fixed threshold value of 0.5 proposed elsewhere. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Optimal Mixing Evolutionary Algorithms
Thierens, D.; Bosman, P.A.N.; Krasnogor, N.
2011-01-01
A key search mechanism in Evolutionary Algorithms is the mixing or juxtaposing of partial solutions present in the parent solutions. In this paper we look at the efficiency of mixing in genetic algorithms (GAs) and estimation-of-distribution algorithms (EDAs). We compute the mixing probabilities of
A two-layer recurrent neural network for nonsmooth convex optimization problems.
Qin, Sitian; Xue, Xiaoping
2015-06-01
In this paper, a two-layer recurrent neural network is proposed to solve the nonsmooth convex optimization problem subject to convex inequality and linear equality constraints. Compared with existing neural network models, the proposed neural network has a low model complexity and avoids penalty parameters. It is proved that from any initial point, the state of the proposed neural network reaches the equality feasible region in finite time and stays there thereafter. Moreover, the state is unique if the initial point lies in the equality feasible region. The equilibrium point set of the proposed neural network is proved to be equivalent to the Karush-Kuhn-Tucker optimality set of the original optimization problem. It is further proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov. Moreover, from any initial point, the state is proved to be convergent to an equilibrium point of the proposed neural network. Finally, as applications, the proposed neural network is used to solve nonlinear convex programming with linear constraints and L1 -norm minimization problems.
A Global Optimization Algorithm for Sum of Linear Ratios Problem
Directory of Open Access Journals (Sweden)
Yuelin Gao
2013-01-01
Full Text Available We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.
多分类问题的凸包收缩方法%Multi-classification algorithm based on contraction of closed convex hull
Institute of Scientific and Technical Information of China (English)
李雪辉; 魏立力
2011-01-01
在最大边缘线性分类器和闭凸包收缩思想的基础上,针对二分类问题,通过闭凸包收缩技术,将线性不可分问题转化为线性可分问题.将上述思想推广到解决多分类问题中,提出了一类基于闭凸包收缩的多分类算法.该方法几何意义明确,在一定程度上克服了以往多分类方法目标函数过于复杂的缺点,并利用核思想将其推广到非线性分类问题上.%According to the maximal margin linear classifier and the contraction of closed convex hull, 2-classification linearly non-separable problem can be transformed to linearly separable problem by using proposed contraction methods of closed convex hull.Multi-classification problem can be solved by contracting closed convex, and multi-classification algorithm based on the contraction of closed convex hull is presented.The geometric meaning of optimization problem is obvious.The shortcomings of complicated objective function in multi-classification are overcame, nonlinear separable multi-classification problem can be solved using kernel method.
Botelho, Fabio
2014-01-01
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Massambone de Oliveira, Rafael; Salomão Helou, Elias; Fontoura Costa, Eduardo
2016-11-01
We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed independently along each string, possibly in parallel, by an incremental subgradient method (ISM). The end-points of all strings are averaged to form the next iterate. The method is useful to solve sparse and large-scale non-smooth convex optimization problems, such as those arising in tomographic imaging. A convergence analysis is provided under realistic, standard conditions. Numerical tests are performed in a tomographic image reconstruction application, showing good performance for the convergence speed when measured as the decrease ratio of the objective function, in comparison to classical ISM.
Institute of Scientific and Technical Information of China (English)
雷耀斌; 吴让泉
2001-01-01
We study the stochastic control problem of maximizing expected utility from terminal wealth and/or consumption, when the portfolio is constrained to take values in a given closed, convex subset of Ra, and in the presence of a higher interest rate for borrowing. The setting is that of a continuous-time, Ito process model for the underlying asset prices. The solution of the unconstrained problem is given. In addition to the original constrained optimization problem, a so-called combined dual problem is introduced. Finally, the existence question of optimal processes for both the dual and the primal problem is settled.
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process
Yuen, Kam Chuen; Shen, Ying
2015-01-01
We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy. PMID:26351655
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process
Directory of Open Access Journals (Sweden)
Chuancun Yin
2015-01-01
Full Text Available We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy.
Directory of Open Access Journals (Sweden)
Tobias Nüesch
2014-02-01
Full Text Available This paper presents a novel method to solve the energy management problem for hybrid electric vehicles (HEVs with engine start and gearshift costs. The method is based on a combination of deterministic dynamic programming (DP and convex optimization. As demonstrated in a case study, the method yields globally optimal results while returning the solution in much less time than the conventional DP method. In addition, the proposed method handles state constraints, which allows for the application to scenarios where the battery state of charge (SOC reaches its boundaries.
Gradient vs. approximation design optimization techniques in low-dimensional convex problems
Fedorik, Filip
2013-10-01
Design Optimization methods' application in structural designing represents a suitable manner for efficient designs of practical problems. The optimization techniques' implementation into multi-physical softwares permits designers to utilize them in a wide range of engineering problems. These methods are usually based on modified mathematical programming techniques and/or their combinations to improve universality and robustness for various human and technical problems. The presented paper deals with the analysis of optimization methods and tools within the frame of one to three-dimensional strictly convex optimization problems, which represent a component of the Design Optimization module in the Ansys program. The First Order method, based on combination of steepest descent and conjugate gradient method, and Supbproblem Approximation method, which uses approximation of dependent variables' functions, accompanying with facilitation of Random, Sweep, Factorial and Gradient Tools, are analyzed, where in different characteristics of the methods are observed.
Genetic algorithm optimization of entanglement
Navarro-Munoz, J C; Rosu, H C; Navarro-Munoz, Jorge C.
2006-01-01
We present an application of a genetic algorithmic computational method to the optimization of the concurrence measure of entanglement for the cases of one dimensional chains, as well as square and triangular lattices in a simple tight-binding approach
2016-05-01
Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games Yat Tin...complexity of the resulting algorithm is polynomial in the problem dimension; hence, it overcomes the curse of dimensionality [1, 2]. We extend previous work...compute the evolution of geometric objects [25], which was first used for reachability problems in [21, 22] to our knowledge . Numerical solutions to HJ PDE
Huang, Wenxuan; Kitchaev, Daniil A.; Dacek, Stephen T.; Rong, Ziqin; Urban, Alexander; Cao, Shan; Luo, Chuan; Ceder, Gerbrand
2016-10-01
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to the study of alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, fluid mechanics, and others. However, the problem of finding and proving the global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved for relatively complex practical systems, with only a limited number of results for highly simplified systems known. In this paper, we present a practical and general algorithm that provides a provable periodically constrained ground state of a complex lattice model up to a given unit cell size and in many cases is able to prove global optimality over all other choices of unit cell. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and nonsmooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy, respectively. By systematically converging these bounds to each other, we may find and prove the exact ground state of realistic Hamiltonians whose exact solutions are difficult, if not impossible, to obtain via traditional methods. Considering that currently such practical Hamiltonians are solved using simulated annealing and genetic algorithms that are often unable to find the true global energy minimum and inherently cannot prove the optimality of their result, our paper opens the door to resolving longstanding uncertainties in lattice models of physical phenomena. An implementation of the algorithm is available at https://github.com/dkitch/maxsat-ising.
Directory of Open Access Journals (Sweden)
MEI, G.
2015-05-01
Full Text Available In the calculating of convex hulls for point sets, a preprocessing procedure that is to filter the input points by discarding non-extreme points is commonly used to improve the computational efficiency. We previously proposed a quite straightforward preprocessing approach for accelerating 2D convex hull computation on the GPU. In this paper, we extend that algorithm to being used in 3D cases. The basic ideas behind these two preprocessing algorithms are similar: first, several groups of extreme points are found according to the original set of input points and several rotated versions of the input set; then, a convex polyhedron is created using the found extreme points; and finally those interior points locating inside the formed convex polyhedron are discarded. Experimental results show that: when employing the proposed preprocessing algorithm, it achieves the speedups of about 4x on average and 5x to 6x in the best cases over the cases where the proposed approach is not used. In addition, more than 95 percent of the input points can be discarded in most experimental tests.
Olariu, S.; Schwing, J.; Zhang, J.
1991-01-01
A bus system that can change dynamically to suit computational needs is referred to as reconfigurable. We present a fast adaptive convex hull algorithm on a two-dimensional processor array with a reconfigurable bus system (2-D PARBS, for short). Specifically, we show that computing the convex hull of a planar set of n points taken O(log n/log m) time on a 2-D PARBS of size mn x n with 3 less than or equal to m less than or equal to n. Our result implies that the convex hull of n points in the plane can be computed in O(1) time in a 2-D PARBS of size n(exp 1.5) x n.
Optimal Policy for Brownian Inventory Models with General Convex Inventory Cost
Institute of Scientific and Technical Information of China (English)
Da-cheng YAO
2013-01-01
We study an inventory system in which products are ordered from outside to meet demands,and the cumulative demand is governed by a Brownian motion.Excessive demand is backlogged.We suppose that the shortage and holding costs associated with the inventory are given by a general convex function.The product ordering from outside incurs a linear ordering cost and a setup fee.There is a constant leadtime when placing an order.The optimal policy is established so as to minimize the discounted cost including the inventory cost and ordering cost.
Institute of Scientific and Technical Information of China (English)
ZHANG Qing-xiang; ZHANG Yong-zhan
2013-01-01
The definition of generalized unified (C,α,p,d)-convex function is given.The concepts of generalized unified (C,α,p,d)-quasiconvexity,generalized unified (C,α,p,d)-pseudoconvexity and generalized unified (C,α,p,d)-strictly pseudoconvex functions are presented.The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.
Comparing a Coevolutionary Genetic Algorithm for Multiobjective Optimization
Lohn, Jason D.; Kraus, William F.; Haith, Gary L.; Clancy, Daniel (Technical Monitor)
2002-01-01
We present results from a study comparing a recently developed coevolutionary genetic algorithm (CGA) against a set of evolutionary algorithms using a suite of multiobjective optimization benchmarks. The CGA embodies competitive coevolution and employs a simple, straightforward target population representation and fitness calculation based on developmental theory of learning. Because of these properties, setting up the additional population is trivial making implementation no more difficult than using a standard GA. Empirical results using a suite of two-objective test functions indicate that this CGA performs well at finding solutions on convex, nonconvex, discrete, and deceptive Pareto-optimal fronts, while giving respectable results on a nonuniform optimization. On a multimodal Pareto front, the CGA finds a solution that dominates solutions produced by eight other algorithms, yet the CGA has poor coverage across the Pareto front.
A New Algorithm for Nondifferentiable Convex O%一个求解不可微凸优化的新算法
Institute of Scientific and Technical Information of China (English)
后六生
2012-01-01
该文结合文献[1]Chen和Fukushima的邻近点拟牛顿方法和过滤集技术，给出了一个求解不可微凸优化问题的新算法．与Chen和Fukushima的方法不同，新算法不用线搜索，而是用过滤集构造接受准则，并借助于过滤集技术，证明了算法的整体收敛性．%A new algorithm for nondifferentiable convex optimization, combining the proximal quasi-Newton method with filter methods, is presented in this paper. The new algorithm uses the filter instead of using the line searching method to accept the trial step, so it is different from proximal quasi-Newton method. The global convergence of the new algorithm has been proved in this study.
Zhao, Dang-Jun; Song, Zheng-Yu
2017-08-01
This study proposes a multiphase convex programming approach for rapid reentry trajectory generation that satisfies path, waypoint and no-fly zone (NFZ) constraints on Common Aerial Vehicles (CAVs). Because the time when the vehicle reaches the waypoint is unknown, the trajectory of the vehicle is divided into several phases according to the prescribed waypoints, rendering a multiphase optimization problem with free final time. Due to the requirement of rapidity, the minimum flight time of each phase index is preferred over other indices in this research. The sequential linearization is used to approximate the nonlinear dynamics of the vehicle as well as the nonlinear concave path constraints on the heat rate, dynamic pressure, and normal load; meanwhile, the convexification techniques are proposed to relax the concave constraints on control variables. Next, the original multiphase optimization problem is reformulated as a standard second-order convex programming problem. Theoretical analysis is conducted to show that the original problem and the converted problem have the same solution. Numerical results are presented to demonstrate that the proposed approach is efficient and effective.
Combinatorial optimization theory and algorithms
Korte, Bernhard
2002-01-01
Combinatorial optimization is one of the youngest and most active areas of discrete mathematics, and is probably its driving force today. This book describes the most important ideas, theoretical results, and algorithms of this field. It is conceived as an advanced graduate text, and it can also be used as an up-to-date reference work for current research. The book includes the essential fundamentals of graph theory, linear and integer programming, and complexity theory. It covers classical topics in combinatorial optimization as well as very recent ones. The emphasis is on theoretical results and algorithms with provably good performance. Some applications and heuristics are mentioned, too.
Constrained Multiobjective Biogeography Optimization Algorithm
Directory of Open Access Journals (Sweden)
Hongwei Mo
2014-01-01
Full Text Available Multiobjective optimization involves minimizing or maximizing multiple objective functions subject to a set of constraints. In this study, a novel constrained multiobjective biogeography optimization algorithm (CMBOA is proposed. It is the first biogeography optimization algorithm for constrained multiobjective optimization. In CMBOA, a disturbance migration operator is designed to generate diverse feasible individuals in order to promote the diversity of individuals on Pareto front. Infeasible individuals nearby feasible region are evolved to feasibility by recombining with their nearest nondominated feasible individuals. The convergence of CMBOA is proved by using probability theory. The performance of CMBOA is evaluated on a set of 6 benchmark problems and experimental results show that the CMBOA performs better than or similar to the classical NSGA-II and IS-MOEA.
Constrained multiobjective biogeography optimization algorithm.
Mo, Hongwei; Xu, Zhidan; Xu, Lifang; Wu, Zhou; Ma, Haiping
2014-01-01
Multiobjective optimization involves minimizing or maximizing multiple objective functions subject to a set of constraints. In this study, a novel constrained multiobjective biogeography optimization algorithm (CMBOA) is proposed. It is the first biogeography optimization algorithm for constrained multiobjective optimization. In CMBOA, a disturbance migration operator is designed to generate diverse feasible individuals in order to promote the diversity of individuals on Pareto front. Infeasible individuals nearby feasible region are evolved to feasibility by recombining with their nearest nondominated feasible individuals. The convergence of CMBOA is proved by using probability theory. The performance of CMBOA is evaluated on a set of 6 benchmark problems and experimental results show that the CMBOA performs better than or similar to the classical NSGA-II and IS-MOEA.
Cabrelli, C; Molter, U; Shonkwiler, R
2000-01-01
A sufficient condition that a region be classifiable by a two-layer feedforward neural net (a two-layer perceptron) using threshold activation functions is that either it be a convex polytope or that intersected with the complement of a convex polytope in its interior, or that intersected with the complement of a convex polytope in its interior or ... recursively. These have been called convex recursive deletion (CoRD) regions.We give a simple algorithm for finding the weights and thresholds in both layers for a feedforward net that implements such a region. The results of this work help in understanding the relationship between the decision region of a perceptron and its corresponding geometry in input space. Our construction extends in a simple way to the case that the decision region is the disjoint union of CoRD regions (requiring three layers). Therefore this work also helps in understanding how many neurons are needed in the second layer of a general three-layer network. In the event that the decision region of a network is known and is the union of CoRD regions, our results enable the calculation of the weights and thresholds of the implementing network directly and rapidly without the need for thousands of backpropagation iterations.
Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Sun, Yue; Rajchl, Martin; Fenster, Aaron
2014-04-01
We propose a novel global optimization-based approach to segmentation of 3-D prostate transrectal ultrasound (TRUS) and T2 weighted magnetic resonance (MR) images, enforcing inherent axial symmetry of prostate shapes to simultaneously adjust a series of 2-D slice-wise segmentations in a "global" 3-D sense. We show that the introduced challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. In this regard, we propose a novel coherent continuous max-flow model (CCMFM), which derives a new and efficient duality-based algorithm, leading to a GPU-based implementation to achieve high computational speeds. Experiments with 25 3-D TRUS images and 30 3-D T2w MR images from our dataset, and 50 3-D T2w MR images from a public dataset, demonstrate that the proposed approach can segment a 3-D prostate TRUS/MR image within 5-6 s including 4-5 s for initialization, yielding a mean Dice similarity coefficient of 93.2%±2.0% for 3-D TRUS images and 88.5%±3.5% for 3-D MR images. The proposed method also yields relatively low intra- and inter-observer variability introduced by user manual initialization, suggesting a high reproducibility, independent of observers.
Engberg, Lovisa; Forsgren, Anders; Hårdemark, Björn
2016-01-01
Given the widespread agreement that doses-at-volume play important roles in quality assessment of radiation therapy treatment plans, planning objectives that correlate well with explicit dose-at-volume optimization are likely to correlate well with plan quality. In this study, planning objectives are formulated to explicitly either minimize or maximize convex approximations of dose-at-volume, namely, mean-tail-doses. This is in contrast to the conventionally used planning objectives, which are used to maximize clinical goal fulfilment by relating to deviations from dose-at-volume thresholds. Advantages of the proposed planning objectives are investigated through juxtaposition with conventional objectives in a computational study of two patient cases, each with three doses-at-volume to be minimized subject to PTV coverage. With proposed planning objectives, this is translated into minimizing three mean-tail-doses. Comparison with conventional objectives is carried out in the dose-at-volume domain and in the no...
Evaluation of Advanced Control for Li-ion Battery Balancing Systems using Convex Optimization
DEFF Research Database (Denmark)
Pinto, Claudio; Barreras, Jorge Varela; Schaltz, Erik
2016-01-01
of energy losses, available capacity or temperature are obtained for the last three categories, even for moderate balancing currents. In particular, remarkable improvements are observed under conditions of high power demand with high variability, i.e., smaller battery sizes and more demanding driving cycles....... systems are evaluated in this paper by means of convex optimization. More than one hundred cases in a pure EV application are evaluated. Balancing circuits' efficiency models are implemented and realistic cell-to-cell parameter distributions are considered based on experimental data. Different battery...... sizes and driving cycles are considered. Balancing circuit topology is taken into account by selecting a specific category of energy transfer: cell-to-heat, bypass, cell-to-pack, pack-to-cell, cell-to-cell shared, cell-to-cell distributed or cell-to-pack-to-cell. In general, better results in terms...
A Line-Search-Based Partial Proximal Alternating Directions Method for Separable Convex Optimization
Directory of Open Access Journals (Sweden)
Yu-hua Zeng
2014-01-01
Full Text Available We propose an appealing line-search-based partial proximal alternating directions (LSPPAD method for solving a class of separable convex optimization problems. These problems under consideration are common in practice. The proposed method solves two subproblems at each iteration: one is solved by a proximal point method, while the proximal term is absent from the other. Both subproblems admit inexact solutions. A line search technique is used to guarantee the convergence. The convergence of the LSPPAD method is established under some suitable conditions. The advantage of the proposed method is that it provides the tractability of the subproblem in which the proximal term is absent. Numerical tests show that the LSPPAD method has better performance compared with the existing alternating projection based prediction-correction (APBPC method if both are employed to solve the described problem.
Simulation of stochastic systems via polynomial chaos expansions and convex optimization
Fagiano, Lorenzo
2012-01-01
Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model, or the computation of large numbers of simulation runs, rendering the approach too time consuming and impracticable for applications with more than a handful of random variables. We introduce a novel computationally tractable technique for computing the coefficients of polynomial chaos expansions. The approach exploits a regularization technique with a particular choice of weighting matrices, which allow to take into account the specific features of Polynomial Chaos expansions. The method, completely based on convex optimization, can be applied to problems with a large number of random variables and uses a modest number of Monte Carlo simulations, while avoiding model manipulations. Additional information on the stochastic process, when available, can be also incorporated i...
A New Evolutionary Algorithm for Solving Multi-Objective Optimization Problems
Institute of Scientific and Technical Information of China (English)
Chen Wen-ping; Kang Li-shan
2003-01-01
Multi-objective optimization is a new focus of evolutionary computation research. This paper puts forward a new algorithm, which can not only converge quickly, but also keep diversity among population efficiently, in order to find the Pareto-optimal set. This new algorithm replaces the worst individual with a newly-created one by "multi parent crossover", so that the population could converge near the true Pareto-optimal solutions in the end. At the same time, this new algorithm adopts niching and fitness-sharing techniques to keep the population in a good distribution. Numerical experiments show that the algorithm is rather effective in solving some Benchmarks. No matter whether the Pareto front of problems is convex or non-convex, continuous or discontinuous, and the problems are with constraints or not, the program turns out to do well.
Qiu, Wu; Yuan, Jing; Kishimoto, Jessica; McLeod, Jonathan; Chen, Yimin; de Ribaupierre, Sandrine; Fenster, Aaron
2015-02-01
A three-dimensional (3-D) ultrasound (US) system has been developed to monitor the intracranial ventricular system of preterm neonates with intraventricular hemorrhage (IVH) and the resultant dilation of the ventricles (ventriculomegaly). To measure ventricular volume from 3-D US images, a semi-automatic convex optimization-based approach is proposed for segmentation of the cerebral ventricular system in preterm neonates with IVH from 3-D US images. The proposed semi-automatic segmentation method makes use of the convex optimization technique supervised by user-initialized information. Experiments using 58 patient 3-D US images reveal that our proposed approach yielded a mean Dice similarity coefficient of 78.2% compared with the surfaces that were manually contoured, suggesting good agreement between these two segmentations. Additional metrics, the mean absolute distance of 0.65 mm and the maximum absolute distance of 3.2 mm, indicated small distance errors for a voxel spacing of 0.22 × 0.22 × 0.22 mm(3). The Pearson correlation coefficient (r = 0.97, p < 0.001) indicated a significant correlation of algorithm-generated ventricular system volume (VSV) with the manually generated VSV. The calculated minimal detectable difference in ventricular volume change indicated that the proposed segmentation approach with 3-D US images is capable of detecting a VSV difference of 6.5 cm(3) with 95% confidence, suggesting that this approach might be used for monitoring IVH patients' ventricular changes using 3-D US imaging. The mean segmentation times of the graphics processing unit (GPU)- and central processing unit-implemented algorithms were 50 ± 2 and 205 ± 5 s for one 3-D US image, respectively, in addition to 120 ± 10 s for initialization, less than the approximately 35 min required by manual segmentation. In addition, repeatability experiments indicated that the intra-observer variability ranges from 6.5% to 7.5%, and the inter-observer variability is 8.5% in terms
The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization
Jafarizadeh, M A; Aali, M
2009-01-01
Using the convex optimization method and Helstrom family of ensembles introduced in Ref. [1], we have discussed optimal ambiguous discrimination in qubit systems. We have analyzed the problem of the optimal discrimination of N known quantum states and have obtained maximum success probability and optimal measurement for N known quantum states with equiprobable prior probabilities and equidistant from center of the Bloch ball, not all of which are on the one half of the Bloch ball and all of the conjugate states are pure. An exact solution has also been given for arbitrary three known quantum states. The given examples which use our method include: 1. Diagonal N mixed states; 2. N equiprobable states and equidistant from center of the Bloch ball which their corresponding Bloch vectors are inclined at the equal angle from z axis; 3. Three mirror-symmetric states; 4. States that have been prepared with equal prior probabilities on vertices of a Platonic solid. Keywords: minimum-error discrimination, success prob...
Genetic Algorithm for Optimization: Preprocessor and Algorithm
Sen, S. K.; Shaykhian, Gholam A.
2006-01-01
Genetic algorithm (GA) inspired by Darwin's theory of evolution and employed to solve optimization problems - unconstrained or constrained - uses an evolutionary process. A GA has several parameters such the population size, search space, crossover and mutation probabilities, and fitness criterion. These parameters are not universally known/determined a priori for all problems. Depending on the problem at hand, these parameters need to be decided such that the resulting GA performs the best. We present here a preprocessor that achieves just that, i.e., it determines, for a specified problem, the foregoing parameters so that the consequent GA is a best for the problem. We stress also the need for such a preprocessor both for quality (error) and for cost (complexity) to produce the solution. The preprocessor includes, as its first step, making use of all the information such as that of nature/character of the function/system, search space, physical/laboratory experimentation (if already done/available), and the physical environment. It also includes the information that can be generated through any means - deterministic/nondeterministic/graphics. Instead of attempting a solution of the problem straightway through a GA without having/using the information/knowledge of the character of the system, we would do consciously a much better job of producing a solution by using the information generated/created in the very first step of the preprocessor. We, therefore, unstintingly advocate the use of a preprocessor to solve a real-world optimization problem including NP-complete ones before using the statistically most appropriate GA. We also include such a GA for unconstrained function optimization problems.
The optimal solution of a non-convex state-dependent LQR problem and its applications.
Directory of Open Access Journals (Sweden)
Xudan Xu
Full Text Available This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR problem, in which the control penalty weighting matrix [Formula: see text] in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting [Formula: see text]. It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting [Formula: see text], in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions.
Energy Technology Data Exchange (ETDEWEB)
Wang, Li; Gao, Yaozong; Shi, Feng; Liao, Shu; Li, Gang [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 (United States); Chen, Ken Chung [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Stomatology, National Cheng Kung University Medical College and Hospital, Tainan, Taiwan 70403 (China); Shen, Steve G. F.; Yan, Jin [Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People' s Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Lee, Philip K. M.; Chow, Ben [Hong Kong Dental Implant and Maxillofacial Centre, Hong Kong, China 999077 (China); Liu, Nancy X. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 and Department of Oral and Maxillofacial Surgery, Peking University School and Hospital of Stomatology, Beijing, China 100050 (China); Xia, James J. [Department of Oral and Maxillofacial Surgery, Houston Methodist Hospital Research Institute, Houston, Texas 77030 (United States); Department of Surgery (Oral and Maxillofacial Surgery), Weill Medical College, Cornell University, New York, New York 10065 (United States); Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People' s Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 (China); Shen, Dinggang, E-mail: dgshen@med.unc.edu [Department of Radiology and BRIC, University of North Carolina at Chapel Hill, North Carolina 27599 and Department of Brain and Cognitive Engineering, Korea University, Seoul, 136701 (Korea, Republic of)
2014-04-15
Purpose: Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Accurate segmentation of CBCT image is an essential step to generate three-dimensional (3D) models for the diagnosis and treatment planning of the patients with CMF deformities. However, due to the poor image quality, including very low signal-to-noise ratio and the widespread image artifacts such as noise, beam hardening, and inhomogeneity, it is challenging to segment the CBCT images. In this paper, the authors present a new automatic segmentation method to address these problems. Methods: To segment CBCT images, the authors propose a new method for fully automated CBCT segmentation by using patch-based sparse representation to (1) segment bony structures from the soft tissues and (2) further separate the mandible from the maxilla. Specifically, a region-specific registration strategy is first proposed to warp all the atlases to the current testing subject and then a sparse-based label propagation strategy is employed to estimate a patient-specific atlas from all aligned atlases. Finally, the patient-specific atlas is integrated into amaximum a posteriori probability-based convex segmentation framework for accurate segmentation. Results: The proposed method has been evaluated on a dataset with 15 CBCT images. The effectiveness of the proposed region-specific registration strategy and patient-specific atlas has been validated by comparing with the traditional registration strategy and population-based atlas. The experimental results show that the proposed method achieves the best segmentation accuracy by comparison with other state-of-the-art segmentation methods. Conclusions: The authors have proposed a new CBCT segmentation method by using patch-based sparse representation and convex optimization, which can achieve considerably accurate segmentation results in CBCT
A case study in the performance and scalability of optimization algorithms.
Energy Technology Data Exchange (ETDEWEB)
Benson, S. J.; McInnes, L. C.; More, J. J.; Mathematics and Computer Science
2001-09-01
We analyze the performance and scalabilty of algorithms for the solution of large optimization problems on high-performance parallel architectures. Our case study uses the GPCG (gradient projection, conjugate gradient) algorithm for solving bound-constrained convex quadratic problems. Our implementation of the GPCG algorithm within the Toolkit for Advanced Optimization (TAO) is available for a wide range of high-performance architectures and has been tested on problems with over 2.5 million variables. We analyze the performance as a function of the number of variables, the number of free variables, and the preconditioner. In addition, we discuss how the software design facilitates algorithmic comparisons.
Chen, Shibing; Wang, Xu-Jia
2016-01-01
In this paper we prove the strict c-convexity and the C 1, α regularity for potential functions in optimal transportation under condition (A3w). These results were obtained by Caffarelli [1,3,4] for the cost c (x, y) =| x - y | 2, by Liu [11], Loeper [15], Trudinger and Wang [20] for costs satisfying the condition (A3). For costs satisfying the condition (A3w), the results have also been proved by Figalli, Kim, and McCann [6], assuming that the initial and target domains are uniformly c-convex, see also [21]; and by Guillen and Kitagawa [8], assuming the cost function satisfies A3w in larger domains. In this paper we prove the strict c-convexity and the C 1, α regularity assuming either the support of source density is compactly contained in a larger domain where the cost function satisfies A3w, or the dimension 2 ≤ n ≤ 4.
Egalitarianism in Convex Fuzzy Games
Brânzei, R.; Dimitrov, D.A.; Tijs, S.H.
2002-01-01
In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a f
Chen, Yunjie; Zhao, Bo; Zhang, Jianwei; Zheng, Yuhui
2014-09-01
Accurate segmentation of magnetic resonance (MR) images remains challenging mainly due to the intensity inhomogeneity, which is also commonly known as bias field. Recently active contour models with geometric information constraint have been applied, however, most of them deal with the bias field by using a necessary pre-processing step before segmentation of MR data. This paper presents a novel automatic variational method, which can segment brain MR images meanwhile correcting the bias field when segmenting images with high intensity inhomogeneities. We first define a function for clustering the image pixels in a smaller neighborhood. The cluster centers in this objective function have a multiplicative factor that estimates the bias within the neighborhood. In order to reduce the effect of the noise, the local intensity variations are described by the Gaussian distributions with different means and variances. Then, the objective functions are integrated over the entire domain. In order to obtain the global optimal and make the results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. Our method is able to estimate the bias of quite general profiles, even in 7T MR images. Moreover, our model can also distinguish regions with similar intensity distribution with different variances. The proposed method has been rigorously validated with images acquired on variety of imaging modalities with promising results.
Optimization of LMS Algorithm for System Identification
Prasad, Saurabh R.; Godbole, Bhalchandra B.
2017-01-01
An adaptive filter is defined as a digital filter that has the capability of self adjusting its transfer function under the control of some optimizing algorithms. Most common optimizing algorithms are Least Mean Square (LMS) and Recursive Least Square (RLS). Although RLS algorithm perform superior to LMS algorithm, it has very high computational complexity so not useful in most of the practical scenario. So most feasible choice of the adaptive filtering algorithm is the LMS algorithm includin...
An optimized algorithm for multiscale wideband deconvolution of radio astronomical images
Offringa, A. R.; Smirnov, O.
2017-10-01
We describe a new multiscale deconvolution algorithm that can also be used in a multifrequency mode. The algorithm only affects the minor clean loop. In single-frequency mode, the minor loop of our improved multiscale algorithm is over an order of magnitude faster than the casa multiscale algorithm, and produces results of similar quality. For multifrequency deconvolution, a technique named joined-channel cleaning is used. In this mode, the minor loop of our algorithm is two to three orders of magnitude faster than casa msmfs. We extend the multiscale mode with automated scale-dependent masking, which allows structures to be cleaned below the noise. We describe a new scale-bias function for use in multiscale cleaning. We test a second deconvolution method that is a variant of the moresane deconvolution technique, and uses a convex optimization technique with isotropic undecimated wavelets as dictionary. On simple well-calibrated data, the convex optimization algorithm produces visually more representative models. On complex or imperfect data, the convex optimization algorithm has stability issues.
Balandin, DV; Kogan, MM
2004-01-01
An algorithm for checking feasibility of the robust H-infinity-control problem for systems with time-varying norm bounded uncertainty is suggested. This algorithm is an iterative procedure on each step of which an optimization problem for a linear function under convex constraints determined by LMIs
改进的多边形凸包算法%An improved algorithm of polygon convex hull
Institute of Scientific and Technical Information of China (English)
张林
2013-01-01
A real-time convex hull incremental algorithm to deal with the arbitrary polygon is put forward .By analyzing every area of the appeared incremental ends , we offer the corresponding solutions ,so the efficiency of the algorithm is improved .It is show n that the algorithm is efficient under the the average time complexity .%提出了一种处理任意多边形的凸包实时增量算法，通过分析增量边端点出现的区域，根据每个区域特点提出了解决方案，最后详细分析了算法效率提高的原因。分析表明，算法在平均时间复杂度下可以达到较高的执行效率。
Optimal Merging Algorithms for Lossless Codes with Generalized Criteria
Charalambous, Themistoklis; Rezaei, Farzad
2011-01-01
This paper presents lossless prefix codes optimized with respect to a pay-off criterion consisting of a convex combination of maximum codeword length and average codeword length. The optimal codeword lengths obtained are based on a new coding algorithm which transforms the initial source probability vector into a new probability vector according to a merging rule. The coding algorithm is equivalent to a partition of the source alphabet into disjoint sets on which a new transformed probability vector is defined as a function of the initial source probability vector and a scalar parameter. The pay-off criterion considered encompasses a trade-off between maximum and average codeword length; it is related to a pay-off criterion consisting of a convex combination of average codeword length and average of an exponential function of the codeword length, and to an average codeword length pay-off criterion subject to a limited length constraint. A special case of the first related pay-off is connected to coding proble...
Extended Range Guided Munition Parameter Optimization Based on Genetic Algorithms
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Many factors influencing range of extended range guided munition (ERGM) are analyzed. The definition domain of the most important three parameters are ascertained by preparatory mathematical simulation, the optimized mathematical model of ERGM maximum range with boundary conditions is created, and parameter optimization based on genetic algorithm (GA) is adopted. In the GA design, three-point crossover is used and the best chromosome is kept so that the convergence speed becomes rapid. Simulation result shows that GA is feasible, the result is good and it can be easy to attain global optimization solution, especially when the objective function is not the convex one for independent variables and it is a multi-parameter problem.
Nedjar, Sebastien; Cicchetti, Rosine; Lakhal, Lotfi; 10.3166/isi.11.6.11-31
2010-01-01
In various approaches, data cubes are pre-computed in order to answer efficiently OLAP queries. The notion of data cube has been declined in various ways: iceberg cubes, range cubes or differential cubes. In this paper, we introduce the concept of convex cube which captures all the tuples of a datacube satisfying a constraint combination. It can be represented in a very compact way in order to optimize both computation time and required storage space. The convex cube is not an additional structure appended to the list of cube variants but we propose it as a unifying structure that we use to characterize, in a simple, sound and homogeneous way, the other quoted types of cubes. Finally, we introduce the concept of emerging cube which captures the significant trend inversions. characterizations.
Setting Optimal Bounds on Risk in Asset Allocation - a Convex Program
Directory of Open Access Journals (Sweden)
James E. Falk
2002-10-01
Full Text Available The 'Portfolio Selection Problem' is traditionally viewed as selecting a mix of investment opportunities that maximizes the expected return subject to a bound on risk. However, in reality, portfolios are made up of a few 'asset classes' that consist of similar opportunities. The asset classes are managed by individual `sub-managers', under guidelines set by an overall portfolio manager. Once a benchmark (the `strategic' allocation has been set, an overall manager may choose to allow the sub-managers some latitude in which opportunities make up the classes. He may choose some overall bound on risk (as measured by the variance and wish to set bounds that constrain the submanagers. Mathematically we show that the problem is equivalent to finding a hyper-rectangle of maximal volume within an ellipsoid. It is a convex program, albeit with potentially a large number of constraints. We suggest a cutting plane algorithm to solve the problem and include computational results on a set of randomly generated problems as well as a real-world problem taken from the literature.
NEW HMM ALGORITHM FOR TOPOLOGY OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Zuo Kongtian; Zhao Yudong; Chen Liping; Zhong Yifang; Huang Yuying
2005-01-01
A new hybrid MMA-MGCMMA (HMM) algorithm for solving topology optimization problems is presented. This algorithm combines the method of moving asymptotes (MMA) algorithm and the modified globally convergent version of the method of moving asymptotes (MGCMMA) algorithm in the optimization process. This algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value existing in the calculation. This algorithm can improve calculation efficiency and accelerate convergence compared with simplex MMA or MGCMMA algorithms, which is proven with an example.
Convex quadratic programming applied to the stability number of a graph
Pacheco, Maria F.; Cardoso, Domingos Moreira; Luz, Carlos J.
2012-01-01
We deal with graphs whose stability number can be determined by a convex quadratic program and describe algorithmic techniques for the determination of maximum stabe sets in such graphs (except there is an induced subgraph with least adjacency eigenvalue and optimal value of the convex quadratic program not changing if the neighbourhood of any vertex is deleted). Such a graph is called adverse. Assuming that every adverse graph has convex-QP stability number, an algorithm for the recognition ...
Directory of Open Access Journals (Sweden)
Siwaporn Saewan
2010-01-01
Full Text Available We introduce a modified block hybrid projection algorithm for solving the convex feasibility problems for an infinite family of closed and uniformly quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results.
Memory Polynomial Predistortion Based on Convex Algorithm%基于凸优化的记忆多项式预失真技术
Institute of Scientific and Technical Information of China (English)
毛云祥; 张进
2013-01-01
An efficient adaptive predistorter for high power amplifier(HPA) was designed to improve the convergence rate of adaptive and the robustness.On the base of traditional predistortion techniques,a memory polynomial predistortion based on convex algorithm was proposed in this paper.This algorithm implemented convex optimization using interior point method and avoided the inverse operation of its correlation matrix.As a result,the numerical value was more robust; the operation process was less complex and its speed was faster,in addition,the precision of constringency was better.Finally,two-tone test signals were taken as examples to carry out a simulation.The simulation results show that the algorithm can further provide the adjacent channel leakage ratio(ACLR) more than 5dB,and verify the advantages of the technology.%研究高功率放大器自适应预失真的过程中,为了提高自适应算法的收敛度和稳定度,在传统预失真技术的基础上,提出了一项凸优化算法的多项式预失真技术.利用内点算法来解决凸优化问题,避免了传统RLS算法中对自相关矩阵的求逆运算,提高了数值的稳定性,并且降低了运算的复杂性,提高了运算速度且具有良好的收敛精度.最后,以双音信号为例进行仿真,结果表明,改进算法对邻带交调(ACLR)的抑制至少有5dB的改善,证明改进算法的优越性.
Algorithms for optimizing drug therapy
Directory of Open Access Journals (Sweden)
Martin Lene
2004-07-01
Full Text Available Abstract Background Drug therapy has become increasingly efficient, with more drugs available for treatment of an ever-growing number of conditions. Yet, drug use is reported to be sub optimal in several aspects, such as dosage, patient's adherence and outcome of therapy. The aim of the current study was to investigate the possibility to optimize drug therapy using computer programs, available on the Internet. Methods One hundred and ten officially endorsed text documents, published between 1996 and 2004, containing guidelines for drug therapy in 246 disorders, were analyzed with regard to information about patient-, disease- and drug-related factors and relationships between these factors. This information was used to construct algorithms for identifying optimum treatment in each of the studied disorders. These algorithms were categorized in order to define as few models as possible that still could accommodate the identified factors and the relationships between them. The resulting program prototypes were implemented in HTML (user interface and JavaScript (program logic. Results Three types of algorithms were sufficient for the intended purpose. The simplest type is a list of factors, each of which implies that the particular patient should or should not receive treatment. This is adequate in situations where only one treatment exists. The second type, a more elaborate model, is required when treatment can by provided using drugs from different pharmacological classes and the selection of drug class is dependent on patient characteristics. An easily implemented set of if-then statements was able to manage the identified information in such instances. The third type was needed in the few situations where the selection and dosage of drugs were depending on the degree to which one or more patient-specific factors were present. In these cases the implementation of an established decision model based on fuzzy sets was required. Computer programs
Algorithmic and Complexity Results for Cutting Planes Derived from Maximal Lattice-Free Convex Sets
Basu, Amitabh; Köppe, Matthias
2011-01-01
We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, Weismantel and Wolsey [Inequalities from two rows of a simplex tableau, Proc. IPCO 2007, LNCS, vol. 4513, Springer, pp. 1--15]. We describe the facets of this mixed integer linear program via the extreme points of a well-defined polyhedron. We then utilize this description to give polynomial time algorithms to derive valid inequalities with optimal l_p norm for arbitrary, but fixed m. For the case of m=2, we give a refinement and a new proof of a characterization of the facets by Cornuejols and Margot [On the facets of mixed integer programs with two integer variables and two constraints, Math. Programming 120 (2009), 429--456]. The key point of our approach is that the conditions are much more explicit and can be tested in a more direct manner, removing the need for a reduction algorithm. These results allow ...
Introducing convex layers to the Traveling Salesman Problem
Liew, Sing
2012-01-01
In this paper, we will propose convex layers to the Traveling Salesman Problem (TSP). Firstly, we will focus on human performance on the TSP. Experimental data shows that untrained humans appear to have the ability to perform well in the TSP. On the other hand, experimental data also supports the hypothesis of convex hull i.e. human relies on convex hull to search for the optimal tour for the TSP. Secondly, from the paper published by Bonabeau, Dorigo and Theraulaz, social insect behavior would be able to help in some of the optimizing problems, especially the TSP. Thus, we propose convex layers to the TSP based on the argument that, by the analogy to the social insect behavior, untrained humans' cognition should be able to help in the TSP. Lastly, we will use Tour Improvement algorithms on convex layers to search for an optimal tour for a 13-cities problem to demonstrate the idea.
Fire Evacuation using Ant Colony Optimization Algorithm
National Research Council Canada - National Science Library
Kanika Singhal; Shashank Sahu
2016-01-01
... planning.The objective of the algorithm is to minimizes the entire rescue time of all evacuees.The ant colony optimization algorithm is used to solve the complications of shortest route planning. Presented paper gives a comparative overview of various emergency scenarios using ant colony optimization algorithm.
Footstep Planning on Uneven Terrain with Mixed-Integer Convex Optimization
2014-08-01
variables to absorb any non-convex constraints. We handle orientation of the footstep placements by approximating the trigonometric sin and cos...must enforce that sj and cj approximate sin and cos without introducing non-convex trigonometric constraints. We choose instead to create a simple...goal and identical cost weights on the displacement from each footstep to the next. To control the number of footsteps used in the plan, and thus the
DEFF Research Database (Denmark)
Stolpe, Mathias
2007-01-01
We consider equivalent reformulations of nonlinear mixed 0–1 optimization problems arising from a broad range of recent applications of topology optimization for the design of continuum structures and composite materials. We show that the considered problems can equivalently be cast as either...... linear or convex quadratic mixed 0–1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design...
DEFF Research Database (Denmark)
Stolpe, Mathias
2004-01-01
We consider equivalent reformulations of nonlinear mixed 0-1 optimization problems arising from a broad range of recent applications of topology optimization for the design of continuum structures and composite materials. It is shown that the considered problems may equivalently be cast as either...... linear or as convex quadratic mixed 0-1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design...
Online Optimal Controller Design using Evolutionary Algorithm with Convergence Properties
Directory of Open Access Journals (Sweden)
Yousef Alipouri
2014-06-01
Full Text Available Many real-world applications require minimization of a cost function. This function is the criterion that figures out optimally. In the control engineering, this criterion is used in the design of optimal controllers. Cost function optimization has difficulties including calculating gradient function and lack of information about the system and the control loop. In this article, for the first time, gradient memetic evolutionary programming is proposed for minimization of non-convex cost functions that have been defined in control engineering. Moreover, stability and convergence of the proposed algorithm are proved. Besides, it is modified to be used in online optimization. To achieve this, the sign of the gradient function is utilized. For calculating the sign of the gradient, there is no need to know the cost-function’s shape. The gradient functions are estimated by the algorithm. The proposed algorithm is used to design a PI controller for nonlinear benchmark system CSTR (Continuous Stirred Tank Reactor by online and off-line approaches.
Subset Selection by Local Convex Approximation
DEFF Research Database (Denmark)
Øjelund, Henrik; Sadegh, Payman; Madsen, Henrik
1999-01-01
least squares criterion. We propose an optimization technique for the posed probelm based on a modified version of the Newton-Raphson iterations, combined with a backward elimination type algorithm. THe Newton-Raphson modification concerns iterative approximations to the non-convex cost function...
A New Nonmonotonic Trust Region Algorithm for A Class of Unconstraied Nonsmooth Optimization
Institute of Scientific and Technical Information of China (English)
欧宜贵; 侯定丕
2002-01-01
This paper preasents a new trust region algorithm for solving a class of composite nonsmooth optimizations.It is distinguished by the fact that this method does not enforce strict monotonicity of the objective function values at successive itereates and that this method extends the existing results for this type of nonlinear optimization with smooth ,or piecewis somooth,or convex objective functions or their composition It is pyoved that this algorithm is globally convergent under certain conditions.Finally,some numerical results for several optimization problems are reported which show that the nonmonotonic trust region method is competitive with the usual trust region method.
A new algorithm for the robust optimization of rotor-bearing systems
Lopez, R. H.; Ritto, T. G.; Sampaio, Rubens; Souza de Cursi, J. E.
2014-08-01
This article presents a new algorithm for the robust optimization of rotor-bearing systems. The goal of the optimization problem is to find the values of a set of parameters for which the natural frequencies of the system are as far away as possible from the rotational speeds of the machine. To accomplish this, the penalization proposed by Ritto, Lopez, Sampaio, and Souza de Cursi in 2011 is employed. Since the rotor-bearing system is subject to uncertainties, such a penalization is modelled as a random variable. The robust optimization is performed by minimizing the expected value and variance of the penalization, resulting in a multi-objective optimization problem (MOP). The objective function of this MOP is known to be non-convex and it is shown that its resulting Pareto front (PF) is also non-convex. Thus, a new algorithm is proposed for solving the MOP: the normal boundary intersection (NBI) is employed to discretize the PF handling its non-convexity, and a global optimization algorithm based on a restart procedure and local searches are employed to minimize the NBI subproblems tackling the non-convexity of the objective function. A numerical analysis section shows the advantage of using the proposed algorithm over the weighted-sum (WS) and NSGA-II approaches. In comparison with the WS, the proposed approach obtains a much more even and useful set of Pareto points. Compared with the NSGA-II approach, the proposed algorithm provides a better approximation of the PF requiring much lower computational cost.
Optimal Multistage Algorithm for Adjoint Computation
Energy Technology Data Exchange (ETDEWEB)
Aupy, Guillaume; Herrmann, Julien; Hovland, Paul; Robert, Yves
2016-01-01
We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs; a well-known example is the binomial checkpointing algorithm of Griewank and Walther. Stumm and Walther extended that binomial checkpointing algorithm to the case of two levels of checkpoints, but they did not provide any optimality results. We bridge the gap by designing the first optimal algorithm in this context. We experimentally compare our optimal algorithm with that of Stumm and Walther to assess the difference in performance.
Genetic algorithms and fuzzy multiobjective optimization
Sakawa, Masatoshi
2002-01-01
Since the introduction of genetic algorithms in the 1970s, an enormous number of articles together with several significant monographs and books have been published on this methodology. As a result, genetic algorithms have made a major contribution to optimization, adaptation, and learning in a wide variety of unexpected fields. Over the years, many excellent books in genetic algorithm optimization have been published; however, they focus mainly on single-objective discrete or other hard optimization problems under certainty. There appears to be no book that is designed to present genetic algorithms for solving not only single-objective but also fuzzy and multiobjective optimization problems in a unified way. Genetic Algorithms And Fuzzy Multiobjective Optimization introduces the latest advances in the field of genetic algorithm optimization for 0-1 programming, integer programming, nonconvex programming, and job-shop scheduling problems under multiobjectiveness and fuzziness. In addition, the book treats a w...
Metaheuristic Optimization: Algorithm Analysis and Open Problems
2012-01-01
Metaheuristic algorithms are becoming an important part of modern optimization. A wide range of metaheuristic algorithms have emerged over the last two decades, and many metaheuristics such as particle swarm optimization are becoming increasingly popular. Despite their popularity, mathematical analysis of these algorithms lacks behind. Convergence analysis still remains unsolved for the majority of metaheuristic algorithms, while efficiency analysis is equally challenging. In this paper, we i...
Directory of Open Access Journals (Sweden)
Ahmet Demir
2017-01-01
Full Text Available In the fields which require finding the most appropriate value, optimization became a vital approach to employ effective solutions. With the use of optimization techniques, many different fields in the modern life have found solutions to their real-world based problems. In this context, classical optimization techniques have had an important popularity. But after a while, more advanced optimization problems required the use of more effective techniques. At this point, Computer Science took an important role on providing software related techniques to improve the associated literature. Today, intelligent optimization techniques based on Artificial Intelligence are widely used for optimization problems. The objective of this paper is to provide a comparative study on the employment of classical optimization solutions and Artificial Intelligence solutions for enabling readers to have idea about the potential of intelligent optimization techniques. At this point, two recently developed intelligent optimization algorithms, Vortex Optimization Algorithm (VOA and Cognitive Development Optimization Algorithm (CoDOA, have been used to solve some multidisciplinary optimization problems provided in the source book Thomas' Calculus 11th Edition and the obtained results have compared with classical optimization solutions.
Interactive Evolutionary Multi-Objective Optimization Algorithm Using Cone Dominance
Institute of Scientific and Technical Information of China (English)
Dalaijargal Purevsuren; Saif ur Rehman; Gang Cui; Jianmin Bao; Nwe Nwe Htay Win
2015-01-01
As the number of objectives increases, the performance of the Pareto dominance⁃based Evolutionary Multi⁃objective Optimization ( EMO) algorithms such as NSGA⁃II, SPEA2 severely deteriorates due to the drastic increase in the Pareto⁃incomparable solutions. We propose a sorting method which classifies these incomparable solutions into several ordered classes by using the decision maker's ( DM) preference information. This is accomplished by designing an interactive evolutionary algorithm and constructing convex cones. This method allows the DMs to drive the search process toward a preferred region of the Pareto optimal front. The performance of the proposed algorithm is assessed for two, three, and four⁃objective knapsack problems. The results demonstrate the algorithm's ability to converge to the most preferred point. The evaluation and comparison of the results indicate that the proposed approach gives better solutions than that of NSGA⁃II. In addition, the approach is more efficient compared to NSGA⁃II in terms of the number of generations required to reach the preferred point.
Function Optimization Based on Quantum Genetic Algorithm
Ying Sun; Hegen Xiong
2014-01-01
Optimization method is important in engineering design and application. Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on. It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed, which is called Variable-boundary-coded Quantum Genetic Algorithm (vbQGA) in which qubit chromosomes are collapsed into variable-boundary-coded chromosomes instead of binary-coded c...
Parallel algorithms for unconstrained optimizations by multisplitting
Energy Technology Data Exchange (ETDEWEB)
He, Qing [Arizona State Univ., Tempe, AZ (United States)
1994-12-31
In this paper a new parallel iterative algorithm for unconstrained optimization using the idea of multisplitting is proposed. This algorithm uses the existing sequential algorithms without any parallelization. Some convergence and numerical results for this algorithm are presented. The experiments are performed on an Intel iPSC/860 Hyper Cube with 64 nodes. It is interesting that the sequential implementation on one node shows that if the problem is split properly, the algorithm converges much faster than one without splitting.
Memetic firefly algorithm for combinatorial optimization
Fister, Iztok; Fister, Iztok; Brest, Janez
2012-01-01
Firefly algorithms belong to modern meta-heuristic algorithms inspired by nature that can be successfully applied to continuous optimization problems. In this paper, we have been applied the firefly algorithm, hybridized with local search heuristic, to combinatorial optimization problems, where we use graph 3-coloring problems as test benchmarks. The results of the proposed memetic firefly algorithm (MFFA) were compared with the results of the Hybrid Evolutionary Algorithm (HEA), Tabucol, and the evolutionary algorithm with SAW method (EA-SAW) by coloring the suite of medium-scaled random graphs (graphs with 500 vertices) generated using the Culberson random graph generator. The results of firefly algorithm were very promising and showed a potential that this algorithm could successfully be applied in near future to the other combinatorial optimization problems as well.
Simulated annealing algorithm for optimal capital growth
Luo, Yong; Zhu, Bo; Tang, Yong
2014-08-01
We investigate the problem of dynamic optimal capital growth of a portfolio. A general framework that one strives to maximize the expected logarithm utility of long term growth rate was developed. Exact optimization algorithms run into difficulties in this framework and this motivates the investigation of applying simulated annealing optimized algorithm to optimize the capital growth of a given portfolio. Empirical results with real financial data indicate that the approach is inspiring for capital growth portfolio.
Directory of Open Access Journals (Sweden)
Zuliang Lu
2014-01-01
Full Text Available The aim of this work is to investigate the discretization of general linear hyperbolic convex optimal control problems by using the mixed finite element methods. The state and costate are approximated by the k order (k≥0 Raviart-Thomas mixed finite elements and the control is approximated by piecewise polynomials of order k. By applying the elliptic projection operators and Gronwall’s lemma, we derive a priori error estimates of optimal order for both the coupled state and the control approximation.
Kurtosis based weighted sparse model with convex optimization technique for bearing fault diagnosis
Zhang, Han; Chen, Xuefeng; Du, Zhaohui; Yan, Ruqiang
2016-12-01
The bearing failure, generating harmful vibrations, is one of the most frequent reasons for machine breakdowns. Thus, performing bearing fault diagnosis is an essential procedure to improve the reliability of the mechanical system and reduce its operating expenses. Most of the previous studies focused on rolling bearing fault diagnosis could be categorized into two main families, kurtosis-based filter method and wavelet-based shrinkage method. Although tremendous progresses have been made, their effectiveness suffers from three potential drawbacks: firstly, fault information is often decomposed into proximal frequency bands and results in impulsive feature frequency band splitting (IFFBS) phenomenon, which significantly degrades the performance of capturing the optimal information band; secondly, noise energy spreads throughout all frequency bins and contaminates fault information in the information band, especially under the heavy noisy circumstance; thirdly, wavelet coefficients are shrunk equally to satisfy the sparsity constraints and most of the feature information energy are thus eliminated unreasonably. Therefore, exploiting two pieces of prior information (i.e., one is that the coefficient sequences of fault information in the wavelet basis is sparse, and the other is that the kurtosis of the envelope spectrum could evaluate accurately the information capacity of rolling bearing faults), a novel weighted sparse model and its corresponding framework for bearing fault diagnosis is proposed in this paper, coined KurWSD. KurWSD formulates the prior information into weighted sparse regularization terms and then obtains a nonsmooth convex optimization problem. The alternating direction method of multipliers (ADMM) is sequentially employed to solve this problem and the fault information is extracted through the estimated wavelet coefficients. Compared with state-of-the-art methods, KurWSD overcomes the three drawbacks and utilizes the advantages of both family
OPTIMIZED STRAPDOWN CONING CORRECTION ALGORITHM
Institute of Scientific and Technical Information of China (English)
黄磊; 刘建业; 曾庆化
2013-01-01
Traditional coning algorithms are based on the first-order coning correction reference model .Usually they reduce the algorithm error of coning axis (z) by increasing the sample numbers in one iteration interval .But the increase of sample numbers requires the faster output rates of sensors .Therefore ,the algorithms are often lim-ited in practical use .Moreover ,the noncommutivity error of rotation usually exists on all three axes and the in-crease of sample numbers has little positive effect on reducing the algorithm errors of orthogonal axes (x ,y) . Considering the errors of orthogonal axes cannot be neglected in the high-precision applications ,a coning algorithm with an additional second-order coning correction term is developed to further improve the performance of coning algorithm .Compared with the traditional algorithms ,the new second-order coning algorithm can effectively reduce the algorithm error without increasing the sample numbers .Theoretical analyses validate that in a coning environ-ment with low frequency ,the new algorithm has the better performance than the traditional time-series and fre-quency-series coning algorithms ,while in a maneuver environment the new algorithm has the same order accuracy as the traditional time-series and frequency-series algorithms .Finally ,the practical feasibility of the new coning al-gorithm is demonstrated by digital simulations and practical turntable tests .
Bredies, Kristian
2009-01-01
We consider the task of computing an approximate minimizer of the sum of a smooth and a non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert space, we propose a generalization which involves the iterative solution of simpler subproblems. Descent and convergence properties of this new algorithm are studied. Furthermore, the results are applied to the minimization of Tikhonov-functionals associated with linear inverse problems and semi-norm penalization in Banach spaces. With the help of Bregman-Taylor-distance estimates, rates of convergence for the forward-backward splitting procedure are obtained. Examples which demonstrate the applicability are given, in particular, a generalization of the iterative soft-thresholding method by Daubechies, Defrise and De Mol to Banach spaces as well as total-variation-based image restoration in higher dimensions are presented.
Optimized QoS Routing Algorithm
Institute of Scientific and Technical Information of China (English)
石明洪; 王思兵; 白英彩
2004-01-01
QoS routing is one of the key technologies for providing guaranteed service in IP networks. The paper focuses on the optimization problem for bandwidth constrained QoS routing, and proposes an optimal algorithm based on the global optimization of path bandwidth and hop counts. The main goal of the algorithm is to minimize the consumption of network resource, and at the same time to minimize the network congestion caused by irrational path selection. The simulation results show that our algorithm has lower call blocking rate and higher throughput than traditional algorithms.
Tetris Agent Optimization Using Harmony Search Algorithm
Directory of Open Access Journals (Sweden)
Victor II M. Romero
2011-01-01
Full Text Available Harmony Search (HS algorithm, a relatively recent meta-heuristic optimization algorithm based on the music improvisation process of musicians, is applied to one of today's most appealing problems in the field of Computer Science, Tetris. Harmony Search algorithm was used as the underlying optimization algorithm to facilitate the learning process of an intelligent agent whose objective is to play the game of Tetris in the most optimal way possible, that is, to clear as many rows as possible. The application of Harmony Search algorithm to Tetris is a good illustration of the involvement of optimization process to decision-making problems. Experiment results show that Harmony Search algorithm found the best possible solution for the problem at hand given a random sequence of Tetrominos.
GLOBAL OPTIMIZATION OF PUMP CONFIGURATION PROBLEM USING EXTENDED CROWDING GENETIC ALGORITHM
Institute of Scientific and Technical Information of China (English)
Zhang Guijun; Wu Tihua; Ye Rong
2004-01-01
An extended crowding genetic algorithm (ECGA) is introduced for solving optimal pump configuration problem,which was presented by T.Westerlund in 1994.This problem has been found to be non-convex,and the objective function contained several local optima and global optimality could not be ensured by all the traditional MINLP optimization method.The concepts of species conserving and composite encoding are introduced to crowding genetic algorithm (CGA) for maintain the diversity of population more effectively and coping with the continuous and/or discrete variables in MINLP problem.The solution of three-levels pump configuration got from DICOPT++ software (OA algorithm) is also given.By comparing with the solutions obtained from DICOPT++,ECP method,and MIN-MIN method,the ECGA algorithm proved to be very effective in finding the global optimal solution of multi-levels pump configuration via using the problem-specific information.
An Efficient Algorithm for Unconstrained Optimization
Directory of Open Access Journals (Sweden)
Sergio Gerardo de-los-Cobos-Silva
2015-01-01
Full Text Available This paper presents an original and efficient PSO algorithm, which is divided into three phases: (1 stabilization, (2 breadth-first search, and (3 depth-first search. The proposed algorithm, called PSO-3P, was tested with 47 benchmark continuous unconstrained optimization problems, on a total of 82 instances. The numerical results show that the proposed algorithm is able to reach the global optimum. This work mainly focuses on unconstrained optimization problems from 2 to 1,000 variables.
DEFF Research Database (Denmark)
M. Gaspar, Raquel; Murgoci, Agatha
2010-01-01
of particular importance to practitioners: yield convexity adjustments, forward versus futures convexity adjustments, timing and quanto convexity adjustments. We claim that the appropriate way to look into any of these adjustments is as a side effect of a measure change, as proposed by Pelsser (2003...
Optimal Fungal Space Searching Algorithms.
Asenova, Elitsa; Lin, Hsin-Yu; Fu, Eileen; Nicolau, Dan V; Nicolau, Dan V
2016-10-01
Previous experiments have shown that fungi use an efficient natural algorithm for searching the space available for their growth in micro-confined networks, e.g., mazes. This natural "master" algorithm, which comprises two "slave" sub-algorithms, i.e., collision-induced branching and directional memory, has been shown to be more efficient than alternatives, with one, or the other, or both sub-algorithms turned off. In contrast, the present contribution compares the performance of the fungal natural algorithm against several standard artificial homologues. It was found that the space-searching fungal algorithm consistently outperforms uninformed algorithms, such as Depth-First-Search (DFS). Furthermore, while the natural algorithm is inferior to informed ones, such as A*, this under-performance does not importantly increase with the increase of the size of the maze. These findings suggest that a systematic effort of harvesting the natural space searching algorithms used by microorganisms is warranted and possibly overdue. These natural algorithms, if efficient, can be reverse-engineered for graph and tree search strategies.
Drilling Path Optimization Based on Particle Swarm Optimization Algorithm
Institute of Scientific and Technical Information of China (English)
ZHU Guangyu; ZHANG Weibo; DU Yuexiang
2006-01-01
This paper presents a new approach based on the particle swarm optimization (PSO) algorithm for solving the drilling path optimization problem belonging to discrete space. Because the standard PSO algorithm is not guaranteed to be global convergence or local convergence, based on the mathematical algorithm model, the algorithm is improved by adopting the method of generate the stop evolution particle over again to get the ability of convergence to the global optimization solution. And the operators are improved by establishing the duality transposition method and the handle manner for the elements of the operator, the improved operator can satisfy the need of integer coding in drilling path optimization. The experiment with small node numbers indicates that the improved algorithm has the characteristics of easy realize, fast convergence speed, and better global convergence characteristics, hence the new PSO can play a role in solving the problem of drilling path optimization in drilling holes.
Institute of Scientific and Technical Information of China (English)
鲍蕊娜; 李向新; 麻明; 孙晓丽; 贺瑞喜
2011-01-01
As an important expression of DEM, the generation algorithm of TIN drew people' s attention. the principle of traditional generation algorithms according are summarized and analyzed to there characteristics, described the principle and method to establish TIN with the convex hull. In accordance with the state that many of computational geometry books simplified the process of building the convex hull by limiting points, this paper shows an improvement in the process of forming a convex hull. The improved algorithm, which eliminates the repeat point when the points are sorting; it also eliminate co-line in the process of constructing new convex hull. When all the points are contained in the convex hull, the process of establishing the triangulation is completed. LOP optimization based on the triangle public edge which makes all the triangles satisfy the rule of the Delaunay triangulation.Through tests, its running speed faster than the traditional generation algorithms, at the sane time, the improved algorithm can deal with some particular cases, such as repeat points, three points are on a straight line.%TIN作为DEM的一种重要表达模型,其生成算法一直备受关注.首先对传统的生成算法原理进行总结,并针对其特点进行了分析,对利用凸壳建立TIN的原理和方法进行简单描述.由于许多计算几何学对点集进行限制以简化凸壳的建立过程,对凸壳的生成过程进行了改进.在点集的排序过程中剔除重复点,将点联入原凸壳过程中,排除共线这一特殊情况,建立新的凸壳,直至所有点都被包含在凸壳中.至此,三角网建立完毕.通过对三角形公共边进行LOP优化,使其满足Delaunay三角网的特性.当所有三角形满足特性时,Delaunay三角网构建完毕.该算法的优势在于构网速度较快,并能够对重复点进行处理,同时在生成网的过程中对共线这种特殊情况进行处理.
An Algorithmic Framework for Multiobjective Optimization
Ganesan, T.; Elamvazuthi, I.; Shaari, Ku Zilati Ku; Vasant, P.
2013-01-01
Multiobjective (MO) optimization is an emerging field which is increasingly being encountered in many fields globally. Various metaheuristic techniques such as differential evolution (DE), genetic algorithm (GA), gravitational search algorithm (GSA), and particle swarm optimization (PSO) have been used in conjunction with scalarization techniques such as weighted sum approach and the normal-boundary intersection (NBI) method to solve MO problems. Nevertheless, many challenges still arise especially when dealing with problems with multiple objectives (especially in cases more than two). In addition, problems with extensive computational overhead emerge when dealing with hybrid algorithms. This paper discusses these issues by proposing an alternative framework that utilizes algorithmic concepts related to the problem structure for generating efficient and effective algorithms. This paper proposes a framework to generate new high-performance algorithms with minimal computational overhead for MO optimization. PMID:24470795
An algorithmic framework for multiobjective optimization.
Ganesan, T; Elamvazuthi, I; Shaari, Ku Zilati Ku; Vasant, P
2013-01-01
Multiobjective (MO) optimization is an emerging field which is increasingly being encountered in many fields globally. Various metaheuristic techniques such as differential evolution (DE), genetic algorithm (GA), gravitational search algorithm (GSA), and particle swarm optimization (PSO) have been used in conjunction with scalarization techniques such as weighted sum approach and the normal-boundary intersection (NBI) method to solve MO problems. Nevertheless, many challenges still arise especially when dealing with problems with multiple objectives (especially in cases more than two). In addition, problems with extensive computational overhead emerge when dealing with hybrid algorithms. This paper discusses these issues by proposing an alternative framework that utilizes algorithmic concepts related to the problem structure for generating efficient and effective algorithms. This paper proposes a framework to generate new high-performance algorithms with minimal computational overhead for MO optimization.
An Algorithmic Framework for Multiobjective Optimization
Directory of Open Access Journals (Sweden)
T. Ganesan
2013-01-01
Full Text Available Multiobjective (MO optimization is an emerging field which is increasingly being encountered in many fields globally. Various metaheuristic techniques such as differential evolution (DE, genetic algorithm (GA, gravitational search algorithm (GSA, and particle swarm optimization (PSO have been used in conjunction with scalarization techniques such as weighted sum approach and the normal-boundary intersection (NBI method to solve MO problems. Nevertheless, many challenges still arise especially when dealing with problems with multiple objectives (especially in cases more than two. In addition, problems with extensive computational overhead emerge when dealing with hybrid algorithms. This paper discusses these issues by proposing an alternative framework that utilizes algorithmic concepts related to the problem structure for generating efficient and effective algorithms. This paper proposes a framework to generate new high-performance algorithms with minimal computational overhead for MO optimization.
An optimization algorithm of collaborative indoor locating
Directory of Open Access Journals (Sweden)
SHI Ying
2014-06-01
Full Text Available Based on triangular centroid locating algorithm,this paper will use the idea of collaboration to indoor locating system.On account of the condition which has two nodes to be located in the test environment,we have designed a circular type optimization algorithm.Verified simulation results show that the circular type optimization algorithm,compared with the triangular centroid locating algorithm,can decrease the average error by 11.62%,decrease the maximum error by 7.74% and decrease the minimum error by 22.66%.The maximum value of the optimize degree of the circular type optimization algorithm is 28.63%,and the minimum value of that is 0.05%.
Dinh, Quoc Tran; Michiels, Wim; Diehl, Moritz
2011-01-01
A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem.Applications to various output feedback controller synthesis problems are presented. In these applications the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from COMPleib library.
Institute of Scientific and Technical Information of China (English)
赵强; 郭希娟
2015-01-01
In the calculation of the exact collision detection between the actual object,the traditional Minkowski sum algorithm are dif⁃ficult to directly obtain data required for operation,so there needs for large amounts of data pre⁃processing.In order to improve the computing speed,reduce the amount of data processing,a new calculation method of 3D convex hull is designed and used to calculate the Minkowski sum of two spatial convex polyhedrons directly through their point cloud information.And the Minkowski sum boundary information is represented by the calculated results of convex hull face set.A detailed description of the algorithm is given and the complexity of the algorithm is analyzed.The results show that the algorithm is effectiveness through comparing the experimental data.%传统的 Minkowski 和算法在计算实际物体间的精确的碰撞干涉时，很难直接获取运算所需的数据，进而需要进行大量的数据预处理。为了提高运算速度，减少数据处理量，本文设计了一种新的三维凸包计算方法，通过空间两凸多面体外表的点云信息直接计算其 Minkowski 和，用计算得到的凸包的面集表示 Minkowski 和的边界信息。然后，给出详细的算法描述和复杂度分析，并通过对比分析实验数据，验证了该算法的有效性。
Distributed Algorithms for Time Optimal Reachability Analysis
DEFF Research Database (Denmark)
Zhang, Zhengkui; Nielsen, Brian; Larsen, Kim Guldstrand
2016-01-01
. We propose distributed computing to accelerate time optimal reachability analysis. We develop five distributed state exploration algorithms, implement them in \\uppaal enabling it to exploit the compute resources of a dedicated model-checking cluster. We experimentally evaluate the implemented...... algorithms with four models in terms of their ability to compute near- or proven-optimal solutions, their scalability, time and memory consumption and communication overhead. Our results show that distributed algorithms work much faster than sequential algorithms and have good speedup in general....
Optimizing neural network forecast by immune algorithm
Institute of Scientific and Technical Information of China (English)
YANG Shu-xia; LI Xiang; LI Ning; YANG Shang-dong
2006-01-01
Considering multi-factor influence, a forecasting model was built. The structure of BP neural network was designed, and immune algorithm was applied to optimize its network structure and weight. After training the data of power demand from the year 1980 to 2005 in China, a nonlinear network model was obtained on the relationship between power demand and the factors which had impacts on it, and thus the above proposed method was verified. Meanwhile, the results were compared to those of neural network optimized by genetic algorithm. The results show that this method is superior to neural network optimized by genetic algorithm and is one of the effective ways of time series forecast.
Exact and Approximate Sizes of Convex Datacubes
Nedjar, Sébastien
In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.
NP-completeness of weakly convex and convex dominating set decision problems
Directory of Open Access Journals (Sweden)
Joanna Raczek
2004-01-01
Full Text Available The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are \\(NP\\-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex.
A Novel Particle Swarm Optimization Algorithm for Global Optimization.
Wang, Chun-Feng; Liu, Kui
2016-01-01
Particle Swarm Optimization (PSO) is a recently developed optimization method, which has attracted interest of researchers in various areas due to its simplicity and effectiveness, and many variants have been proposed. In this paper, a novel Particle Swarm Optimization algorithm is presented, in which the information of the best neighbor of each particle and the best particle of the entire population in the current iteration is considered. Meanwhile, to avoid premature, an abandoned mechanism is used. Furthermore, for improving the global convergence speed of our algorithm, a chaotic search is adopted in the best solution of the current iteration. To verify the performance of our algorithm, standard test functions have been employed. The experimental results show that the algorithm is much more robust and efficient than some existing Particle Swarm Optimization algorithms.
Chemical optimization algorithm for fuzzy controller design
Astudillo, Leslie; Castillo, Oscar
2014-01-01
In this book, a novel optimization method inspired by a paradigm from nature is introduced. The chemical reactions are used as a paradigm to propose an optimization method that simulates these natural processes. The proposed algorithm is described in detail and then a set of typical complex benchmark functions is used to evaluate the performance of the algorithm. Simulation results show that the proposed optimization algorithm can outperform other methods in a set of benchmark functions. This chemical reaction optimization paradigm is also applied to solve the tracking problem for the dynamic model of a unicycle mobile robot by integrating a kinematic and a torque controller based on fuzzy logic theory. Computer simulations are presented confirming that this optimization paradigm is able to outperform other optimization techniques applied to this particular robot application
Cheung, Ngaam J; Shen, Hong-Bin
2014-11-01
The stable conformation of a molecule is greatly important to uncover the secret of its properties and functions. Generally, the conformation of a molecule will be the most stable when it is of the minimum potential energy. Accordingly, the determination of the conformation can be solved in the optimization framework. It is, however, not an easy task to achieve the only conformation with the lowest energy among all the potential ones because of the high complexity of the energy landscape and the exponential computation increasing with molecular size. In this paper, we develop a hierarchical and heterogeneous particle swarm optimizer (HHPSO) to deal with the problem in the minimization of the potential energy. The proposed method is evaluated over a scalable simplified molecular potential energy function with up to 200 degrees of freedom and a realistic energy function of pseudo-ethane molecule. The experimental results are compared with other six PSO variants and four genetic algorithms. The results show HHPSO is significantly better than the compared PSOs with p-value less than 0.01277 over molecular potential energy function.
Spaceborne SAR Imaging Algorithm for Coherence Optimized.
Directory of Open Access Journals (Sweden)
Zhiwei Qiu
Full Text Available This paper proposes SAR imaging algorithm with largest coherence based on the existing SAR imaging algorithm. The basic idea of SAR imaging algorithm in imaging processing is that output signal can have maximum signal-to-noise ratio (SNR by using the optimal imaging parameters. Traditional imaging algorithm can acquire the best focusing effect, but would bring the decoherence phenomenon in subsequent interference process. Algorithm proposed in this paper is that SAR echo adopts consistent imaging parameters in focusing processing. Although the SNR of the output signal is reduced slightly, their coherence is ensured greatly, and finally the interferogram with high quality is obtained. In this paper, two scenes of Envisat ASAR data in Zhangbei are employed to conduct experiment for this algorithm. Compared with the interferogram from the traditional algorithm, the results show that this algorithm is more suitable for SAR interferometry (InSAR research and application.
Institute of Scientific and Technical Information of China (English)
Hong Xia YIN; Dong Lei DU
2007-01-01
The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is convex (or even uniformly convex). We propose to solve unconstrained nonconvex optimization problems by a self-scaling BFGS algorithm with nonmonotone linear search. Nonmonotone line search has been recognized in numerical practices as a competitive approach for solving large-scale nonlinear problems. We consider two different nonmonotone line search forms and study the global convergence of these nonmonotone self-scale BFGS algorithms. We prove that, under some weaker condition than that in the literature, both forms of the self-scaling BFGS algorithm are globally convergent for unconstrained nonconvex optimization problems.
Algorithmic Differentiation for Calculus-based Optimization
Walther, Andrea
2010-10-01
For numerous applications, the computation and provision of exact derivative information plays an important role for optimizing the considered system but quite often also for its simulation. This presentation introduces the technique of Algorithmic Differentiation (AD), a method to compute derivatives of arbitrary order within working precision. Quite often an additional structure exploitation is indispensable for a successful coupling of these derivatives with state-of-the-art optimization algorithms. The talk will discuss two important situations where the problem-inherent structure allows a calculus-based optimization. Examples from aerodynamics and nano optics illustrate these advanced optimization approaches.
Optimization strategies for discrete multi-material stiffness optimization
DEFF Research Database (Denmark)
Hvejsel, Christian Frier; Lund, Erik; Stolpe, Mathias
2011-01-01
Design of composite laminated lay-ups are formulated as discrete multi-material selection problems. The design problem can be modeled as a non-convex mixed-integer optimization problem. Such problems are in general only solvable to global optimality for small to moderate sized problems. To attack...... larger problem instances we formulate convex and non-convex continuous relaxations which can be solved using gradient based optimization algorithms. The convex relaxation yields a lower bound on the attainable performance. The optimal solution to the convex relaxation is used as a starting guess...
Distributed Algorithms for Time Optimal Reachability Analysis
DEFF Research Database (Denmark)
Zhang, Zhengkui; Nielsen, Brian; Larsen, Kim Guldstrand
2016-01-01
Time optimal reachability analysis is a novel model based technique for solving scheduling and planning problems. After modeling them as reachability problems using timed automata, a real-time model checker can compute the fastest trace to the goal states which constitutes a time optimal schedule....... We propose distributed computing to accelerate time optimal reachability analysis. We develop five distributed state exploration algorithms, implement them in \\uppaal enabling it to exploit the compute resources of a dedicated model-checking cluster. We experimentally evaluate the implemented...... algorithms with four models in terms of their ability to compute near- or proven-optimal solutions, their scalability, time and memory consumption and communication overhead. Our results show that distributed algorithms work much faster than sequential algorithms and have good speedup in general....
Schrodinger Equation As a General Optimization Algorithm
Huang, Xiaofei
2009-01-01
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the quantum state of a physical system. It has been found that the time-independent version of the equation can be derived from a general optimization algorithm. Instead of arguing for a new interpretation and possible deeper principle for quantum mechanics, this paper elaborates a few points of the equation as a general global optimization algorithm. Benchmarked against randomly generated hard optimization problems, this paper shows that the algorithm significantly outperformed a classic local optimization algorithm. The former found a solution in one second with a single trial better than the best one found by the latter around one hour after one hundred thousand trials.
Adaptive cuckoo search algorithm for unconstrained optimization.
Ong, Pauline
2014-01-01
Modification of the intensification and diversification approaches in the recently developed cuckoo search algorithm (CSA) is performed. The alteration involves the implementation of adaptive step size adjustment strategy, and thus enabling faster convergence to the global optimal solutions. The feasibility of the proposed algorithm is validated against benchmark optimization functions, where the obtained results demonstrate a marked improvement over the standard CSA, in all the cases.
Heuristic Algorithm in Optimal Discrete Structural Designs
Directory of Open Access Journals (Sweden)
Alongkorn Lamom
2008-01-01
Full Text Available This study proposes a Heuristic Algorithm for Material Size Selection (HAMSS. It is developed to handle discrete structural optimization problems. The proposed algorithm (HAMSS, Simulated Annealing Algorithm (SA and the conventional design algorithm obtained from a structural steel design software are studied with three selected examples. The HAMSS, in fact, is the adaptation from the traditional SA. Although the SA is one of the easiest optimization algorithms available, a huge number of function evaluations deter its use in structural optimizations. To obtain the optimum answers by the SA, possible answers are first generated randomly. Many of these possible answers are rejected because they do not pass the constraints. To effectively handle this problem, the behavior of optimal structural design problems is incorporated into the algorithm. The new proposed algorithm is called the HAMSS. The efficiency comparison between the SA and the HAMSS is illustrated in term of number of finite element analysis cycles. Results from the study show that HAMSS can significantly reduce the number of structural analysis cycles while the optimized efficiency is not different.
Global Optimality of the Successive Maxbet Algorithm.
Hanafi, Mohamed; ten Berge, Jos M. F.
2003-01-01
It is known that the Maxbet algorithm, which is an alternative to the method of generalized canonical correlation analysis and Procrustes analysis, may converge to local maxima. Discusses an eigenvalue criterion that is sufficient, but not necessary, for global optimality of the successive Maxbet algorithm. (SLD)
DYNAMIC LABELING BASED FPGA DELAY OPTIMIZATION ALGORITHM
Institute of Scientific and Technical Information of China (English)
吕宗伟; 林争辉; 张镭
2001-01-01
DAG-MAP is an FPGA technology mapping algorithm for delay optimization and the labeling phase is the algorithm's kernel. This paper studied the labeling phase and presented an improved labeling method. It is shown through the experimental results on MCNC benchmarks that the improved method is more effective than the original method while the computation time is almost the same.
Belief Propagation Algorithm for Portfolio Optimization Problems.
Shinzato, Takashi; Yasuda, Muneki
2015-01-01
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.
Belief Propagation Algorithm for Portfolio Optimization Problems.
Directory of Open Access Journals (Sweden)
Takashi Shinzato
Full Text Available The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.
A working-set framework for sequential convex approximation methods
DEFF Research Database (Denmark)
Stolpe, Mathias
2008-01-01
to guarantee global convergence of the method. The algorithm works directly on the nonlinear constraints in the convex sub-problems and solves a sequence of relaxations of the current sub-problem. The algorithm terminates with the optimal solution to the sub-problem after solving a finite number of relaxations.......We present an active-set algorithmic framework intended as an extension to existing implementations of sequential convex approximation methods for solving nonlinear inequality constrained programs. The framework is independent of the choice of approximations and the stabilization technique used...
A working-set framework for sequential convex approximation methods
DEFF Research Database (Denmark)
Stolpe, Mathias
2008-01-01
We present an active-set algorithmic framework intended as an extension to existing implementations of sequential convex approximation methods for solving nonlinear inequality constrained programs. The framework is independent of the choice of approximations and the stabilization technique used...... to guarantee global convergence of the method. The algorithm works directly on the nonlinear constraints in the convex sub-problems and solves a sequence of relaxations of the current sub-problem. The algorithm terminates with the optimal solution to the sub-problem after solving a finite number of relaxations....
Asynchronous Parallel Evolutionary Algorithms for Constrained Optimizations
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Recently Guo Tao proposed a stochastic search algorithm in his PhD thesis for solving function op-timization problems. He combined the subspace search method (a general multi-parent recombination strategy) with the population hill-climbing method. The former keeps a global search for overall situation,and the latter keeps the convergence of the algorithm. Guo's algorithm has many advantages ,such as the sim-plicity of its structure ,the higher accuracy of its results, the wide range of its applications ,and the robustness of its use. In this paper a preliminary theoretical analysis of the algorithm is given and some numerical experiments has been done by using Guo's algorithm for demonstrating the theoretical results. Three asynchronous paral-lel evolutionary algorithms with different granularities for MIMD machines are designed by parallelizing Guo's Algorithm.
Wolf Pack Algorithm for Unconstrained Global Optimization
Directory of Open Access Journals (Sweden)
Hu-Sheng Wu
2014-01-01
Full Text Available The wolf pack unites and cooperates closely to hunt for the prey in the Tibetan Plateau, which shows wonderful skills and amazing strategies. Inspired by their prey hunting behaviors and distribution mode, we abstracted three intelligent behaviors, scouting, calling, and besieging, and two intelligent rules, winner-take-all generation rule of lead wolf and stronger-survive renewing rule of wolf pack. Then we proposed a new heuristic swarm intelligent method, named wolf pack algorithm (WPA. Experiments are conducted on a suit of benchmark functions with different characteristics, unimodal/multimodal, separable/nonseparable, and the impact of several distance measurements and parameters on WPA is discussed. What is more, the compared simulation experiments with other five typical intelligent algorithms, genetic algorithm, particle swarm optimization algorithm, artificial fish swarm algorithm, artificial bee colony algorithm, and firefly algorithm, show that WPA has better convergence and robustness, especially for high-dimensional functions.
Algorithms for optimal dyadic decision trees
Energy Technology Data Exchange (ETDEWEB)
Hush, Don [Los Alamos National Laboratory; Porter, Reid [Los Alamos National Laboratory
2009-01-01
A new algorithm for constructing optimal dyadic decision trees was recently introduced, analyzed, and shown to be very effective for low dimensional data sets. This paper enhances and extends this algorithm by: introducing an adaptive grid search for the regularization parameter that guarantees optimal solutions for all relevant trees sizes, revising the core tree-building algorithm so that its run time is substantially smaller for most regularization parameter values on the grid, and incorporating new data structures and data pre-processing steps that provide significant run time enhancement in practice.
An algorithm for online optimization of accelerators
Energy Technology Data Exchange (ETDEWEB)
Huang, Xiaobiao [SLAC National Accelerator Lab., Menlo Park, CA (United States); Corbett, Jeff [SLAC National Accelerator Lab., Menlo Park, CA (United States); Safranek, James [SLAC National Accelerator Lab., Menlo Park, CA (United States); Wu, Juhao [SLAC National Accelerator Lab., Menlo Park, CA (United States)
2013-10-01
We developed a general algorithm for online optimization of accelerator performance, i.e., online tuning, using the performance measure as the objective function. This method, named robust conjugate direction search (RCDS), combines the conjugate direction set approach of Powell's method with a robust line optimizer which considers the random noise in bracketing the minimum and uses parabolic fit of data points that uniformly sample the bracketed zone. Moreover, it is much more robust against noise than traditional algorithms and is therefore suitable for online application. Simulation and experimental studies have been carried out to demonstrate the strength of the new algorithm.
Efficient evolutionary algorithms for optimal control
López Cruz, I.L.
2002-01-01
If optimal control problems are solved by means of gradient based local search methods, convergence to local solutions is likely. Recently, there has been an increasing interest in the use of global optimisation algorithms to solve optimal control problems, wh
Heterogeneous architecture to process swarm optimization algorithms
Directory of Open Access Journals (Sweden)
Maria A. Dávila-Guzmán
2014-01-01
Full Text Available Since few years ago, the parallel processing has been embedded in personal computers by including co-processing units as the graphics processing units resulting in a heterogeneous platform. This paper presents the implementation of swarm algorithms on this platform to solve several functions from optimization problems, where they highlight their inherent parallel processing and distributed control features. In the swarm algorithms, each individual and dimension problem are parallelized by the granularity of the processing system which also offer low communication latency between individuals through the embedded processing. To evaluate the potential of swarm algorithms on graphics processing units we have implemented two of them: the particle swarm optimization algorithm and the bacterial foraging optimization algorithm. The algorithms’ performance is measured using the acceleration where they are contrasted between a typical sequential processing platform and the NVIDIA GeForce GTX480 heterogeneous platform; the results show that the particle swarm algorithm obtained up to 36.82x and the bacterial foraging swarm algorithm obtained up to 9.26x. Finally, the effect to increase the size of the population is evaluated where we show both the dispersion and the quality of the solutions are decreased despite of high acceleration performance since the initial distribution of the individuals can converge to local optimal solution.
Glowworm swarm optimization theory, algorithms, and applications
Kaipa, Krishnanand N
2017-01-01
This book provides a comprehensive account of the glowworm swarm optimization (GSO) algorithm, including details of the underlying ideas, theoretical foundations, algorithm development, various applications, and MATLAB programs for the basic GSO algorithm. It also discusses several research problems at different levels of sophistication that can be attempted by interested researchers. The generality of the GSO algorithm is evident in its application to diverse problems ranging from optimization to robotics. Examples include computation of multiple optima, annual crop planning, cooperative exploration, distributed search, multiple source localization, contaminant boundary mapping, wireless sensor networks, clustering, knapsack, numerical integration, solving fixed point equations, solving systems of nonlinear equations, and engineering design optimization. The book is a valuable resource for researchers as well as graduate and undergraduate students in the area of swarm intelligence and computational intellige...
Space mapping optimization algorithms for engineering design
DEFF Research Database (Denmark)
Koziel, Slawomir; Bandler, John W.; Madsen, Kaj
2006-01-01
A simple, efficient optimization algorithm based on space mapping (SM) is presented. It utilizes input SM to reduce the misalignment between the coarse and fine models of the optimized object over a region of interest, and output space mapping (OSM) to ensure matching of response and first......-order derivatives between the mapped coarse model and the fine model at the current iteration point. We also consider an enhanced version in which the input SM coefficients are frequency dependent. The performance of our new algorithms is comparable with the recently published SMIS algorithm when applied...... to a benchmark problem. In comparison with SMIS, the models presented are simple and have a small number of parameters that need to be extracted. The new algorithm is applied to the optimization of coupled-line band-pass filter....
Modified evolutionary algorithm for global optimization
Institute of Scientific and Technical Information of China (English)
郭崇慧; 陆玉昌; 唐焕文
2004-01-01
A modification of evolutionary programming or evolution strategies for n-dimensional global optimization is proposed. Based on the ergodicity and inherent-randomness of chaos, the main characteristic of the new algorithm which includes two phases is that chaotic behavior is exploited to conduct a rough search of the problem space in order to find the promising individuals in Phase Ⅰ. Adjustment strategy of step-length and intensive searches in Phase Ⅱ are employed.The population sequences generated by the algorithm asymptotically converge to global optimal solutions with probability one. The proposed algorithm is applied to several typical test problems. Numerical results illustrate that this algorithm can more efficiently solve complex global optimization problems than evolutionary programming and evolution strategies in most cases.
Novel multi-objective optimization algorithm
Institute of Scientific and Technical Information of China (English)
Jie Zeng; Wei Nie
2014-01-01
Many multi-objective evolutionary algorithms (MOEAs) can converge to the Pareto optimal front and work wel on two or three objectives, but they deteriorate when faced with many-objective problems. Indicator-based MOEAs, which adopt various indicators to evaluate the fitness values (instead of the Pareto-dominance relation to select candidate solutions), have been regarded as promising schemes that yield more satisfactory re-sults than wel-known algorithms, such as non-dominated sort-ing genetic algorithm (NSGA-II) and strength Pareto evolution-ary algorithm (SPEA2). However, they can suffer from having a slow convergence speed. This paper proposes a new indicator-based multi-objective optimization algorithm, namely, the multi-objective shuffled frog leaping algorithm based on the ε indicator (ε-MOSFLA). This algorithm adopts a memetic meta-heuristic, namely, the SFLA, which is characterized by the powerful capa-bility of global search and quick convergence as an evolutionary strategy and a simple and effective ε-indicator as a fitness as-signment scheme to conduct the search procedure. Experimental results, in comparison with other representative indicator-based MOEAs and traditional Pareto-based MOEAs on several standard test problems with up to 50 objectives, show thatε-MOSFLA is the best algorithm for solving many-objective optimization problems in terms of the solution quality as wel as the speed of convergence.
Ant colony search algorithm for optimal reactive power optimization
Directory of Open Access Journals (Sweden)
Lenin K.
2006-01-01
Full Text Available The paper presents an (ACSA Ant colony search Algorithm for Optimal Reactive Power Optimization and voltage control of power systems. ACSA is a new co-operative agents’ approach, which is inspired by the observation of the behavior of real ant colonies on the topic of ant trial formation and foraging methods. Hence, in the ACSA a set of co-operative agents called "Ants" co-operates to find good solution for Reactive Power Optimization problem. The ACSA is applied for optimal reactive power optimization is evaluated on standard IEEE, 30, 57, 191 (practical test bus system. The proposed approach is tested and compared to genetic algorithm (GA, Adaptive Genetic Algorithm (AGA.
Gems of combinatorial optimization and graph algorithms
Skutella, Martin; Stiller, Sebastian; Wagner, Dorothea
2015-01-01
Are you looking for new lectures for your course on algorithms, combinatorial optimization, or algorithmic game theory? Maybe you need a convenient source of relevant, current topics for a graduate student or advanced undergraduate student seminar? Or perhaps you just want an enjoyable look at some beautiful mathematical and algorithmic results, ideas, proofs, concepts, and techniques in discrete mathematics and theoretical computer science? Gems of Combinatorial Optimization and Graph Algorithms is a handpicked collection of up-to-date articles, carefully prepared by a select group of international experts, who have contributed some of their most mathematically or algorithmically elegant ideas. Topics include longest tours and Steiner trees in geometric spaces, cartograms, resource buying games, congestion games, selfish routing, revenue equivalence and shortest paths, scheduling, linear structures in graphs, contraction hierarchies, budgeted matching problems, and motifs in networks. This ...
Optimization in engineering models and algorithms
Sioshansi, Ramteen
2017-01-01
This textbook covers the fundamentals of optimization, including linear, mixed-integer linear, nonlinear, and dynamic optimization techniques, with a clear engineering focus. It carefully describes classical optimization models and algorithms using an engineering problem-solving perspective, and emphasizes modeling issues using many real-world examples related to a variety of application areas. Providing an appropriate blend of practical applications and optimization theory makes the text useful to both practitioners and students, and gives the reader a good sense of the power of optimization and the potential difficulties in applying optimization to modeling real-world systems. The book is intended for undergraduate and graduate-level teaching in industrial engineering and other engineering specialties. It is also of use to industry practitioners, due to the inclusion of real-world applications, opening the door to advanced courses on both modeling and algorithm development within the industrial engineering ...
Algorithms for worst-case tolerance optimization
DEFF Research Database (Denmark)
Schjær-Jacobsen, Hans; Madsen, Kaj
1979-01-01
New algorithms are presented for the solution of optimum tolerance assignment problems. The problems considered are defined mathematically as a worst-case problem (WCP), a fixed tolerance problem (FTP), and a variable tolerance problem (VTP). The basic optimization problem without tolerances...... is solved by a double-iterative algorithm in which the inner iteration is performed by the FTP- algorithm. The application of the algorithm is demonstrated by means of relatively simple numerical examples. Basic properties, such as convergence properties, are displayed based on the examples....
A generalization of the convex Kakeya problem
Ahn, Heekap
2012-01-01
We consider the following geometric alignment problem: Given a set of line segments in the plane, find a convex region of smallest area that contains a translate of each input segment. This can be seen as a generalization of Kakeya\\'s problem of finding a convex region of smallest area such that a needle can be turned through 360 degrees within this region. Our main result is an optimal Θ(n log n)-time algorithm for our geometric alignment problem, when the input is a set of n line segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then the optimum placement is when the midpoints of the segments coincide. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of any rotated copy of G. © 2012 Springer-Verlag Berlin Heidelberg.
Optimal Hops-Based Adaptive Clustering Algorithm
Xuan, Xin; Chen, Jian; Zhen, Shanshan; Kuo, Yonghong
This paper proposes an optimal hops-based adaptive clustering algorithm (OHACA). The algorithm sets an energy selection threshold before the cluster forms so that the nodes with less energy are more likely to go to sleep immediately. In setup phase, OHACA introduces an adaptive mechanism to adjust cluster head and load balance. And the optimal distance theory is applied to discover the practical optimal routing path to minimize the total energy for transmission. Simulation results show that OHACA prolongs the life of network, improves utilizing rate and transmits more data because of energy balance.
计算平面点集凸包的实时插入算法%Real-time Insert Algorithm for Computing Convex Hull of Finite Planar Sets
Institute of Scientific and Technical Information of China (English)
刘萍
2013-01-01
讨论平面点集的凸包实时插入算法.算法基于Graham扫描算法,对3个点检测顺序的转向.本文证明,当S的N个点以流的形式进入系统,计算S的凸包所需的检测次数小于3N.%In this paper, based on Graham scan algorithm, a real-time algorithm for computing convex hull of a finite planar set is proposed to check the sequential turn of 3 points. If N points of S are to be computed as stream, the number of tests for computing convex hull of S is lower than 3N.
Optimization Algorithms for Fully Automatic Optimizing Cross-cut Saw
Institute of Scientific and Technical Information of China (English)
LI Xiaochun; DING Qingxin; ZHAO Honglin; SUN Guangbin; XI Jiaxing
2010-01-01
The optimization of boards by grades plays an important role in the production for cross cutting boards, and the outturn rate and utilization of boards are directly affected by the optimization results of boards by grades. At present, the OptiCut series fully automatic optimizing cross-cut saw(FAOCCS) from Germany Weinig Group occupies the main markets in the world, but no report about the relative theories on the optimization technology and its algorithms is available. There exist some disadvantages in woodworking machinery and equipment used for cross cutting boards in China, for example, low sawing precision, outturn rate of boards and productivity, and difficulty in making statistics on the sawing results. Three optimization modes are presented for the optimization algorithms for FAOCCS, namely, optimization of fixed length, optimization of finger-jointed lumber and mixed optimization. Mathematical models are then established for these three optimization modes, and the corresponding software for realizing the optimization is prepared. Finally, Synthetic evaluation on the established mathematical models is presented through three practical examples. The results of synthetic evaluation indicate that FAOCCS using the optimization modes may raise the outturn rate of boards approximately 8% and the productivity obviously, and allows accurate statistics on the cross cut products of boards. The mathematical models of above three optimization modes are useful for increasing the outturn rate and utilization ratio of boards.
Design of a multiple kernel learning algorithm for LS-SVM by convex programming.
Jian, Ling; Xia, Zhonghang; Liang, Xijun; Gao, Chuanhou
2011-06-01
As a kernel based method, the performance of least squares support vector machine (LS-SVM) depends on the selection of the kernel as well as the regularization parameter (Duan, Keerthi, & Poo, 2003). Cross-validation is efficient in selecting a single kernel and the regularization parameter; however, it suffers from heavy computational cost and is not flexible to deal with multiple kernels. In this paper, we address the issue of multiple kernel learning for LS-SVM by formulating it as semidefinite programming (SDP). Furthermore, we show that the regularization parameter can be optimized in a unified framework with the kernel, which leads to an automatic process for model selection. Extensive experimental validations are performed and analyzed.
Minimax-optimal rates for sparse additive models over kernel classes via convex programming
Raskutti, Garvesh; Yu, Bin
2010-01-01
Sparse additive models are families of $d$-variate functions that have the additive decomposition \\mbox{$f^* = \\sum_{j \\in S} f^*_j$,} where $S$ is a unknown subset of cardinality $s \\ll d$. We consider the case where each component function $f^*_j$ lies in a reproducing kernel Hilbert space, and analyze a simple kernel-based convex program for estimating the unknown function $f^*$. Working within a high-dimensional framework that allows both the dimension $d$ and sparsity $s$ to scale, we derive convergence rates in the $L^2(\\mathbb{P})$ and $L^2(\\mathbb{P}_n)$ norms. These rates consist of two terms: a \\emph{subset selection term} of the order $\\frac{s \\log d}{n}$, corresponding to the difficulty of finding the unknown $s$-sized subset, and an \\emph{estimation error} term of the order $s \\, \
A cuckoo search algorithm for multimodal optimization.
Cuevas, Erik; Reyna-Orta, Adolfo
2014-01-01
Interest in multimodal optimization is expanding rapidly, since many practical engineering problems demand the localization of multiple optima within a search space. On the other hand, the cuckoo search (CS) algorithm is a simple and effective global optimization algorithm which can not be directly applied to solve multimodal optimization problems. This paper proposes a new multimodal optimization algorithm called the multimodal cuckoo search (MCS). Under MCS, the original CS is enhanced with multimodal capacities by means of (1) the incorporation of a memory mechanism to efficiently register potential local optima according to their fitness value and the distance to other potential solutions, (2) the modification of the original CS individual selection strategy to accelerate the detection process of new local minima, and (3) the inclusion of a depuration procedure to cyclically eliminate duplicated memory elements. The performance of the proposed approach is compared to several state-of-the-art multimodal optimization algorithms considering a benchmark suite of fourteen multimodal problems. Experimental results indicate that the proposed strategy is capable of providing better and even a more consistent performance over existing well-known multimodal algorithms for the majority of test problems yet avoiding any serious computational deterioration.
Optimal Algorithm for Algebraic Factoring
Institute of Scientific and Technical Information of China (English)
支丽红
1997-01-01
This paper presents on optimized method for factoring multivariate polynomials over algebraic extension fields defined by an irreducible ascending set. The basic idea is to convert multivariate polynomials to univariate polynomials and algebraic extension fields to algebraic number fields by suitable integer substituteions.Then factorize the univariate polynomials over the algebraic number fields.Finally,construct mulativariate factors of the original polynomial by Hensel lemma and TRUEFACTOR test.Some examples with timing are included.
An Efficient Chemical Reaction Optimization Algorithm for Multiobjective Optimization.
Bechikh, Slim; Chaabani, Abir; Ben Said, Lamjed
2015-10-01
Recently, a new metaheuristic called chemical reaction optimization was proposed. This search algorithm, inspired by chemical reactions launched during collisions, inherits several features from other metaheuristics such as simulated annealing and particle swarm optimization. This fact has made it, nowadays, one of the most powerful search algorithms in solving mono-objective optimization problems. In this paper, we propose a multiobjective variant of chemical reaction optimization, called nondominated sorting chemical reaction optimization, in an attempt to exploit chemical reaction optimization features in tackling problems involving multiple conflicting criteria. Since our approach is based on nondominated sorting, one of the main contributions of this paper is the proposal of a new quasi-linear average time complexity quick nondominated sorting algorithm; thereby making our multiobjective algorithm efficient from a computational cost viewpoint. The experimental comparisons against several other multiobjective algorithms on a variety of benchmark problems involving various difficulties show the effectiveness and the efficiency of this multiobjective version in providing a well-converged and well-diversified approximation of the Pareto front.
一种改进的最小凸包生成算法%AN IMPROVED ALGORITHM FOR PRODUCING MINIMUM CONVEX HULL
Institute of Scientific and Technical Information of China (English)
刘人午; 杨德宏; 李燕; 谌柯
2011-01-01
为解决最小凸包算法在计算超过106数量级的点数时计算时间比较长的问题,提出一种将数据点集进行一次扫描,得到横向和纵向排序点表,并建立初始凸包,再运用增点法逐步从外向内判别数据点是否加入凸包表的改进算法.该方法稳定性高、计算速度快.%At present, there are various algorithms for producing the Minimum Convex Hull, but these algorithms consume relatively long computing time when the sum of spatial data points are more than 106. An improved algorithm which are of stability and efficiency is designed. Through scanning the data points one time, we can get two tables: Lateral Sorting Table and Longitudinal Sorting Table, and a Initial Minimum Convex Hull. After the scanning, we judge whether the current point can be classified in the Minimum Convex Hull based on Increase point Method.
BMI optimization by using parallel UNDX real-coded genetic algorithm with Beowulf cluster
Handa, Masaya; Kawanishi, Michihiro; Kanki, Hiroshi
2007-12-01
This paper deals with the global optimization algorithm of the Bilinear Matrix Inequalities (BMIs) based on the Unimodal Normal Distribution Crossover (UNDX) GA. First, analyzing the structure of the BMIs, the existence of the typical difficult structures is confirmed. Then, in order to improve the performance of algorithm, based on results of the problem structures analysis and consideration of BMIs characteristic properties, we proposed the algorithm using primary search direction with relaxed Linear Matrix Inequality (LMI) convex estimation. Moreover, in these algorithms, we propose two types of evaluation methods for GA individuals based on LMI calculation considering BMI characteristic properties more. In addition, in order to reduce computational time, we proposed parallelization of RCGA algorithm, Master-Worker paradigm with cluster computing technique.
On the optimality of the neighbor-joining algorithm
Directory of Open Access Journals (Sweden)
Pachter Lior
2008-04-01
Full Text Available Abstract The popular neighbor-joining (NJ algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME tree associated to a dissimilarity map. From this point of view, NJ is "optimal" when the algorithm outputs the tree which minimizes the balanced minimum evolution criterion. We use the fact that the NJ tree topology and the BME tree topology are determined by polyhedral subdivisions of the spaces of dissimilarity maps R+(n2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaWenfgDOvwBHrxAJfwnHbqeg0uy0HwzTfgDPnwy1aaceaGae83gHi1aa0baaSqaaiabgUcaRaqaamaabmaabaqbaeqabiqaaaqaaiabd6gaUbqaaiabikdaYaaaaiaawIcacaGLPaaaaaaaaa@3BA1@ to study the optimality of the neighbor-joining algorithm. In particular, we investigate and compare the polyhedral subdivisions for n ≤ 8. This requires the measurement of volumes of spherical polytopes in high dimension, which we obtain using a combination of Monte Carlo methods and polyhedral algorithms. Our results include a demonstration that highly unrelated trees can be co-optimal in BME reconstruction, and that NJ regions are not convex. We obtain the l2 radius for neighbor-joining for n = 5 and we conjecture that the ability of the neighbor-joining algorithm to recover the BME tree depends on the diameter of the BME tree.
Some Characterizations of Total Duality for a Composed Convex Optimization%复合凸优化问题全对偶性的等价刻画
Institute of Scientific and Technical Information of China (English)
孙祥凯
2015-01-01
We first introduced the dual schemes for a composed convex optimization problem.Then, using the properties of subdifferential, we introduced a new Moreau-Rockafellar formula for a composed convex function.And using the Moreau-Rockafellar formula,we obtained some necessary and sufficient conditions which characterize the stable total duality for the composed convex optimization problem.%先建立一类复合凸优化问题的对偶问题，再利用次微分性质引入关于复合凸函数的一类新的 Moreau-Rockafellar 法则，等价刻画了该复合凸优化问题的稳定全对偶及全对偶。
Continuity of Convex Set-valued Maps and a Fundamental Duality Formula for Set-valued Optimization
Heyde, Frank
2011-01-01
Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For scalar duality theory, continuity of convex functions plays an important role. For set-valued maps different notions of continuity exist. We will compare the most prevalent ones in the special case that the image space is the set of upper closed subsets of a preordered topological vector space and analyze which of the results can be conveyed from the extended real-valued case. Moreover, we present a fundamental duality formula for set-valued optimization, using the weakest of the continuity concepts under consideration for a regularity condition.
A new optimization algorithm based on chaos
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this article, some methods are proposed for enhancing the converging velocity of the COA (chaos optimization algorithm) based on using carrier wave two times, which can greatly increase the speed and efficiency of the first carrier wave's search for the optimal point in implementing the sophisticated searching during the second carrier wave is faster and more accurate.In addition, the concept of using the carrier wave three times is proposed and put into practice to tackle the multi-variables optimization problems, where the searching for the optimal point of the last several variables is frequently worse than the first several ones.
Energy Technology Data Exchange (ETDEWEB)
Redmond, J. [Sandia National Labs., Albuquerque, NM (United States); Parker, G. [State Univ. of New York, Buffalo, NY (United States)
1993-07-01
This paper examines the role of the control objective and the control time in determining fuel-optimal actuator placement for structural vibration suppression. A general theory is developed that can be easily extended to include alternative performance metrics such as energy and time-optimal control. The performance metric defines a convex admissible control set which leads to a max-min optimization problem expressing optimal location as a function of initial conditions and control time. A solution procedure based on a nested Genetic Algorithm is presented and applied to an example problem. Results indicate that the optimal locations vary widely as a function of control time and initial conditions.
A Hybrid Evolutionary Algorithm for Discrete Optimization
Directory of Open Access Journals (Sweden)
J. Bhuvana
2015-03-01
Full Text Available Most of the real world multi-objective problems demand us to choose one Pareto optimal solution out of a finite set of choices. Flexible job shop scheduling problem is one such problem whose solutions are required to be selected from a discrete solution space. In this study we have designed a hybrid genetic algorithm to solve this scheduling problem. Hybrid genetic algorithms combine both the aspects of the search, exploration and exploitation of the search space. Proposed algorithm, Hybrid GA with Discrete Local Search, performs global search through the GA and exploits the locality through discrete local search. Proposed hybrid algorithm not only has the ability to generate Pareto optimal solutions and also identifies them with less computation. Five different benchmark test instances are used to evaluate the performance of the proposed algorithm. Results observed shown that the proposed algorithm has produced the known Pareto optimal solutions through exploration and exploitation of the search space with less number of functional evaluations.
Optimized Bayesian dynamic advising theory and algorithms
Karny, Miroslav
2006-01-01
Written by one of the world's leading groups in the area of Bayesian identification, control, and decision making, this book provides the theoretical and algorithmic basis of optimized probabilistic advising. Starting from abstract ideas and formulations, and culminating in detailed algorithms, the book comprises a unified treatment of an important problem of the design of advisory systems supporting supervisors of complex processes. It introduces the theoretical and algorithmic basis of developed advising, relying on novel and powerful combination black-box modelling by dynamic mixture models
Immune Algorithm For Document Query Optimization
Institute of Scientific and Technical Information of China (English)
WangZiqiang; FengBoqin
2005-01-01
To efficiently retrieve relevant document from the rapid proliferation of large information collections, a novel immune algorithm for document query optimization is proposed. The essential ideal of the immune algorithm is that the crossover and mutation of operator are constructed according to its own characteristics of information retrieval. Immune operator is adopted to avoid degeneracy. Relevant documents retrieved am merged to a single document list according to rank formula. Experimental results show that the novel immune algorithm can lead to substantial improvements of relevant document retrieval effectiveness.
Improvements To Glowworm Swarm Optimization Algorithm
Directory of Open Access Journals (Sweden)
Piotr Oramus
2010-01-01
Full Text Available Glowworm Swarm Optimization algorithm is applied for the simultaneous capture of multipleoptima of multimodal functions. The algorithm uses an ensemble of agents, which scan thesearch space and exchange information concerning a fitness of their current position. Thefitness is represented by a level of a luminescent quantity called luciferin. An agent movesin direction of randomly chosen neighbour, which broadcasts higher value of the luciferin.Unfortunately, in the absence of neighbours, the agent does not move at all. This is anunwelcome feature, because it diminishes the performance of the algorithm. Additionally,in the case of parallel processing, this feature can lead to unbalanced loads. This paperpresents simple modifications of the original algorithm, which improve performance of thealgorithm by limiting situations, in which the agent cannot move. The paper provides resultsof comparison of an original and modified algorithms calculated for several multimodal testfunctions.
An Optimization Synchronization Algorithm for TDDM Signal
Directory of Open Access Journals (Sweden)
Fang Liu
2016-01-01
Full Text Available The time division data modulation (TDDM mechanism is recommended to improve the communications quality and enhance the antijamming capability of the spread spectrum communication system, which will be used in the next generation global navigation satellite (GNSS systems. According to the principle and the characteristics of TDDM signal, an optimization synchronization algorithm is proposed. In the new algorithm, the synchronization accuracy and environmental adaptability have been improved with the special local sequence structure, the multicorrelation processing, and the proportion threshold mechanism. Thus, the inversion estimation formula was established. The simulation results demonstrate that the new algorithm can eliminate the illegibility threat in the synchronization process and can adapt to a lower SNR. In addition, this algorithm is better than the traditional algorithms in terms of synchronization accuracy and adaptability.
New efficient algorithm for creating convex hull for planar point set%新的高效平面点集凸壳构建算法
Institute of Scientific and Technical Information of China (English)
徐胜攀; 刘正军; 左志权
2013-01-01
This paper presented a new algorithm for creating convex hull for planar point set.It used the strategy of divide-conquer to calculate the convex hull by triangle-region processing,finding trait-points in pair by means of trait-angle calculation,decreasing the scale of the problem by the mechanism of initial triangle-region partition and updating,thereby rapidly approaching to the edge of the convex hull.For large scale data set of points,the idea of iteration was introduced in,which used the ability of quickly deleting the non convex hull points to accelerate the process of getting convex hull,making the performance of the algorithm enhanced further.Both of the time complexity and the space complexity of the algorithm are 0(n).The experiments manifest that it is a feasible,efficient and stable algorithm.Furthermore,this algorithm is easy to be extended to three-dimensional space as well as be improved to parallel type.%提出一种新的平面点集凸壳构建算法,算法基于角域处理的过程对点集分而治之计算凸壳,基于特征角计算的方法成对查找角域特征点,利用初始角域划分和角域更新的机制不断缩小问题规模,从而迅速逼近凸壳边.针对大规模数据点集,算法又引入迭代思想,利用算法本身对非凸壳点的快速删除能力进一步加速凸壳求解进程,使得算法性能进一步提升,算法时间复杂度和空间复杂度均为O(n).实验结果表明,这是一个可行、高效而且稳定的算法,易于推广到三维,也容易改进成并行算法.
金字塔凸壳算法的并行化处理%Parallel Processing of Pyramid Convex Hull Algorithms
Institute of Scientific and Technical Information of China (English)
张忠武; 王文仲; 桂丹; 周宇
2014-01-01
A parallel algorithms based on pyramid convex hull algorithm was presented .Message-passing algorithm was used on a PC cluster interconnect parallel computing system .The feasibility , accuracy and effi-ciency of the algorithm were verified by the comparison with the original serial algorithm .%提出了在金字塔凸壳算法基础上的并行算法。在由多个PC机相互连接所构成的机群并行计算系统之上，采用消息传递方式执行该算法，经过与原串行金字塔算法进行对比，验证本并行处理算法的正确性、可行性和高效性。
Derivative-free generation and interpolation of convex Pareto optimal IMRT plans.
Hoffmann, A.L.; Siem, A.Y.; Hertog, D. den; Kaanders, J.H.A.M.; Huizenga, H.
2006-01-01
In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be co
Function Optimization Based on Quantum Genetic Algorithm
Directory of Open Access Journals (Sweden)
Ying Sun
2014-01-01
Full Text Available Optimization method is important in engineering design and application. Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on. It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed, which is called Variable-boundary-coded Quantum Genetic Algorithm (vbQGA in which qubit chromosomes are collapsed into variable-boundary-coded chromosomes instead of binary-coded chromosomes. Therefore much shorter chromosome strings can be gained. The method of encoding and decoding of chromosome is first described before a new adaptive selection scheme for angle parameters used for rotation gate is put forward based on the core ideas and principles of quantum computation. Eight typical functions are selected to optimize to evaluate the effectiveness and performance of vbQGA against standard Genetic Algorithm (sGA and Genetic Quantum Algorithm (GQA. The simulation results show that vbQGA is significantly superior to sGA in all aspects and outperforms GQA in robustness and solving velocity, especially for multidimensional and complicated functions.
A generalization of the convex Kakeya problem
Ahn, Heekap
2013-09-19
Given a set of line segments in the plane, not necessarily finite, what is a convex region of smallest area that contains a translate of each input segment? This question can be seen as a generalization of Kakeya\\'s problem of finding a convex region of smallest area such that a needle can be rotated through 360 degrees within this region. We show that there is always an optimal region that is a triangle, and we give an optimal Θ(nlogn)-time algorithm to compute such a triangle for a given set of n segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then placing the segments with their midpoint at the origin and taking their convex hull results in an optimal solution. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of every rotated copy of G. © 2013 Springer Science+Business Media New York.
Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
Negahban, Sahand
2010-01-01
We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with high probability, it satisfies a form of restricted strong convexity with respect to weighted Frobenius norm. Using this property, we obtain as corollaries a number of error bounds on matrix completion in the weighted Frobenius norm under noisy sampling and for both exact and near low-rank matrices. Our results are based on measures of the "spikiness" and "low-rankness" of matrices that are less restrictive than the incoherence conditions imposed in previous work. Our technique involves an $M$-estimator that includes controls on both the rank and spikiness of the solution, and we establish non-asymptotic error bounds in weighted Frobenius norm for recovering matrices lying with $\\ell_q$-"balls" of bounded spikiness. Using information-theoretic methods, we show that no algo...
Angelic Hierarchical Planning: Optimal and Online Algorithms
2008-12-06
restrict our attention to plans in I∗(Act, s0). Definition 2. ( Parr and Russell , 1998) A plan ah∗ is hierarchically optimal iff ah∗ = argmina∈I∗(Act,s0):T...Murdock, Dan Wu, and Fusun Yaman. SHOP2: An HTN planning system. JAIR, 20:379–404, 2003. Ronald Parr and Stuart Russell . Reinforcement Learning with...Angelic Hierarchical Planning: Optimal and Online Algorithms Bhaskara Marthi Stuart J. Russell Jason Wolfe Electrical Engineering and Computer
Introducing the Adaptive Convex Enveloping
Yu, Sheng
2011-01-01
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an accurate, fast and reliable algorithm for solving convex dynamic programs with multivariate continuous states and actions, called Adaptive Convex Enveloping. This is a short introduction of the core technique created and used in my dissertation, so it is less formal, and misses some parts, such as literature review and reference, compared to a full journal paper.
Gorissen, B.L.; Ben-Tal, A.; Blanc, J.P.C.; den Hertog, D.
2012-01-01
Abstract: We propose a new way to derive tractable robust counterparts of a linear conic optimization problem by using the theory of Beck and Ben-Tal [2] on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new convex reformulation of the
Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing
Acikmese, Behcet; Blackmore, James C.; Scharf, Daniel P.
2011-01-01
An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s
Worst-case Optimal Join Algorithms
Ngo, Hung Q; Ré, Christopher; Rudra, Atri
2012-01-01
Efficient join processing is one of the most fundamental and well-studied tasks in database research. In this work, we examine algorithms for natural join queries over many relations and describe a novel algorithm to process these queries optimally in terms of worst-case data complexity. Our result builds on recent work by Atserias, Grohe, and Marx, who gave bounds on the size of a full conjunctive query in terms of the sizes of the individual relations in the body of the query. These bounds, however, are not constructive: they rely on Shearer's entropy inequality which is information-theoretic. Thus, the previous results leave open the question of whether there exist algorithms whose running time achieve these optimal bounds. An answer to this question may be interesting to database practice, as it is known that any algorithm based on the traditional select-project-join style plans typically employed in an RDBMS are asymptotically slower than the optimal for some queries. We construct an algorithm whose runn...
Combinatorial Multiobjective Optimization Using Genetic Algorithms
Crossley, William A.; Martin. Eric T.
2002-01-01
The research proposed in this document investigated multiobjective optimization approaches based upon the Genetic Algorithm (GA). Several versions of the GA have been adopted for multiobjective design, but, prior to this research, there had not been significant comparisons of the most popular strategies. The research effort first generalized the two-branch tournament genetic algorithm in to an N-branch genetic algorithm, then the N-branch GA was compared with a version of the popular Multi-Objective Genetic Algorithm (MOGA). Because the genetic algorithm is well suited to combinatorial (mixed discrete / continuous) optimization problems, the GA can be used in the conceptual phase of design to combine selection (discrete variable) and sizing (continuous variable) tasks. Using a multiobjective formulation for the design of a 50-passenger aircraft to meet the competing objectives of minimizing takeoff gross weight and minimizing trip time, the GA generated a range of tradeoff designs that illustrate which aircraft features change from a low-weight, slow trip-time aircraft design to a heavy-weight, short trip-time aircraft design. Given the objective formulation and analysis methods used, the results of this study identify where turboprop-powered aircraft and turbofan-powered aircraft become more desirable for the 50 seat passenger application. This aircraft design application also begins to suggest how a combinatorial multiobjective optimization technique could be used to assist in the design of morphing aircraft.
TWO ALGORITHMS FOR LC1 UNCONSTRAINED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Wen-yu Sun; R.J.B.de Sampaio; Jin-Yun Yuan
2000-01-01
In this paper we present two algorithms for LC1 unconstrained optimization problems which use the second order Dini upper directional derivative. These methods are simple and easy to perform. We discuss the related properties of the iteration function, and establish the global and superlinear convergence of our methods.
Advances in metaheuristic algorithms for optimal design of structures
Kaveh, A
2014-01-01
This book presents efficient metaheuristic algorithms for optimal design of structures. Many of these algorithms are developed by the author and his colleagues, consisting of Democratic Particle Swarm Optimization, Charged System Search, Magnetic Charged System Search, Field of Forces Optimization, Dolphin Echolocation Optimization, Colliding Bodies Optimization, Ray Optimization. These are presented together with algorithms which were developed by other authors and have been successfully applied to various optimization problems. These consist of Particle Swarm Optimization, Big Bang-Big Crunch Algorithm, Cuckoo Search Optimization, Imperialist Competitive Algorithm, and Chaos Embedded Metaheuristic Algorithms. Finally a multi-objective optimization method is presented to solve large-scale structural problems based on the Charged System Search algorithm. The concepts and algorithms presented in this book are not only applicable to optimization of skeletal structures and finite element models, but can equally ...
Advances in metaheuristic algorithms for optimal design of structures
Kaveh, A
2017-01-01
This book presents efficient metaheuristic algorithms for optimal design of structures. Many of these algorithms are developed by the author and his colleagues, consisting of Democratic Particle Swarm Optimization, Charged System Search, Magnetic Charged System Search, Field of Forces Optimization, Dolphin Echolocation Optimization, Colliding Bodies Optimization, Ray Optimization. These are presented together with algorithms which were developed by other authors and have been successfully applied to various optimization problems. These consist of Particle Swarm Optimization, Big Bang-Big Crunch Algorithm, Cuckoo Search Optimization, Imperialist Competitive Algorithm, and Chaos Embedded Metaheuristic Algorithms. Finally a multi-objective optimization method is presented to solve large-scale structural problems based on the Charged System Search algorithm. The concepts and algorithms presented in this book are not only applicable to optimization of skeletal structures and finite element models, but can equally ...
Ma, Xudong
2008-01-01
In this paper, we consider the demodulation and equalization problem of differential Impulse Radio (IR) Ultra-WideBand (UWB) Systems with Inter-Symbol-Interference (ISI). The differential IR UWB systems have been extensively discussed recently. The advantage of differential IR UWB systems include simple receiver frontend structure. One challenge in the demodulation and equalization of such systems with ISI is that the systems have a rather complex model. The input and output signals of the systems follow a second-order Volterra model. Furthermore, the noise at the output is data dependent. In this paper, we propose a reduced-complexity joint demodulation and equalization algorithm. The algorithm is based on reformulating the nearest neighborhood decoding problem into a mixed quadratic programming and utilizing a semi-definite relaxation. The numerical results show that the proposed demodulation and equalization algorithm has low computational complexity, and at the same time, has almost the same error probabi...
Algorithm of capacity expansion on networks optimization
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The paper points out the relationship between the bottleneck and the minimum cutset of the network, and presents a capacity expansion algorithm of network optimization to solve the network bottleneck problem. The complexity of the algorithm is also analyzed. As required by the algorithm, some virtual sources are imported through the whole positive direction subsection in the network, in which a certain capacity value is given. Simultaneously, a corresponding capacity-expanded network is constructed to search all minimum cutsets. For a given maximum flow value of the network, the authors found an adjustment value of each minimum cutset arc's group with gradually reverse calculation and marked out the feasible flow on the capacity-extended networks again with the adjustment value increasing. All this has been done repeatedly until the original topology structure is resumed. So the algorithm can increase the capacity of networks effectively and solve the bottleneck problem of networks.
Warehouse Optimization Model Based on Genetic Algorithm
Directory of Open Access Journals (Sweden)
Guofeng Qin
2013-01-01
Full Text Available This paper takes Bao Steel logistics automated warehouse system as an example. The premise is to maintain the focus of the shelf below half of the height of the shelf. As a result, the cost time of getting or putting goods on the shelf is reduced, and the distance of the same kind of goods is also reduced. Construct a multiobjective optimization model, using genetic algorithm to optimize problem. At last, we get a local optimal solution. Before optimization, the average cost time of getting or putting goods is 4.52996 s, and the average distance of the same kinds of goods is 2.35318 m. After optimization, the average cost time is 4.28859 s, and the average distance is 1.97366 m. After analysis, we can draw the conclusion that this model can improve the efficiency of cargo storage.
Optimization Algorithms in Optimal Predictions of Atomistic Properties by Kriging.
Di Pasquale, Nicodemo; Davie, Stuart J; Popelier, Paul L A
2016-04-12
The machine learning method kriging is an attractive tool to construct next-generation force fields. Kriging can accurately predict atomistic properties, which involves optimization of the so-called concentrated log-likelihood function (i.e., fitness function). The difficulty of this optimization problem quickly escalates in response to an increase in either the number of dimensions of the system considered or the size of the training set. In this article, we demonstrate and compare the use of two search algorithms, namely, particle swarm optimization (PSO) and differential evolution (DE), to rapidly obtain the maximum of this fitness function. The ability of these two algorithms to find a stationary point is assessed by using the first derivative of the fitness function. Finally, the converged position obtained by PSO and DE is refined through the limited-memory Broyden-Fletcher-Goldfarb-Shanno bounded (L-BFGS-B) algorithm, which belongs to the class of quasi-Newton algorithms. We show that both PSO and DE are able to come close to the stationary point, even in high-dimensional problems. They do so in a reasonable amount of time, compared to that with the Newton and quasi-Newton algorithms, regardless of the starting position in the search space of kriging hyperparameters. The refinement through L-BFGS-B is able to give the position of the maximum with whichever precision is desired.
Finger-knuckle-print Recognition Based on Image Sets and Convex Optimization%面向指背关节纹识别的图像集与凸壳优化算法
Institute of Scientific and Technical Information of China (English)
徐颖; 翟懿奎; 甘俊英
2014-01-01
A finger-knuckle-print (FKP)recognition algorithm based on image set and convex hull optimization model is presented in this paper.Finger-knuckle-print image sets and Local phase quantization are utilized as inputs and feature ex-traction,then convex hull model construction and optimization is adopted for finger-knuckle-print recognition.Simulation experiments show that,the proposed algorithm has achieve good performance on the public FKP database.%本文将指背关节纹作为生物特征识别对象，提出了基于图像集与凸壳优化模型的指背关节识别算法。所提算法以指背关节纹图像集作为输入，并将局部相位特征方法用于指背关节纹特征提取，进而寻求适用于指背关节纹识别的凸壳优化模型，研究凸壳模型的构建方法并对其进行优化，从而完成指背关节纹的识别。仿真实验表明，所提算法在公开的指背关节纹中，均取得了不错的识别结果。
Convex Modeling of Interactions with Strong Heredity
Haris, Asad; Witten, Daniela; Simon, Noah
2015-01-01
We consider the task of fitting a regression model involving interactions among a potentially large set of covariates, in which we wish to enforce strong heredity. We propose FAMILY, a very general framework for this task. Our proposal is a generalization of several existing methods, such as VANISH [Radchenko and James, 2010], hierNet [Bien et al., 2013], the all-pairs lasso, and the lasso using only main effects. It can be formulated as the solution to a convex optimization problem, which we solve using an efficient alternating directions method of multipliers (ADMM) algorithm. This algorithm has guaranteed convergence to the global optimum, can be easily specialized to any convex penalty function of interest, and allows for a straightforward extension to the setting of generalized linear models. We derive an unbiased estimator of the degrees of freedom of FAMILY, and explore its performance in a simulation study and on an HIV sequence data set. PMID:28316461
Computing farthest neighbors on a convex polytope
Cheong, O.; Shin, C.S.; Vigneron, A.
2002-01-01
Let N be a set of n points in convex position in R3. The farthest-point Voronoi diagram of N partitions R³ into n convex cells. We consider the intersection G(N) of the diagram with the boundary of the convex hull of N. We give an algorithm that computes an implicit representation of G(N) in expecte
Computing farthest neighbors on a convex polytope
Cheong, O.; Shin, C.S.; Vigneron, A.
2002-01-01
Let N be a set of n points in convex position in R3. The farthest-point Voronoi diagram of N partitions R³ into n convex cells. We consider the intersection G(N) of the diagram with the boundary of the convex hull of N. We give an algorithm that computes an implicit representation of G(N) in
Generalized Weiszfeld Algorithms for Lq Optimization.
Aftab, Khurrum; Hartley, Richard; Trumpf, Jochen
2015-04-01
In many computer vision applications, a desired model of some type is computed by minimizing a cost function based on several measurements. Typically, one may compute the model that minimizes the L2 cost, that is the sum of squares of measurement errors with respect to the model. However, the Lq solution which minimizes the sum of the qth power of errors usually gives more robust results in the presence of outliers for some values of q, for example, q = 1. The Weiszfeld algorithm is a classic algorithm for finding the geometric L1 mean of a set of points in Euclidean space. It is provably optimal and requires neither differentiation, nor line search. The Weiszfeld algorithm has also been generalized to find the L1 mean of a set of points on a Riemannian manifold of non-negative curvature. This paper shows that the Weiszfeld approach may be extended to a wide variety of problems to find an Lq mean for 1 ≤ q algorithm provably finds the global Lq optimum) and multiple rotation averaging (for which no such proof exists). Experimental results of Lq optimization for rotations show the improved reliability and robustness compared to L2 optimization.
Optimal Search Mechanism Analysis of Light Ray Optimization Algorithm
Institute of Scientific and Technical Information of China (English)
Jihong SHEN; Jialian LI; Bin WEI
2012-01-01
Based on Fermat's principle and the automatic optimization mechanism in the propagation process of light,an optimal searching algorithm named light ray optimization is presented,where the laws of refraction and reflection of light rays are integrated into searching process of optimization.In this algorithm,coordinate space is assumed to be the space that is full of media with different refractivities,then the space is divided by grids,and finally the searching path is assumed to be the propagation path of light rays.With the law of refraction,the search direction is deflected to the direction that makes the value of objective function decrease.With the law of reflection,the search direction is changed,which makes the search continue when it cannot keep going with refraction.Only the function values of objective problems are used and there is no artificial rule in light ray optimization,so it is simple and easy to realize.Theoretical analysis and the results of numerical experiments show that the algorithm is feasible and effective.
Modified constriction particle swarm optimization algorithm
Institute of Scientific and Technical Information of China (English)
Zhe Zhang; Limin Jia; Yong Qin
2015-01-01
To deal with the demerits of constriction particle swarm optimization (CPSO), such as relapsing into local optima, slow convergence velocity, a modified CPSO algorithm is proposed by improving the velocity update formula of CPSO. The random ve-locity operator from local optima to global optima is added into the velocity update formula of CPSO to accelerate the convergence speed of the particles to the global optima and reduce the likeli-hood of being trapped into local optima. Final y the convergence of the algorithm is verified by calculation examples.
Configurable intelligent optimization algorithm design and practice in manufacturing
Tao, Fei; Laili, Yuanjun
2014-01-01
Presenting the concept and design and implementation of configurable intelligent optimization algorithms in manufacturing systems, this book provides a new configuration method to optimize manufacturing processes. It provides a comprehensive elaboration of basic intelligent optimization algorithms, and demonstrates how their improvement, hybridization and parallelization can be applied to manufacturing. Furthermore, various applications of these intelligent optimization algorithms are exemplified in detail, chapter by chapter. The intelligent optimization algorithm is not just a single algorit
Sequential unconstrained minimization algorithms for constrained optimization
Byrne, Charles
2008-02-01
The problem of minimizing a function f(x):RJ → R, subject to constraints on the vector variable x, occurs frequently in inverse problems. Even without constraints, finding a minimizer of f(x) may require iterative methods. We consider here a general class of iterative algorithms that find a solution to the constrained minimization problem as the limit of a sequence of vectors, each solving an unconstrained minimization problem. Our sequential unconstrained minimization algorithm (SUMMA) is an iterative procedure for constrained minimization. At the kth step we minimize the function G_k(x)=f(x)+g_k(x), to obtain xk. The auxiliary functions gk(x):D ⊆ RJ → R+ are nonnegative on the set D, each xk is assumed to lie within D, and the objective is to minimize the continuous function f:RJ → R over x in the set C=\\overline D , the closure of D. We assume that such minimizers exist, and denote one such by \\hat x . We assume that the functions gk(x) satisfy the inequalities 0\\leq g_k(x)\\leq G_{k-1}(x)-G_{k-1}(x^{k-1}), for k = 2, 3, .... Using this assumption, we show that the sequence {f(xk)} is decreasing and converges to f({\\hat x}) . If the restriction of f(x) to D has bounded level sets, which happens if \\hat x is unique and f(x) is closed, proper and convex, then the sequence {xk} is bounded, and f(x^*)=f({\\hat x}) , for any cluster point x*. Therefore, if \\hat x is unique, x^*={\\hat x} and \\{x^k\\}\\rightarrow {\\hat x} . When \\hat x is not unique, convergence can still be obtained, in particular cases. The SUMMA includes, as particular cases, the well-known barrier- and penalty-function methods, the simultaneous multiplicative algebraic reconstruction technique (SMART), the proximal minimization algorithm of Censor and Zenios, the entropic proximal methods of Teboulle, as well as certain cases of gradient descent and the Newton-Raphson method. The proof techniques used for SUMMA can be extended to obtain related results for the induced proximal
Faggian, Silvia
2007-01-01
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author, or by Faggian and Gozzi. Necessary and sufficient optimality conditions for open loop controls are established. Moreover the co-state variable is shown to coincide with the spatial gradient of the value function evaluated along the trajectory of the system, creating a parallel between Maximum Principle and Dynamic Programming. The abstract model applies, as recalled in one of the first sections, to optimal investment with vintage capital.
Institute of Scientific and Technical Information of China (English)
赵玉琴; 张明望; 周意元
2011-01-01
Mehrotra-type predictor-corrector algorithms are the backbone of the most interior point methods based on the software packages. Recently Salahi et al. Consider a variant of Mehrotra's celebrated predictor-corrector algorithm for linear optimization problem. By a numerical example they show that this variant might make very small steps in order to keep the iterate in a certain neightbor-hood of the central path that itself implies the inefficiency of the algorithm. This observation motivat them to incorporate safeguard in their algorithm scheme that gives a lower bound for the step size at each iteration and thus implies polynomial iteration complexity. This paper extends their modified approach to the convex quadratic programming. As the search directions Δχ and Δs are not orthogonal any more, the complexity analysis of the method is different from that of linear programming, correspondingly. We prove that the extended algorithm, in the worst case, will terminate after at most O(nlog((χυ)Ts0)/ε) iterations.
Optimized dynamical decoupling via genetic algorithms
Quiroz, Gregory; Lidar, Daniel A.
2013-11-01
We utilize genetic algorithms aided by simulated annealing to find optimal dynamical decoupling (DD) sequences for a single-qubit system subjected to a general decoherence model under a variety of control pulse conditions. We focus on the case of sequences with equal pulse intervals and perform the optimization with respect to pulse type and order. In this manner, we obtain robust DD sequences, first in the limit of ideal pulses, then when including pulse imperfections such as finite-pulse duration and qubit rotation (flip-angle) errors. Although our optimization is numerical, we identify a deterministic structure that underlies the top-performing sequences. We use this structure to devise DD sequences which outperform previously designed concatenated DD (CDD) and quadratic DD (QDD) sequences in the presence of pulse errors. We explain our findings using time-dependent perturbation theory and provide a detailed scaling analysis of the optimal sequences.
Optimized Dynamical Decoupling via Genetic Algorithms
Quiroz, Gregory
2013-01-01
We utilize genetic algorithms to find optimal dynamical decoupling (DD) sequences for a single-qubit system subjected to a general decoherence model under a variety of control pulse conditions. We focus on the case of sequences with equal pulse-intervals and perform the optimization with respect to pulse type and order. In this manner we obtain robust DD sequences, first in the limit of ideal pulses, then when including pulse imperfections such as finite pulse duration and qubit rotation (flip-angle) errors. Although our optimization is numerical, we identify a deterministic structure underlies the top-performing sequences. We use this structure to devise DD sequences which outperform previously designed concatenated DD (CDD) and quadratic DD (QDD) sequences in the presence of pulse errors. We explain our findings using time-dependent perturbation theory and provide a detailed scaling analysis of the optimal sequences.
Particle algorithms for optimization on binary spaces
Schäfer, Christian
2011-01-01
We propose a general sequential Monte Carlo approach for optimization of pseudo-Boolean objective functions. There are three aspects we particularly address in this work. First, we give a unified approach to stochastic optimization based on sequential Monte Carlo techniques, including the cross-entropy method and simulated annealing as special cases. Secondly, we point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures. We discuss some known and novel binary parametric families and illustrate their usefulness in our numerical experiments. Finally, we provide numerical evidence that particle-driven optimization algorithms yield superior results on strongly multimodal optimization problems while local search heuristics outperform them on easier problems.
On Difference of Convex Optimization to Visualize Statistical Data and Dissimilarities
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
2016-01-01
In this talk we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective ...
On Difference of Convex Optimization to Visualize Statistical Data and Dissimilarities
DEFF Research Database (Denmark)
Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero
2016-01-01
In this talk we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective ...
Algorithms for Optimally Arranging Multicore Memory Structures
Directory of Open Access Journals (Sweden)
Wei-Che Tseng
2010-01-01
Full Text Available As more processing cores are added to embedded systems processors, the relationships between cores and memories have more influence on the energy consumption of the processor. In this paper, we conduct fundamental research to explore the effects of memory sharing on energy in a multicore processor. We study the Memory Arrangement (MA Problem. We prove that the general case of MA is NP-complete. We present an optimal algorithm for solving linear MA and optimal and heuristic algorithms for solving rectangular MA. On average, we can produce arrangements that consume 49% less energy than an all shared memory arrangement and 14% less energy than an all private memory arrangement for randomly generated instances. For DSP benchmarks, we can produce arrangements that, on average, consume 20% less energy than an all shared memory arrangement and 27% less energy than an all private memory arrangement.
FOGSAA: Fast Optimal Global Sequence Alignment Algorithm
Chakraborty, Angana; Bandyopadhyay, Sanghamitra
2013-04-01
In this article we propose a Fast Optimal Global Sequence Alignment Algorithm, FOGSAA, which aligns a pair of nucleotide/protein sequences faster than any optimal global alignment method including the widely used Needleman-Wunsch (NW) algorithm. FOGSAA is applicable for all types of sequences, with any scoring scheme, and with or without affine gap penalty. Compared to NW, FOGSAA achieves a time gain of (70-90)% for highly similar nucleotide sequences (> 80% similarity), and (54-70)% for sequences having (30-80)% similarity. For other sequences, it terminates with an approximate score. For protein sequences, the average time gain is between (25-40)%. Compared to three heuristic global alignment methods, the quality of alignment is improved by about 23%-53%. FOGSAA is, in general, suitable for aligning any two sequences defined over a finite alphabet set, where the quality of the global alignment is of supreme importance.
Trajectory metaheuristic algorithms to optimize problems combinatorics
Directory of Open Access Journals (Sweden)
Natalia Alancay
2016-12-01
Full Text Available The application of metaheuristic algorithms to optimization problems has been very important during the last decades. The main advantage of these techniques is their flexibility and robustness, which allows them to be applied to a wide range of problems. In this work we concentrate on metaheuristics based on Simulated Annealing, Tabu Search and Variable Neighborhood Search trajectory whose main characteristic is that they start from a point and through the exploration of the neighborhood vary the current solution, forming a trajectory. By means of the instances of the selected combinatorial problems, a computational experimentation is carried out that illustrates the behavior of the algorithmic methods to solve them. The main objective of this work is to perform the study and comparison of the results obtained for the selected trajectories metaheuristics in its application for the resolution of a set of academic problems of combinatorial optimization.
Intelligent perturbation algorithms for space scheduling optimization
Kurtzman, Clifford R.
1990-01-01
The optimization of space operations is examined in the light of optimization heuristics for computer algorithms and iterative search techniques. Specific attention is given to the search concepts known collectively as intelligent perturbation algorithms (IPAs) and their application to crew/resource allocation problems. IPAs iteratively examine successive schedules which become progressively more efficient, and the characteristics of good perturbation operators are listed. IPAs can be applied to aerospace systems to efficiently utilize crews, payloads, and resources in the context of systems such as Space-Station scheduling. A program is presented called the MFIVE Space Station Scheduling Worksheet which generates task assignments and resource usage structures. The IPAs can be used to develop flexible manifesting and scheduling for the Industrial Space Facility.
Stress-based upper-bound method and convex optimization: case of the Gurson material
Pastor, Franck; Trillat, Malorie; Pastor, Joseph; Loute, Etienne
2006-04-01
A nonlinear interior point method associated with the kinematic theorem of limit analysis is proposed. Associating these two tools enables one to determine an upper bound of the limit loading of a Gurson material structure from the knowledge of the sole yield criterion. We present the main features of the interior point algorithm and an original method providing a rigorous kinematic bound from a stress formulation of the problem. This method is tested by solving in plane strain the problem of a Gurson infinite bar compressed between rough rigid plates. To cite this article: F. Pastor et al., C. R. Mecanique 334 (2006).
Genetic algorithm optimization for finned channel performance
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Compared to a smooth channel, a finned channel provides a higher heat transfer coefficient; increasing the fin height enhances the heat transfer. However, this heat transfer enhancement is associated with an increase in the pressure drop. This leads to an increased pumping power requirement so that one may seek an optimum design for such systems. The main goal of this paper is to define the exact location and size of fins in such a way that a minimal pressure drop coincides with an optimal heat transfer based on the genetic algorithm. Each fin arrangement is considered a solution to the problem(an individual for genetic algorithm). An initial population is generated randomly at the first step. Then the algorithm has been searched among these solutions and made new solutions iteratively by its functions to find an optimum design as reported in this article.
Optimization of neutron monitor data correction algorithms
Energy Technology Data Exchange (ETDEWEB)
Paschalis, P. [Nuclear and Particle Physics Section, Physics Department, National and Kapodistrian University of Athens, Zografos 15783, Athens (Greece); Mavromichalaki, H., E-mail: emavromi@phys.uoa.gr [Nuclear and Particle Physics Section, Physics Department, National and Kapodistrian University of Athens, Zografos 15783, Athens (Greece)
2013-06-21
Nowadays, several neutron monitor stations worldwide, broadcast their cosmic ray data in real time, in order for the scientific community to be able to use these measurements immediately. In parallel, the development of the Neutron Monitor Database (NMDB; (http://www.nmdb.eu)) which collects all the high resolution real time measurements, allows the implementation of various applications and services by using these data instantly. Therefore, it is obvious that the need for high quality real time data is imperative. The quality of the data is handled by different correction algorithms that filter the real time measurements for undesired instrumental variations. In this work, an optimization of the Median Editor that is currently mainly applied to the neutron monitor data and the recently proposed ANN algorithm based on neural networks is presented. This optimization leads to the implementation of the Median Editor Plus and the ANN Plus algorithms. A direct comparison of these algorithms with the newly appeared Edge Editor is performed and the results are presented.
Chang, J.; Nakshatrala, K.
2014-12-01
It is well know that the standard finite element methods, in general, do not satisfy element-wise mass/species balance properties. It is, however, desirable to have element-wide mass balance property in subsurface modeling. Several studies over the years have aimed to overcome this drawback of finite element formulations. Currently, a post-processing optimization-based methodology is commonly employed to recover the local mass balance for porous media models. However, such a post-processing technique does not respect the underlying variational structure that the finite element formulation may enjoy. Motivated by this, a consistent methodology to satisfy element-wise local mass balance for porous media models is constructed using convex optimization techniques. The assembled system of global equations is reconstructed into a quadratic programming problem subjected to bounded equality constraints that ensure conservation at the element level. The proposed methodology can be applied to any computational mesh and to any non-locally conservative nodal-based finite element method. Herein, we integrate our proposed methodology into the framework of the classical mixed Galerkin formulation using Taylor-Hood elements and the least-squares finite element formulation. Our numerical studies will include computational cost, numerical convergence, and comparision with popular methods. In particular, it will be shown that the accuracy of the solutions is comparable with that of several popular locally conservative finite element formulations like the lowest order Raviart-Thomas formulation. We believe the proposed optimization-based approach is a viable approach to preserve local mass balance on general computational grids and is amenable for large-scale parallel implementation.
H2／l1混合优化问题的凸二次规划解法%Convex Quadratic Programming for Mixed H2／l1 Optimal Control
Institute of Scientific and Technical Information of China (English)
孔亚广; 吴俊; 孙优贤
2001-01-01
采用上逼近算法求解H２／l１混合优化问题。首先将其转化为有限维的凸二次规划问题，并利用Lemke互补转轴算法求解；然后逐次进行逼近。计算示例表明所得结果是正确的。%The mixed H２／l１ optimal control is dealt with. Lowerapproximation solution is used to solve it. First, it is converted into finite dimension convex quadratic programming, and solved with Lemke complementary pivoting algorithm. Then the dimension is added until the solution convergents. At last an example is given to prove this algorithm.
Nonuniqueness versus Uniqueness of Optimal Policies in Convex Discounted Markov Decision Processes
Directory of Open Access Journals (Sweden)
Raúl Montes-de-Oca
2013-01-01
Full Text Available From the classical point of view, it is important to determine if in a Markov decision process (MDP, besides their existence, the uniqueness of the optimal policies is guaranteed. It is well known that uniqueness does not always hold in optimization problems (for instance, in linear programming. On the other hand, in such problems it is possible for a slight perturbation of the functional cost to restore the uniqueness. In this paper, it is proved that the value functions of an MDP and its cost perturbed version stay close, under adequate conditions, which in some sense is a priority. We are interested in the stability of Markov decision processes with respect to the perturbations of the cost-as-you-go function.
Optimization of Transverse Oscillating Fields for Vector Velocity Estimation with Convex Arrays
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt
2013-01-01
;1. lx is maintained between 1.47 and 1.70 mm from 25 mm to 70 mm and is increased to 2.8 mm at a depth of 100 mm. Parabolic profiles are estimated using 16 missions. The optimization gives a reduction in std. from 8.5% to 5.9% with a reduction in bias from 35% to 1.02% at 90 degrees (transverse flow...
Institute of Scientific and Technical Information of China (English)
胡清洁; 肖运海; 陈内萍
2009-01-01
In this paper, some necessary and sufficient optimality conditions are obtained for a fractional multiple objective programming involving semilocal E-convex and related functions. Also, some dual results are established under this kind of generalized convex functions. Our results generalize the ones obtained by Preda[J Math Anal Appl, 288(2003) 365-382].
Institute of Scientific and Technical Information of China (English)
王彩玲; 刘庆怀; 李忠范
2008-01-01
In this paper, we introduce generalized essentially pseudoconvex func-tion and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone efficient solution.We set up Mond-Weir type duality and Craven type duality for nonsmooth multiobjective programming with generalized essentially convex functions, and prove them.
Jianwen Guo; Zhenzhong Sun; Hong Tang; Xuejun Jia; Song Wang; Xiaohui Yan; Guoliang Ye; Guohong Wu
2016-01-01
All equipment must be maintained during its lifetime to ensure normal operation. Maintenance is one of the critical roles in the success of manufacturing enterprises. This paper proposed a preventive maintenance period optimization model (PMPOM) to find an optimal preventive maintenance period. By making use of the advantages of particle swarm optimization (PSO) and cuckoo search (CS) algorithm, a hybrid optimization algorithm of PSO and CS is proposed to solve the PMPOM problem. The test fun...
Algorithmic and technical improvements: Optimal solutions to the (Generalized) Multi-Weber Problem
K.E. Rosing (Kenneth); B. Harris (Britton)
1992-01-01
textabstractRosing has recently demonstrated a new method for obtaining optimal solutions to the (Generalized) Multi-Weber Problem and proved the optimality of the results. The method develops all convex hulls and then covers the destinations with disjoint convex hulls. This paper seeks to improve i
A First-order Prediction-Correction Algorithm for Time-varying (Constrained) Optimization: Preprint
Energy Technology Data Exchange (ETDEWEB)
Dall-Anese, Emiliano [National Renewable Energy Laboratory (NREL), Golden, CO (United States)
2017-07-25
This paper focuses on the design of online algorithms based on prediction-correction steps to track the optimal solution of a time-varying constrained problem. Existing prediction-correction methods have been shown to work well for unconstrained convex problems and for settings where obtaining the inverse of the Hessian of the cost function can be computationally affordable. The prediction-correction algorithm proposed in this paper addresses the limitations of existing methods by tackling constrained problems and by designing a first-order prediction step that relies on the Hessian of the cost function (and do not require the computation of its inverse). Analytical results are established to quantify the tracking error. Numerical simulations corroborate the analytical results and showcase performance and benefits of the algorithms.
Focused Crawler Optimization Using Genetic Algorithm
Directory of Open Access Journals (Sweden)
Hartanto Kusuma Wardana
2011-12-01
Full Text Available As the size of the Web continues to grow, searching it for useful information has become more difficult. Focused crawler intends to explore the Web conform to a specific topic. This paper discusses the problems caused by local searching algorithms. Crawler can be trapped within a limited Web community and overlook suitable Web pages outside its track. A genetic algorithm as a global searching algorithm is modified to address the problems. The genetic algorithm is used to optimize Web crawling and to select more suitable Web pages to be fetched by the crawler. Several evaluation experiments are conducted to examine the effectiveness of the approach. The crawler delivers collections consist of 3396 Web pages from 5390 links which had been visited, or filtering rate of Roulette-Wheel selection at 63% and precision level at 93% in 5 different categories. The result showed that the utilization of genetic algorithm had empowered focused crawler to traverse the Web comprehensively, despite it relatively small collections. Furthermore, it brought up a great potential for building an exemplary collections compared to traditional focused crawling methods.
A GREEDY GENETIC ALGORITHM FOR UNCONSTRAINED GLOBAL OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
ZHAO Xinchao
2005-01-01
The greedy algorithm is a strong local searching algorithm. The genetica lgorithm is generally applied to the global optimization problems. In this paper, we combine the greedy idea and the genetic algorithm to propose the greedy genetic algorithm which incorporates the global exploring ability of the genetic algorithm and the local convergent ability of the greedy algorithm. Experimental results show that greedy genetic algorithm gives much better results than the classical genetic algorithm.
Bioinspired computation in combinatorial optimization: algorithms and their computational complexity
DEFF Research Database (Denmark)
Neumann, Frank; Witt, Carsten
2012-01-01
Bioinspired computation methods, such as evolutionary algorithms and ant colony optimization, are being applied successfully to complex engineering and combinatorial optimization problems, and it is very important that we understand the computational complexity of these algorithms. This tutorials...
Lahanas, M; Baltas, D; Zamboglou, N
2003-02-07
Multiple objectives must be considered in anatomy-based dose optimization for high-dose-rate brachytherapy and a large number of parameters must be optimized to satisfy often competing objectives. For objectives expressed solely in terms of dose variances, deterministic gradient-based algorithms can be applied and a weighted sum approach is able to produce a representative set of non-dominated solutions. As the number of objectives increases, or non-convex objectives are used, local minima can be present and deterministic or stochastic algorithms such as simulated annealing either cannot be used or are not efficient. In this case we employ a modified hybrid version of the multi-objective optimization algorithm NSGA-II. This, in combination with the deterministic optimization algorithm, produces a representative sample of the Pareto set. This algorithm can be used with any kind of objectives, including non-convex, and does not require artificial importance factors. A representation of the trade-off surface can be obtained with more than 1000 non-dominated solutions in 2-5 min. An analysis of the solutions provides information on the possibilities available using these objectives. Simple decision making tools allow the selection of a solution that provides a best fit for the clinical goals. We show an example with a prostate implant and compare results obtained by variance and dose-volume histogram (DVH) based objectives.
Energy Technology Data Exchange (ETDEWEB)
Lahanas, M [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach, 63069 Offenbach (Germany); Baltas, D [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach, 63069 Offenbach (Germany); Zamboglou, N [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach, 63069 Offenbach (Germany)
2003-02-07
Multiple objectives must be considered in anatomy-based dose optimization for high-dose-rate brachytherapy and a large number of parameters must be optimized to satisfy often competing objectives. For objectives expressed solely in terms of dose variances, deterministic gradient-based algorithms can be applied and a weighted sum approach is able to produce a representative set of non-dominated solutions. As the number of objectives increases, or non-convex objectives are used, local minima can be present and deterministic or stochastic algorithms such as simulated annealing either cannot be used or are not efficient. In this case we employ a modified hybrid version of the multi-objective optimization algorithm NSGA-II. This, in combination with the deterministic optimization algorithm, produces a representative sample of the Pareto set. This algorithm can be used with any kind of objectives, including non-convex, and does not require artificial importance factors. A representation of the trade-off surface can be obtained with more than 1000 non-dominated solutions in 2-5 min. An analysis of the solutions provides information on the possibilities available using these objectives. Simple decision making tools allow the selection of a solution that provides a best fit for the clinical goals. We show an example with a prostate implant and compare results obtained by variance and dose-volume histogram (DVH) based objectives.
An Approach In Optimization Of Ad-Hoc Routing Algorithms
Directory of Open Access Journals (Sweden)
Sarvesh Kumar Sharma
2012-06-01
Full Text Available In this paper different optimization of Ad-hoc routing algorithm is surveyed and a new method using training based optimization algorithm for reducing the complexity of routing algorithms is suggested. A binary matrix is assigned to each node in the network and gets updated after each data transfer using the protocols. The use of optimization algorithm in routing algorithm can reduce the complexity of routing to the least amount possible.
Gas pipeline optimization using adaptive algorithms
Energy Technology Data Exchange (ETDEWEB)
Smati, A.; Zemmour, N. [INH, Boumerdes (Algeria)
1996-12-31
Transmission gas pipeline network consume significant amounts of energy. Then, minimizing the energy requirements is a challenging task. Due to the nonlinearity and poor knowledge of the system states, several results, based on the optimal control theory, are obtained only for simple configurations. In this paper an optimization scheme in the face of varying demand is carried out. It is based on the use of a dynamic simulation program as a plant model and the Pareto set technique to sell out useful experiments. Experiments are used for the identification of regression models based on an original class of functions. The nonlinear programming algorithm results. Its connection with regression models permits the definition off-line, and for a long time horizon, of the optimal discharge pressure trajectory for all the compressor stations. The use of adaptive algorithms, with high frequency, permits one to cancel the effect of unknown disturbances and errors in demand forecasts. In this way, an on-line optimization scheme using data of SCADA system is presented.
DEFF Research Database (Denmark)
Hovgaard, Tobias Gybel; Larsen, Lars F. S.; Jørgensen, John Bagterp
2012-01-01
from the wind farm model, enabling us to use a very simple linear relationship for describing the turbine interactions. In addition, we allow individual turbines to be turned on or off introducing integer variables into the optimization problem. We solve this within the same framework of iterative...... is far superior to, a more naive distribution scheme. We employ a fast convex quadratic programming solver to carry out the iterations in the range of microseconds for even large wind farms....
A Survey on Meta-Heuristic Global Optimization Algorithms
Directory of Open Access Journals (Sweden)
Mohammad Khajehzadeh
2011-06-01
Full Text Available Optimization has been an active area of research for several decades. As many real-world optimization problems become increasingly complex, better optimization algorithms are always needed. Recently, metaheuristic global optimization algorithms have become a popular choice for solving complex and intricate problems, which are otherwise difficult to solve by traditional methods. In the present study, an attempt is made to review the most popular and well known metaheuristic global optimization algorithms introduced during the past decades.
Local Routing in Convex Subdivisions
DEFF Research Database (Denmark)
Bose, Prosenjit; Durocher, Stephane; Mondal, Debajyoti;
2015-01-01
In various wireless networking settings, node locations determine a network’s topology, allowing the network to be modelled by a geometric graph drawn in the plane. Without any additional information, local geometric routing algorithms can guarantee delivery to the target node only in restricted...... classes of geometric graphs, such as triangulations. In order to guarantee delivery on more general classes of geometric graphs (e.g., convex subdivisions or planar subdivisions), previous local geometric routing algorithms required Θ(logn) state bits to be stored and passed with the message. We present...... the first local geometric routing algorithm using only one state bit to guarantee delivery on convex subdivisions and the first local geometric memoryless routing algorithm that guarantees delivery on edge-augmented monotone subdivisions (including all convex subdivisions) when the algorithm has knowledge...
OPTIMAL CONTROL ALGORITHMS FOR SECOND ORDER SYSTEMS
Directory of Open Access Journals (Sweden)
Danilo Pelusi
2013-01-01
Full Text Available Proportional Integral Derivative (PID controllers are widely used in industrial processes for their simplicity and robustness. The main application problems are the tuning of PID parameters to obtain good settling time, rise time and overshoot. The challenge is to improve the timing parameters to achieve optimal control performances. Remarkable findings are obtained through the use of Artificial Intelligence techniques as Fuzzy Logic, Genetic Algorithms and Neural Networks. The combination of these theories can give good results in terms of settling time, rise time and overshoot. In this study, suitable controllers able of improving timing performance of second order plants are proposed. The results show that the PID controller has good overshoot values and shows optimal robustness. The genetic-fuzzy controller gives a good value of settling time and a very good overshoot value. The neural-fuzzy controller gives the best timing parameters improving the control performances of the others two approaches. Further improvements are achieved designing a real-time optimization algorithm which works on a genetic-neuro-fuzzy controller.
Intervals in evolutionary algorithms for global optimization
Energy Technology Data Exchange (ETDEWEB)
Patil, R.B.
1995-05-01
Optimization is of central concern to a number of disciplines. Interval Arithmetic methods for global optimization provide us with (guaranteed) verified results. These methods are mainly restricted to the classes of objective functions that are twice differentiable and use a simple strategy of eliminating a splitting larger regions of search space in the global optimization process. An efficient approach that combines the efficient strategy from Interval Global Optimization Methods and robustness of the Evolutionary Algorithms is proposed. In the proposed approach, search begins with randomly created interval vectors with interval widths equal to the whole domain. Before the beginning of the evolutionary process, fitness of these interval parameter vectors is defined by evaluating the objective function at the center of the initial interval vectors. In the subsequent evolutionary process the local optimization process returns an estimate of the bounds of the objective function over the interval vectors. Though these bounds may not be correct at the beginning due to large interval widths and complicated function properties, the process of reducing interval widths over time and a selection approach similar to simulated annealing helps in estimating reasonably correct bounds as the population evolves. The interval parameter vectors at these estimated bounds (local optima) are then subjected to crossover and mutation operators. This evolutionary process continues for predetermined number of generations in the search of the global optimum.
Levin, Mark Sh
2011-01-01
The paper describes a general glance to the use of element exchange techniques for optimization over permutations. A multi-level description of problems is proposed which is a fundamental to understand nature and complexity of optimization problems over permutations (e.g., ordering, scheduling, traveling salesman problem). The description is based on permutation neighborhoods of several kinds (e.g., by improvement of an objective function). Our proposed operational digraph and its kinds can be considered as a way to understand convexity and polynomial solvability for combinatorial optimization problems over permutations. Issues of an analysis of problems and a design of hierarchical heuristics are discussed. The discussion leads to a multi-level adaptive algorithm system which analyzes an individual problem and selects/designs a solving strategy (trajectory).
Directory of Open Access Journals (Sweden)
Jianwen Guo
2016-01-01
Full Text Available All equipment must be maintained during its lifetime to ensure normal operation. Maintenance is one of the critical roles in the success of manufacturing enterprises. This paper proposed a preventive maintenance period optimization model (PMPOM to find an optimal preventive maintenance period. By making use of the advantages of particle swarm optimization (PSO and cuckoo search (CS algorithm, a hybrid optimization algorithm of PSO and CS is proposed to solve the PMPOM problem. The test functions show that the proposed algorithm exhibits more outstanding performance than particle swarm optimization and cuckoo search. Experiment results show that the proposed algorithm has advantages of strong optimization ability and fast convergence speed to solve the PMPOM problem.
Watermark Extraction Optimization Using PSO Algorithm
Directory of Open Access Journals (Sweden)
Mohammad Dehghani Soltani
2013-04-01
Full Text Available In this study we propose an improved method for watermarking based on ML detector that in comparison with similar methods this scheme has more robustness against attacks, with the same embedded length of logo. Embedding the watermark will perform in the low frequency coefficients of wavelet transform of high entropy blocks (blocks which have more information. Then in the watermark extraction step by using PSO algorithm in a way that maximum quality in comparison with previous methods obtain, by optimizing the Lagrange factor in the Neyman-Peyrson test, we extract the watermark. Finally, performance of proposed scheme has been investigated and accuracy of results are shown by simulation.
Optimization Algorithms for Nuclear Reactor Power Control
Energy Technology Data Exchange (ETDEWEB)
Kim, Yeong Min; Oh, Won Jong; Oh, Seung Jin; Chun, Won Gee; Lee, Yoon Joon [Jeju National University, Jeju (Korea, Republic of)
2010-10-15
One of the control techniques that could replace the present conventional PID controllers in nuclear plants is the linear quadratic regulator (LQR) method. The most attractive feature of the LQR method is that it can provide the systematic environments for the control design. However, the LQR approach heavily depends on the selection of cost function and the determination of the suitable weighting matrices of cost function is not an easy task, particularly when the system order is high. The purpose of this paper is to develop an efficient and reliable algorithm that could optimize the weighting matrices of the LQR system
Empirical Investigation of Optimization Algorithms in Neural Machine Translation
Directory of Open Access Journals (Sweden)
Bahar Parnia
2017-06-01
Full Text Available Training neural networks is a non-convex and a high-dimensional optimization problem. In this paper, we provide a comparative study of the most popular stochastic optimization techniques used to train neural networks. We evaluate the methods in terms of convergence speed, translation quality, and training stability. In addition, we investigate combinations that seek to improve optimization in terms of these aspects. We train state-of-the-art attention-based models and apply them to perform neural machine translation. We demonstrate our results on two tasks: WMT 2016 En→Ro and WMT 2015 De→En.
Approximation of Reachable Sets using Optimal Control Algorithms
Baier, Robert; Gerdts, Matthias; Xausa, Ilaria
2013-01-01
To appear; International audience; Numerical experiences with a method for the approximation of reachable sets of nonlinear control systems are reported. The method is based on the formulation of suitable optimal control problems with varying objective functions, whose discretization by Euler's method lead to finite dimensional non-convex nonlinear programs. These are solved by a sequential quadratic programming method. An efficient adjoint method for gradient computation is used to reduce th...
Optimization of PID Controllers Using Ant Colony and Genetic Algorithms
Ünal, Muhammet; Topuz, Vedat; Erdal, Hasan
2013-01-01
Artificial neural networks, genetic algorithms and the ant colony optimization algorithm have become a highly effective tool for solving hard optimization problems. As their popularity has increased, applications of these algorithms have grown in more than equal measure. While many of the books available on these subjects only provide a cursory discussion of theory, the present book gives special emphasis to the theoretical background that is behind these algorithms and their applications. Moreover, this book introduces a novel real time control algorithm, that uses genetic algorithm and ant colony optimization algorithms for optimizing PID controller parameters. In general, the present book represents a solid survey on artificial neural networks, genetic algorithms and the ant colony optimization algorithm and introduces novel practical elements related to the application of these methods to process system control.
Optimization of machining processes using pattern search algorithm
Directory of Open Access Journals (Sweden)
Miloš Madić
2014-04-01
Full Text Available Optimization of machining processes not only increases machining efficiency and economics, but also the end product quality. In recent years, among the traditional optimization methods, stochastic direct search optimization methods such as meta-heuristic algorithms are being increasingly applied for solving machining optimization problems. Their ability to deal with complex, multi-dimensional and ill-behaved optimization problems made them the preferred optimization tool by most researchers and practitioners. This paper introduces the use of pattern search (PS algorithm, as a deterministic direct search optimization method, for solving machining optimization problems. To analyze the applicability and performance of the PS algorithm, six case studies of machining optimization problems, both single and multi-objective, were considered. The PS algorithm was employed to determine optimal combinations of machining parameters for different machining processes such as abrasive waterjet machining, turning, turn-milling, drilling, electrical discharge machining and wire electrical discharge machining. In each case study the optimization solutions obtained by the PS algorithm were compared with the optimization solutions that had been determined by past researchers using meta-heuristic algorithms. Analysis of obtained optimization results indicates that the PS algorithm is very applicable for solving machining optimization problems showing good competitive potential against stochastic direct search methods such as meta-heuristic algorithms. Specific features and merits of the PS algorithm were also discussed.
Applications of metaheuristic optimization algorithms in civil engineering
Kaveh, A
2017-01-01
The book presents recently developed efficient metaheuristic optimization algorithms and their applications for solving various optimization problems in civil engineering. The concepts can also be used for optimizing problems in mechanical and electrical engineering.
A Feedback Optimal Control Algorithm with Optimal Measurement Time Points
Directory of Open Access Journals (Sweden)
Felix Jost
2017-02-01
Full Text Available Nonlinear model predictive control has been established as a powerful methodology to provide feedback for dynamic processes over the last decades. In practice it is usually combined with parameter and state estimation techniques, which allows to cope with uncertainty on many levels. To reduce the uncertainty it has also been suggested to include optimal experimental design into the sequential process of estimation and control calculation. Most of the focus so far was on dual control approaches, i.e., on using the controls to simultaneously excite the system dynamics (learning as well as minimizing a given objective (performing. We propose a new algorithm, which sequentially solves robust optimal control, optimal experimental design, state and parameter estimation problems. Thus, we decouple the control and the experimental design problems. This has the advantages that we can analyze the impact of measurement timing (sampling independently, and is practically relevant for applications with either an ethical limitation on system excitation (e.g., chemotherapy treatment or the need for fast feedback. The algorithm shows promising results with a 36% reduction of parameter uncertainties for the Lotka-Volterra fishing benchmark example.
A NEWTON LIKE ALGORITHM FOR SOLVING MINIMAX OPTIMIZATION PROBLEM%求解Minimax优化问题的Newton型算法
Institute of Scientific and Technical Information of China (English)
薛毅
2004-01-01
In this paper, a Newton like method for solving minimax optimization problems was proposed. The method belong to sequential quadratic programming method,the Hessian of quadratic programming subproblem is a convex combination of Hes-sian of objective functions. When Hessian of quadratic programming subproblem is not positive definite, the strategy to force matrix positive definite is used, so that there are good numerical solution for quadratic programming subproblem.The paper prove that the algorithm has global convergence and q-superlinear con-vergence properties. In order to show the new algorithm having good results, our preliminary numerical experiments are also reported.
Lunar Habitat Optimization Using Genetic Algorithms
SanScoucie, M. P.; Hull, P. V.; Tinker, M. L.; Dozier, G. V.
2007-01-01
Long-duration surface missions to the Moon and Mars will require bases to accommodate habitats for the astronauts. Transporting the materials and equipment required to build the necessary habitats is costly and difficult. The materials chosen for the habitat walls play a direct role in protection against each of the mentioned hazards. Choosing the best materials, their configuration, and the amount required is extremely difficult due to the immense size of the design region. Clearly, an optimization method is warranted for habitat wall design. Standard optimization techniques are not suitable for problems with such large search spaces; therefore, a habitat wall design tool utilizing genetic algorithms (GAs) has been developed. GAs use a "survival of the fittest" philosophy where the most fit individuals are more likely to survive and reproduce. This habitat design optimization tool is a multiobjective formulation of up-mass, heat loss, structural analysis, meteoroid impact protection, and radiation protection. This Technical Publication presents the research and development of this tool as well as a technique for finding the optimal GA search parameters.
OPC recipe optimization using genetic algorithm
Asthana, Abhishek; Wilkinson, Bill; Power, Dave
2016-03-01
Optimization of OPC recipes is not trivial due to multiple parameters that need tuning and their correlation. Usually, no standard methodologies exist for choosing the initial recipe settings, and in the keyword development phase, parameters are chosen either based on previous learning, vendor recommendations, or to resolve specific problems on particular special constructs. Such approaches fail to holistically quantify the effects of parameters on other or possible new designs, and to an extent are based on the keyword developer's intuition. In addition, when a quick fix is needed for a new design, numerous customization statements are added to the recipe, which make it more complex. The present work demonstrates the application of Genetic Algorithm (GA) technique for optimizing OPC recipes. GA is a search technique that mimics Darwinian natural selection and has applications in various science and engineering disciplines. In this case, GA search heuristic is applied to two problems: (a) an overall OPC recipe optimization with respect to selected parameters and, (b) application of GA to improve printing and via coverage at line end geometries. As will be demonstrated, the optimized recipe significantly reduced the number of ORC violations for case (a). For case (b) line end for various features showed significant printing and filling improvement.
Efficient algorithms for the laboratory discovery of optimal quantum controls.
Turinici, Gabriel; Le Bris, Claude; Rabitz, Herschel
2004-01-01
The laboratory closed-loop optimal control of quantum phenomena, expressed as minimizing a suitable cost functional, is currently implemented through an optimization algorithm coupled to the experimental apparatus. In practice, the most commonly used search algorithms are variants of genetic algorithms. As an alternative choice, a direct search deterministic algorithm is proposed in this paper. For the simple simulations studied here, it outperforms the existing approaches. An additional algorithm is introduced in order to reveal some properties of the cost functional landscape.
Sarjaš, Andrej; Chowdhury, Amor; Svečko, Rajko
2016-09-01
This paper presents the synthesis of an optimal robust controller design using the polynomial pole placement technique and multi-criteria optimisation procedure via an evolutionary computation algorithm - differential evolution. The main idea of the design is to provide a reliable fixed-order robust controller structure and an efficient closed-loop performance with a preselected nominally characteristic polynomial. The multi-criteria objective functions have quasi-convex properties that significantly improve convergence and the regularity of the optimal/sub-optimal solution. The fundamental aim of the proposed design is to optimise those quasi-convex functions with fixed closed-loop characteristic polynomials, the properties of which are unrelated and hard to present within formal algebraic frameworks. The objective functions are derived from different closed-loop criteria, such as robustness with metric ?∞, time performance indexes, controller structures, stability properties, etc. Finally, the design results from the example verify the efficiency of the controller design and also indicate broader possibilities for different optimisation criteria and control structures.
Celik, Yuksel; Ulker, Erkan
2013-01-01
Marriage in honey bees optimization (MBO) is a metaheuristic optimization algorithm developed by inspiration of the mating and fertilization process of honey bees and is a kind of swarm intelligence optimizations. In this study we propose improved marriage in honey bees optimization (IMBO) by adding Levy flight algorithm for queen mating flight and neighboring for worker drone improving. The IMBO algorithm's performance and its success are tested on the well-known six unconstrained test functions and compared with other metaheuristic optimization algorithms.
Fast algorithm of computing volume based on convex hull%一种基于凸包近似的快速体积计算方法
Institute of Scientific and Technical Information of China (English)
徐志; 许宏丽
2013-01-01
体积是物体的基本几何属性，在许多应用场合需要频繁地被计算。目前基本上通过重构物体曲面而间接求取体积，增加了许多不必要的工作。提出一种快速求取点云模型体积的方法，使用增量式算法计算点云的凸包用来近似物体，将凸包分解成上下两个三角网格面，使用正投影法分别求取它们的投影体积，它们两者之差即是所求模型体积。实验表明该算法实现简单，可快速地求解处理具有任何几何和拓扑复杂性的点云模型。%Volume, as the basic geometric property of objects, needs to be calculated frequently in many applications. At present, volume is basically calculated through the reconstruction of object surface indirectly, increasing the number of unnecessary work. This paper presents a fast algorithm of computing volume based on convex hull. The method computes the convex hull of the point cloud by using incremental algorithm to approximate the 3D object, and then breaks the hull down into the high and lower triangular mesh surface. Both of the two shells’volume are calculated by the projection method and the difference between them is the object’s volume. This algorithm has been proven simple to implement and can process cloud models with arbitrary geometry and topology.
Optimal Genetic View Selection Algorithm for Data Warehouse
Institute of Scientific and Technical Information of China (English)
Wang Ziqiang; Feng Boqin
2005-01-01
To efficiently solve the materialized view selection problem, an optimal genetic algorithm of how to select a set of views to be materialized is proposed so as to achieve both good query performance and low view maintenance cost under a storage space constraint. First, a pre-processing algorithm based on the maximum benefit per unit space is used to generate initial solutions. Then, the initial solutions are improved by the genetic algorithm having the mixture of optimal strategies. Furthermore, the generated infeasible solutions during the evolution process are repaired by loss function. The experimental results show that the proposed algorithm outperforms the heuristic algorithm and canonical genetic algorithm in finding optimal solutions.
Deterministic oscillatory search: a new meta-heuristic optimization algorithm
Indian Academy of Sciences (India)
N ARCHANA; R VIDHYAPRIYA; ANTONY BENEDICT; KARTHIK CHANDRAN
2017-06-01
The paper proposes a new optimization algorithm that is extremely robust in solving mathematical and engineering problems. The algorithm combines the deterministic nature of classical methods of optimization and global converging characteristics of meta-heuristic algorithms. Common traits of nature-inspired algorithms like randomness and tuning parameters (other than population size) are eliminated. The proposed algorithm is tested with mathematical benchmark functions and compared to other popular optimization algorithms. Theresults show that the proposed algorithm is superior in terms of robustness and problem solving capabilities to other algorithms. The paradigm is also applied to an engineering problem to prove its practicality. It is applied to find the optimal location of multi-type FACTS devices in a power system and tested in the IEEE 39 bus system and UPSEB 75 bus system. Results show better performance over other standard algorithms in terms of voltage stability, real power loss and sizing and cost of FACTS devices.
基于凸包的视锥体裁剪精度优化%Precision Optimeization of View Frustum Culling Based on Convex Hull
Institute of Scientific and Technical Information of China (English)
曾磊夫; 刘爽
2016-01-01
According to the space object frustum clipping ,a kind of precision optimization method has been put forward that is based on the convex hull .First of all ,the method get the 2d plane projection from 3d object ,and organize projective coordinate to a convex hull ,finally get the visibility of objects according to the line form the coordinate of convex hull and the camera ,whole optimization needs any extra memory to save the data of convex hull only .The experimental results show that this method implement simply ,it can reduce the unreasonable result from the sphere detection or cylinder detection ,improving the whole efficiency of 3D rendering system .%针对视锥体对空间中物体的裁剪 ,提出一种新的基于凸包的精度优化方法 ,该方法首先得到三维物体到二维平面的投影 ,然后对投影坐标进行凸包组织 ,最后根据凸包上的坐标点和摄像机的连线得到物体的可见性 ,整个优化法只需一些额外的存储空间来存储物体的凸包信息即可 .实验结果表明 ,该方法易于实现 ,能减少通常的包围球、圆柱体检测法中出现的不合理结果 ,进而提高整个三维渲染系统的效率 .
Efficient Genetic Algorithm sets for optimizing constrained building design problem
National Research Council Canada - National Science Library
Wright, Jonathan; Alajmi, Ali
2016-01-01
.... This requires trying large possible solutions which need heuristic optimization algorithms. A comparison between several heuristic optimization algorithms showed that Genetic Algorithm (GA) is robust on getting the optimum(s) simulation ( Wetter and Wright, 2004; Brownlee et al., 2011; Bichiou and Krarti, 2011; Sahu et al., 2012 ) while the building simulat...
A Hybrid Algorithm for Optimizing Multi- Modal Functions
Institute of Scientific and Technical Information of China (English)
Li Qinghua; Yang Shida; Ruan Youlin
2006-01-01
A new genetic algorithm is presented based on the musical performance. The novelty of this algorithm is that a new genetic algorithm, mimicking the musical process of searching for a perfect state of harmony, which increases the robustness of it greatly and gives a new meaning of it in the meantime, has been developed. Combining the advantages of the new genetic algorithm, simplex algorithm and tabu search, a hybrid algorithm is proposed. In order to verify the effectiveness of the hybrid algorithm, it is applied to solving some typical numerical function optimization problems which are poorly solved by traditional genetic algorithms. The experimental results show that the hybrid algorithm is fast and reliable.
Enhanced Bee Colony Algorithm for Complex Optimization Problems
Directory of Open Access Journals (Sweden)
S.Suriya
2012-01-01
Full Text Available Optimization problems are considered to be one kind of NP hard problems. Usually heuristic approaches are found to provide solutions for NP hard problems. There are a plenty of heuristic algorithmsavailable to solve optimization problems namely: Ant Colony Optimization, Particle Swarm Optimization, Bee Colony Optimization, etc. The basic Bee Colony algorithm, a population based search algorithm, is analyzed to be a novel tool for complex optimization problems. The algorithm mimics the food foraging behavior of swarmsof honey bees. This paper deals with a modified fitness function of Bee Colony algorithm. The effect of problem dimensionality on the performance of the algorithms will be investigated. This enhanced Bee Colony Optimization will be evaluated based on the well-known benchmark problems. The testing functions like Rastrigin, Rosenbrock, Ackley, Griewank and Sphere are used to evaluavate the performance of the enhanced Bee Colony algorithm. The simulation will be developed on MATLAB.
Covering Numbers for Convex Functions
Guntuboyina, Adityanand
2012-01-01
In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $\\epsilon$-covering number of $\\C([a, b]^d, B)$, in the $L_p$-metric, $1 \\le p 0$, and $\\C([a,b]^d, B)$ denotes the set of all convex functions on $[a, b]^d$ that are uniformly bounded by $B$. We summarize previously known results on covering numbers for convex functions and also provide alternate proofs of some known results. Our results have direct implications in the study of rates of convergence of empirical minimization procedures as well as optimal convergence rates in the numerous convexity constrained function estimation problems.
Klee, Victor; Ziegler, Günter
2003-01-01
"The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way." (Gil Kalai, The Hebrew University of Jerusalem) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The or...
Jafarizadeh, Saber
2010-01-01
Providing an analytical solution for the problem of finding Fastest Distributed Consensus (FDC) is one of the challenging problems in the field of sensor networks. Most of the methods proposed so far deal with the FDC averaging algorithm problem by numerical convex optimization methods and in general no closed-form solution for finding FDC has been offered up to now except in [3] where the conjectured answer for path has been proved. Here in this work we present an analytical solution for the problem of Fastest Distributed Consensus for the Path network using semidefinite programming particularly solving the slackness conditions, where the optimal weights are obtained by inductive comparing of the characteristic polynomials initiated by slackness conditions.
Niching genetic algorithms for optimization in electromagnetics - I. Fundamentals
Sareni, Bruno; Krähenbühl, Laurent; Nicolas, Alain
1998-01-01
Niching methods extend genetic algorithms and permit the investigation of multiple optimal solutions in the search space. In this paper, we review and discuss various strategies of niching for optimization in electromagnetics. Traditional mathematical problems and an electromagnetic benchmark are solved using niching genetic algorithms to show their interest in real world optimization.
A Hybrid Aggressive Space Mapping Algorithm for EM Optimization
DEFF Research Database (Denmark)
Bakr, M.; Bandler, J. W.; Georgieva, N.;
1999-01-01
We present a novel, Hybrid Aggressive Space Mapping (HASM) optimization algorithm. HASM is a hybrid approach exploiting both the Trust Region Aggressive Space Mapping (TRASM) algorithm and direct optimization. It does not assume that the final space-mapped design is the true optimal design and is...
Dynamic Planar Convex Hull with Optimal Query Time and O(log n · log log n ) Update Time
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Jakob, Riko
2000-01-01
The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log log n) time, point deletions in amortized O(log n · log log n) time...
PDE Nozzle Optimization Using a Genetic Algorithm
Billings, Dana; Turner, James E. (Technical Monitor)
2000-01-01
Genetic algorithms, which simulate evolution in natural systems, have been used to find solutions to optimization problems that seem intractable to standard approaches. In this study, the feasibility of using a GA to find an optimum, fixed profile nozzle for a pulse detonation engine (PDE) is demonstrated. The objective was to maximize impulse during the detonation wave passage and blow-down phases of operation. Impulse of each profile variant was obtained by using the CFD code Mozart/2.0 to simulate the transient flow. After 7 generations, the method has identified a nozzle profile that certainly is a candidate for optimum solution. The constraints on the generality of this possible solution remain to be clarified.
Evolutionary Algorithm Geometry Optimization of Optical Antennas
Directory of Open Access Journals (Sweden)
Ramón Díaz de León-Zapata
2016-01-01
Full Text Available Printed circuit antennas have been used for the detection of electromagnetic radiation at a wide range of frequencies that go from radio frequencies (RF up to optical frequencies. The design of printed antennas at optical frequencies has been done by using design rules derived from the radio frequency domain which do not take into account the dispersion of material parameters at optical frequencies. This can make traditional RF antenna design not suitable for optical antenna design. This work presents the results of using a genetic algorithm (GA for obtaining an optimized geometry (unconventional geometries that may be used as optical regime antennas to capture electromagnetic waves. The radiation patterns and optical properties of the GA generated geometries were compared with the conventional dipole geometry. The characterizations were conducted via finite element method (FEM computational simulations.
A homogeneous interior-point algorithm for nonsymmetric convex conic optimization
DEFF Research Database (Denmark)
Skajaa, Anders; Ye, Yinyu
2014-01-01
a new Runge–Kutta type second order search direction suitable for the general nonsymmetric conic problem. Moreover, quasi-Newton updating is used to reduce the number of factorizations needed, implemented so that data sparsity can still be exploited. Extensive and promising computational results...
Uilhoorn, F. E.
2016-10-01
In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.
DEFF Research Database (Denmark)
Awasthi, Abhishek; Venkitusamy, Karthikeyan; Padmanaban, Sanjeevikumar
2017-01-01
, a hybrid algorithm based on genetic algorithm and improved version of conventional particle swarm optimization is utilized for finding optimal placement of charging station in the Allahabad distribution system. The particle swarm optimization algorithm re-optimizes the received sub-optimal solution (site...... and the size of the station) which leads to an improvement in the algorithm functionality and enhances quality of solution. The genetic algorithm and improved version of conventional particle swarm optimization algorithm will also be compared with a conventional genetic algorithm and particle swarm...... optimization. Through simulation studies on a real time system of Allahabad city, the superior performance of the aforementioned technique with respect to genetic algorithm and particle swarm optimization in terms of improvement in voltage profile and quality....
Artificial bee colony algorithm variants on constrained optimization
National Research Council Canada - National Science Library
Bahriye Akay; Dervis Karaboga
2017-01-01
.... In this study, the performance analysis of artificial bee colony algorithm (ABC), one of the intelligent optimization techniques, is examined on constrained problems and the effect of some modifications on the performance of the algorithm is examined...
Genetic algorithm and particle swarm optimization combined with Powell method
Bento, David; Pinho, Diana; Pereira, Ana I.; Lima, Rui
2013-10-01
In recent years, the population algorithms are becoming increasingly robust and easy to use, based on Darwin's Theory of Evolution, perform a search for the best solution around a population that will progress according to several generations. This paper present variants of hybrid genetic algorithm - Genetic Algorithm and a bio-inspired hybrid algorithm - Particle Swarm Optimization, both combined with the local method - Powell Method. The developed methods were tested with twelve test functions from unconstrained optimization context.
Practice Utilization of Algorithms for Analog Filter Group Delay Optimization
Directory of Open Access Journals (Sweden)
K. Hajek
2007-04-01
Full Text Available This contribution deals with an application of three different algorithms which optimize a group delay of analog filters. One of them is a part of the professional circuit simulator Micro Cap 7 and the others two original algorithms are developed in the MATLAB environment. An all-pass network is used to optimize the group delay of an arbitrary analog filter. Introduced algorithms look for an optimal order and optimal coefficients of an all-pass network transfer function. Theoretical foundations are introduced and all algorithms are tested using the optimization of testing analog filter. The optimization is always run three times because the second, third and fourth-order all-pass network is used. An equalization of the original group delay is a main objective of these optimizations. All outputs of all algorithms are critically evaluated and also described.
Optimal Pid Controller Design Using Adaptive Vurpso Algorithm
Zirkohi, Majid Moradi
2015-04-01
The purpose of this paper is to improve theVelocity Update Relaxation Particle Swarm Optimization algorithm (VURPSO). The improved algorithm is called Adaptive VURPSO (AVURPSO) algorithm. Then, an optimal design of a Proportional-Integral-Derivative (PID) controller is obtained using the AVURPSO algorithm. An adaptive momentum factor is used to regulate a trade-off between the global and the local exploration abilities in the proposed algorithm. This operation helps the system to reach the optimal solution quickly and saves the computation time. Comparisons on the optimal PID controller design confirm the superiority of AVURPSO algorithm to the optimization algorithms mentioned in this paper namely the VURPSO algorithm, the Ant Colony algorithm, and the conventional approach. Comparisons on the speed of convergence confirm that the proposed algorithm has a faster convergence in a less computation time to yield a global optimum value. The proposed AVURPSO can be used in the diverse areas of optimization problems such as industrial planning, resource allocation, scheduling, decision making, pattern recognition and machine learning. The proposed AVURPSO algorithm is efficiently used to design an optimal PID controller.
Adaptive Central Force Optimization Algorithm Based on the Stability Analysis
Directory of Open Access Journals (Sweden)
Weiyi Qian
2015-01-01
Full Text Available In order to enhance the convergence capability of the central force optimization (CFO algorithm, an adaptive central force optimization (ACFO algorithm is presented by introducing an adaptive weight and defining an adaptive gravitational constant. The adaptive weight and gravitational constant are selected based on the stability theory of discrete time-varying dynamic systems. The convergence capability of ACFO algorithm is compared with the other improved CFO algorithm and evolutionary-based algorithm using 23 unimodal and multimodal benchmark functions. Experiments results show that ACFO substantially enhances the performance of CFO in terms of global optimality and solution accuracy.
Improved hybrid optimization algorithm for 3D protein structure prediction.
Zhou, Changjun; Hou, Caixia; Wei, Xiaopeng; Zhang, Qiang
2014-07-01
A new improved hybrid optimization algorithm - PGATS algorithm, which is based on toy off-lattice model, is presented for dealing with three-dimensional protein structure prediction problems. The algorithm combines the particle swarm optimization (PSO), genetic algorithm (GA), and tabu search (TS) algorithms. Otherwise, we also take some different improved strategies. The factor of stochastic disturbance is joined in the particle swarm optimization to improve the search ability; the operations of crossover and mutation that are in the genetic algorithm are changed to a kind of random liner method; at last tabu search algorithm is improved by appending a mutation operator. Through the combination of a variety of strategies and algorithms, the protein structure prediction (PSP) in a 3D off-lattice model is achieved. The PSP problem is an NP-hard problem, but the problem can be attributed to a global optimization problem of multi-extremum and multi-parameters. This is the theoretical principle of the hybrid optimization algorithm that is proposed in this paper. The algorithm combines local search and global search, which overcomes the shortcoming of a single algorithm, giving full play to the advantage of each algorithm. In the current universal standard sequences, Fibonacci sequences and real protein sequences are certified. Experiments show that the proposed new method outperforms single algorithms on the accuracy of calculating the protein sequence energy value, which is proved to be an effective way to predict the structure of proteins.
Accelerating ATM Optimization Algorithms Using High Performance Computing Hardware Project
National Aeronautics and Space Administration — NASA is developing algorithms and methodologies for efficient air-traffic management (ATM). Several researchers have adopted an optimization framework for solving...
An Effective Hybrid Optimization Algorithm for Capacitated Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.
Accelerating ATM Optimization Algorithms Using High Performance Computing Hardware Project
National Aeronautics and Space Administration — NASA is developing algorithms and methodologies for efficient air-traffic management. Several researchers have adopted an optimization framework for solving problems...
de Graaf, Joost; Filion, Laura; Marechal, Matthieu; van Roij, René; Dijkstra, Marjolein
2012-12-01
In this paper, we describe the way to set up the floppy-box Monte Carlo (FBMC) method [L. Filion, M. Marechal, B. van Oorschot, D. Pelt, F. Smallenburg, and M. Dijkstra, Phys. Rev. Lett. 103, 188302 (2009), 10.1103/PhysRevLett.103.188302] to predict crystal-structure candidates for colloidal particles. The algorithm is explained in detail to ensure that it can be straightforwardly implemented on the basis of this text. The handling of hard-particle interactions in the FBMC algorithm is given special attention, as (soft) short-range and semi-long-range interactions can be treated in an analogous way. We also discuss two types of algorithms for checking for overlaps between polyhedra, the method of separating axes and a triangular-tessellation based technique. These can be combined with the FBMC method to enable crystal-structure prediction for systems composed of highly shape-anisotropic particles. Moreover, we present the results for the dense crystal structures predicted using the FBMC method for 159 (non)convex faceted particles, on which the findings in [J. de Graaf, R. van Roij, and M. Dijkstra, Phys. Rev. Lett. 107, 155501 (2011), 10.1103/PhysRevLett.107.155501] were based. Finally, we comment on the process of crystal-structure prediction itself and the choices that can be made in these simulations.
Improved symbiotic organisms search algorithm for solving unconstrained function optimization
Directory of Open Access Journals (Sweden)
Sukanta Nama
2016-09-01
Full Text Available Recently, Symbiotic Organisms Search (SOS algorithm is being used for solving complex problems of optimization. This paper proposes an Improved Symbiotic Organisms Search (I-SOS algorithm for solving different complex unconstrained global optimization problems. In the improved algorithm, a random weighted reflective parameter and predation phase are suggested to enhance the performance of the algorithm. The performances of this algorithm are compared with the other state-of-the-art algorithms. The parametric study of the common control parameter has also been performed.
Composite multiobjective optimization beamforming based on genetic algorithms
Institute of Scientific and Technical Information of China (English)
Shi Jing; Meng Weixiao; Zhang Naitong; Wang Zheng
2006-01-01
All thc parameters of beamforming are usually optimized simultaneously in implementing the optimization of antenna array pattern with multiple objectives and parameters by genetic algorithms (GAs).Firstly, this paper analyzes the performance of fitness functions of previous algorithms. It shows that original algorithms make the fitness functions too complex leading to large amount of calculation, and also the selection of the weight of parameters very sensitive due to many parameters optimized simultaneously. This paper proposes a kind of algorithm of composite beamforming, which detaches the antenna array into two parts corresponding to optimization of different objective parameters respectively. New algorithm substitutes the previous complex fitness function with two simpler functions. Both theoretical analysis and simulation results show that this method simplifies the selection of weighting parameters and reduces the complexity of calculation. Furthermore, the algorithm has better performance in lowering side lobe and interferences in comparison with conventional algorithms of beamforming in the case of slightly widening the main lobe.
Function Optimization Based on Quantum Genetic Algorithm
Ying Sun; Yuesheng Gu; Hegen Xiong
2013-01-01
Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on.It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed ,which is called variable-boundary-coded quantum genetic algorithm (vbQGA) in which qubit chromosomes are collapsed into variableboundary- coded chromosomes instead of binary-coded chromosomes. Therefore much shorter chromosome strings can be gained.The m...
2012-08-01
number of practical problems can be formulated in the form of (1.1) such as convex problems: (group) Lasso [64,74] or the basis pursuit ( denoising ) [15...K) ) ) 1 ν ≤ CN− 1−θ 2θ−1 , for sufficiently large C and N . This completes the proof. 21 REFERENCES [1] M. Aharon, M. Elad, and A. Bruckstein, K- SVD
Algorithm for correcting optimization convergence errors in Eclipse.
Zacarias, Albert S; Mills, Michael D
2009-10-14
IMRT plans generated in Eclipse use a fast algorithm to evaluate dose for optimization and a more accurate algorithm for a final dose calculation, the Analytical Anisotropic Algorithm. The use of a fast optimization algorithm introduces optimization convergence errors into an IMRT plan. Eclipse has a feature where optimization may be performed on top of an existing base plan. This feature allows for the possibility of arriving at a recursive solution to optimization that relies on the accuracy of the final dose calculation algorithm and not the optimizer algorithm. When an IMRT plan is used as a base plan for a second optimization, the second optimization can compensate for heterogeneity and modulator errors in the original base plan. Plans with the same field arrangement as the initial base plan may be added together by adding the initial plan optimal fluence to the dose correcting plan optimal fluence.A simple procedure to correct for optimization errors is presented that may be implemented in the Eclipse treatment planning system, along with an Excel spreadsheet to add optimized fluence maps together.
Algorithmic Aspects of Several Data Transfer Service Optimization Problems
Andreica, Mugurel Ionut; Ionescu, Florin; Andreica, Cristina Teodora
2009-01-01
Optimized data transfer services are highly demanded nowadays, due to the large amounts of data which are frequently being produced and accessed. In this paper we consider several data transfer service optimization problems (optimal server location in path networks, optimal packet sequencing and minimum makespan packet scheduling), for which we provide novel algorithmic solutions.
Optimization of machining processes using pattern search algorithm
Miloš Madić; Miroslav Radovanović
2014-01-01
Optimization of machining processes not only increases machining efficiency and economics, but also the end product quality. In recent years, among the traditional optimization methods, stochastic direct search optimization methods such as meta-heuristic algorithms are being increasingly applied for solving machining optimization problems. Their ability to deal with complex, multi-dimensional and ill-behaved optimization problems made them the preferred optimization tool by most researchers a...
Automatic Circuit Design and Optimization Using Modified PSO Algorithm
Directory of Open Access Journals (Sweden)
Subhash Patel
2016-04-01
Full Text Available In this work, we have proposed modified PSO algorithm based optimizer for automatic circuit design. The performance of the modified PSO algorithm is compared with two other evolutionary algorithms namely ABC algorithm and standard PSO algorithm by designing two stage CMOS operational amplifier and bulk driven OTA in 130nm technology. The results show the robustness of the proposed algorithm. With modified PSO algorithm, the average design error for two stage op-amp is only 0.054% in contrast to 3.04% for standard PSO algorithm and 5.45% for ABC algorithm. For bulk driven OTA, average design error is 1.32% with MPSO compared to 4.70% with ABC algorithm and 5.63% with standard PSO algorithm.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
The set of all surface tensors of a convex body K (Minkowski tensors derived from the surface area measure of K) determine K up to translation, and hereby, the surface tensors of K contain all information on the shape of K. Here, shape means the equivalence class of all convex bodies...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available....... The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...
Directory of Open Access Journals (Sweden)
Insub Choi
2016-12-01
Full Text Available Existing vision-based displacement sensors (VDSs extract displacement data through changes in the movement of a target that is identified within the image using natural or artificial structure markers. A target-less vision-based displacement sensor (hereafter called “TVDS” is proposed. It can extract displacement data without targets, which then serve as feature points in the image of the structure. The TVDS can extract and track the feature points without the target in the image through image convex hull optimization, which is done to adjust the threshold values and to optimize them so that they can have the same convex hull in every image frame and so that the center of the convex hull is the feature point. In addition, the pixel coordinates of the feature point can be converted to physical coordinates through a scaling factor map calculated based on the distance, angle, and focal length between the camera and target. The accuracy of the proposed scaling factor map was verified through an experiment in which the diameter of a circular marker was estimated. A white-noise excitation test was conducted, and the reliability of the displacement data obtained from the TVDS was analyzed by comparing the displacement data of the structure measured with a laser displacement sensor (LDS. The dynamic characteristics of the structure, such as the mode shape and natural frequency, were extracted using the obtained displacement data, and were compared with the numerical analysis results. TVDS yielded highly reliable displacement data and highly accurate dynamic characteristics, such as the natural frequency and mode shape of the structure. As the proposed TVDS can easily extract the displacement data even without artificial or natural markers, it has the advantage of extracting displacement data from any portion of the structure in the image.
Choi, Insub; Kim, JunHee; Kim, Donghyun
2016-12-08
Existing vision-based displacement sensors (VDSs) extract displacement data through changes in the movement of a target that is identified within the image using natural or artificial structure markers. A target-less vision-based displacement sensor (hereafter called "TVDS") is proposed. It can extract displacement data without targets, which then serve as feature points in the image of the structure. The TVDS can extract and track the feature points without the target in the image through image convex hull optimization, which is done to adjust the threshold values and to optimize them so that they can have the same convex hull in every image frame and so that the center of the convex hull is the feature point. In addition, the pixel coordinates of the feature point can be converted to physical coordinates through a scaling factor map calculated based on the distance, angle, and focal length between the camera and target. The accuracy of the proposed scaling factor map was verified through an experiment in which the diameter of a circular marker was estimated. A white-noise excitation test was conducted, and the reliability of the displacement data obtained from the TVDS was analyzed by comparing the displacement data of the structure measured with a laser displacement sensor (LDS). The dynamic characteristics of the structure, such as the mode shape and natural frequency, were extracted using the obtained displacement data, and were compared with the numerical analysis results. TVDS yielded highly reliable displacement data and highly accurate dynamic characteristics, such as the natural frequency and mode shape of the structure. As the proposed TVDS can easily extract the displacement data even without artificial or natural markers, it has the advantage of extracting displacement data from any portion of the structure in the image.
Application of Bees Algorithm in Multi-Join Query Optimization
Directory of Open Access Journals (Sweden)
Mohammad Alamery
2012-09-01
Full Text Available Multi-join query optimization is an important technique for designing and implementing database management system. It is a crucial factor that affects the capability of database. This paper proposes a Bees algorithm that simulates the foraging behavior of honey bee swarm to solve Multi-join query optimization problem. The performance of the Bees algorithm and Ant Colony Optimization algorithm are compared with respect to computational time and the simulation result indicates that Bees algorithm is more effective and efficient.
General Object-oriented Framework for Iterative Optimization Algorithms
Mornar, Vedran; Vanjak, Zvonimir
2001-01-01
It is usually impossible to exactly solve the hard optimization problems. One is thus directed to iterative algorithms. In implementation of these iterative algorithms, some common characteristics can be observed, which can be generalized in an object-oriented framework. This can significantly reduce the time needed for implementation of an iterative algorithm.
Biology-Derived Algorithms in Engineering Optimization
Yang, Xin-She
2010-01-01
Biology-derived algorithms are an important part of computational sciences, which are essential to many scientific disciplines and engineering applications. Many computational methods are derived from or based on the analogy to natural evolution and biological activities, and these biologically inspired computations include genetic algorithms, neural networks, cellular automata, and other algorithms.
Hybrid Algorithm for Optimal Load Sharing in Grid Computing
Directory of Open Access Journals (Sweden)
A. Krishnan
2012-01-01
Full Text Available Problem statement: Grid Computing is the fast growing industry, which shares the resources in the organization in an effective manner. Resource sharing requires more optimized algorithmic structure, otherwise the waiting time and response time are increased and the resource utilization is reduced. Approach: In order to avoid such reduction in the performances of the grid system, an optimal resource sharing algorithm is required. In recent days, many load sharing technique are proposed, which provides feasibility but there are many critical issues are still present in these algorithms. Results: In this study a hybrid algorithm for optimization of load sharing is proposed. The hybrid algorithm contains two components which are Hash Table (HT and Distributed Hash Table (DHT. Conclusion: The results of the proposed study show that the hybrid algorithm will optimize the task than existing systems.
Teaching learning based optimization algorithm and its engineering applications
Rao, R Venkata
2016-01-01
Describing a new optimization algorithm, the “Teaching-Learning-Based Optimization (TLBO),” in a clear and lucid style, this book maximizes reader insights into how the TLBO algorithm can be used to solve continuous and discrete optimization problems involving single or multiple objectives. As the algorithm operates on the principle of teaching and learning, where teachers influence the quality of learners’ results, the elitist version of TLBO algorithm (ETLBO) is described along with applications of the TLBO algorithm in the fields of electrical engineering, mechanical design, thermal engineering, manufacturing engineering, civil engineering, structural engineering, computer engineering, electronics engineering, physics and biotechnology. The book offers a valuable resource for scientists, engineers and practitioners involved in the development and usage of advanced optimization algorithms.
A FUZZY CLOPE ALGORITHM AND ITS OPTIMAL PARAMETER CHOICE
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Among the available clustering algorithms in data mining, the CLOPE algorithm attracts much more attention with its high speed and good performance. However, the proper choice of some parameters in the CLOPE algorithm directly affects the validity of the clustering results, which is still an open issue. For this purpose, this paper proposes a fuzzy CLOPE algorithm, and presents a method for the optimal parameter choice by defining a modified partition fuzzy degree as a clustering validity function. The experimental results with real data set illustrate the effectiveness of the proposed fuzzy CLOPE algorithm and optimal parameter choice method based on the modified partition fuzzy degree.
A NEW FAMILY OF TRUST REGION ALGORITHMS FOR UNCONSTRAINED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Yuhong Dai; Dachuan Xu
2003-01-01
Trust region (TR) algorithms are a class of recently developed algorithms for nonlinear optimization. A new family of TR algorithms for unconstrained optimization, which is the extension of the usual TR method, is presented in this paper. When the objective function is bounded below and continuously. differentiable, and the norm of the Hesse approximations increases at most linearly with the iteration number, we prove the global convergence of the algorithms. Limited numerical results are reported, which indicate that our new TR algorithm is competitive.
Particle swarm optimization - Genetic algorithm (PSOGA) on linear transportation problem
Rahmalia, Dinita
2017-08-01
Linear Transportation Problem (LTP) is the case of constrained optimization where we want to minimize cost subject to the balance of the number of supply and the number of demand. The exact method such as northwest corner, vogel, russel, minimal cost have been applied at approaching optimal solution. In this paper, we use heurisitic like Particle Swarm Optimization (PSO) for solving linear transportation problem at any size of decision variable. In addition, we combine mutation operator of Genetic Algorithm (GA) at PSO to improve optimal solution. This method is called Particle Swarm Optimization - Genetic Algorithm (PSOGA). The simulations show that PSOGA can improve optimal solution resulted by PSO.
An optimal scheduling algorithm based on task duplication
Institute of Scientific and Technical Information of China (English)
Ruan Youlin; Liu Gan; Zhu Guangxi; Lu Xiaofeng
2005-01-01
When the communication time is relatively shorter than the computation time for every task, the task duplication based scheduling (TDS) algorithm proposed by Darbha and Agrawal generates an optimal schedule. Park and Choe also proposed an extended TDS algorithm whose optimality condition is less restricted than that of TDS algorithm, but the condition is very complex and is difficult to satisfy when the number of tasks is large. An efficient algorithm is proposed whose optimality condition is less restricted and simpler than both of the algorithms, and the schedule length is also shorter than both of the algorithms. The time complexity of the proposed algorithm is O ( v2 ), where v represents the number of tasks.
Earth Observation Satellites Scheduling Based on Decomposition Optimization Algorithm
Directory of Open Access Journals (Sweden)
Feng Yao
2010-11-01
Full Text Available A decomposition-based optimization algorithm was proposed for solving Earth Observation Satellites scheduling problem. The problem was decomposed into task assignment main problem and single satellite scheduling sub-problem. In task assignment phase, the tasks were allocated to the satellites, and each satellite would schedule the task respectively in single satellite scheduling phase. We adopted an adaptive ant colony optimization algorithm to search the optimal task assignment scheme. Adaptive parameter adjusting strategy and pheromone trail smoothing strategy were introduced to balance the exploration and the exploitation of search process. A heuristic algorithm and a very fast simulated annealing algorithm were proposed to solve the single satellite scheduling problem. The task assignment scheme was valued by integrating the observation scheduling result of multiple satellites. The result was responded to the ant colony optimization algorithm, which can guide the search process of ant colony optimization. Computation results showed that the approach was effective to the satellites observation scheduling problem.
Transonic Wing Shape Optimization Using a Genetic Algorithm
Holst, Terry L.; Pulliam, Thomas H.; Kwak, Dochan (Technical Monitor)
2002-01-01
A method for aerodynamic shape optimization based on a genetic algorithm approach is demonstrated. The algorithm is coupled with a transonic full potential flow solver and is used to optimize the flow about transonic wings including multi-objective solutions that lead to the generation of pareto fronts. The results indicate that the genetic algorithm is easy to implement, flexible in application and extremely reliable.
A novel hybrid algorithm of GSA with Kepler algorithm for numerical optimization
Directory of Open Access Journals (Sweden)
Soroor Sarafrazi
2015-07-01
Full Text Available It is now well recognized that pure algorithms can be promisingly improved by hybridization with other techniques. One of the relatively new metaheuristic algorithms is Gravitational Search Algorithm (GSA which is based on the Newton laws. In this paper, to enhance the performance of GSA, a novel algorithm called “Kepler”, inspired by the astrophysics, is introduced. The Kepler algorithm is based on the principle of the first Kepler law. The hybridization of GSA and Kepler algorithm is an efficient approach to provide much stronger specialization in intensification and/or diversification. The performance of GSA–Kepler is evaluated by applying it to 14 benchmark functions with 20–1000 dimensions and the optimal approximation of linear system as a practical optimization problem. The results obtained reveal that the proposed hybrid algorithm is robust enough to optimize the benchmark functions and practical optimization problems.
The genealogy of convex solids
Domokos, Gabor; Szabó, Timea
2012-01-01
The shape of homogeneous, smooth convex bodies as described by the Euclidean distance from the center of gravity represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale functions on S^2 by exhausting all combinatorial possibilities: every 2-colored quadrangulation of the sphere is isomorphic to a suitably represented Morse-Smale complex associated with a function in M_C (and vice versa). We prove our claim by an inductive algorithm, starting from the path graph P_2 and generating convex bodies corresponding to quadrangulations with increasing number of vertices by performing each combinatorially possible vertex splitting by a convexity- preserving local manipulation of the surface. Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist, this algorithm not only proves our claim but also defines a hierarchical order among convex solids and general- izes the known classification scheme in [35], ...
Novel Approach to Nonlinear PID Parameter Optimization Using Ant Colony Optimization Algorithm
Institute of Scientific and Technical Information of China (English)
Duan Hai-bin; Wang Dao-bo; Yu Xiu-fen
2006-01-01
This paper presents an application of an Ant Colony Optimization (ACO) algorithm to optimize the parameters in the design of a type of nonlinear PID controller. The ACO algorithm is a novel heuristic bionic algorithm, which is based on the behaviour of real ants in nature searching for food. In order to optimize the parameters of the nonlinear PID controller using ACO algorithm,an objective function based on position tracing error was constructed, and elitist strategy was adopted in the improved ACO algorithm. Detailed simulation steps are presented. This nonlinear PID controller using the ACO algorithm has high precision of control and quick response.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Institute of Scientific and Technical Information of China (English)
李鑫; 季萍; 张明望
2015-01-01
In this paper, we propose a new full-Newton step primal-dual interior-point algorithm for solving convex quadratic semi-definite programming. By establishing and using new technical results, we show that the iteration complexity of algorithm asO(nlogn)ε is as good as the currently best iteration complexity for small-update interior-point algorithms of convex quadratic semi-definite programming.%对凸二次半定规划提出了一种新的全-Newton步原始-对偶内点算法.通过建立和应用一些新的技术性结果,证明了算法的迭代复杂性为O( n log n )ε ,这与目前凸二次半定规划的小步校正内点算法最好的迭代复杂性一致.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A novel method of global optimal path planning for mobile robot was proposed based on the improved Dijkstra algorithm and ant system algorithm. This method includes three steps: the first step is adopting the MAKLINK graph theory to establish the free space model of the mobile robot, the second step is adopting the improved Dijkstra algorithm to find out a sub-optimal collision-free path, and the third step is using the ant system algorithm to adjust and optimize the location of the sub-optimal path so as to generate the global optimal path for the mobile robot. The computer simulation experiment was carried out and the results show that this method is correct and effective. The comparison of the results confirms that the proposed method is better than the hybrid genetic algorithm in the global optimal path planning.
Resource Allocation in Public Cluster with Extended Optimization Algorithm
Akbar, Z.; Handoko, L. T.
2007-01-01
We introduce an optimization algorithm for resource allocation in the LIPI Public Cluster to optimize its usage according to incoming requests from users. The tool is an extended and modified genetic algorithm developed to match specific natures of public cluster. We present a detail analysis of optimization, and compare the results with the exact calculation. We show that it would be very useful and could realize an automatic decision making system for public clusters.
Genetic-Algorithm Tool For Search And Optimization
Wang, Lui; Bayer, Steven
1995-01-01
SPLICER computer program used to solve search and optimization problems. Genetic algorithms adaptive search procedures (i.e., problem-solving methods) based loosely on processes of natural selection and Darwinian "survival of fittest." Algorithms apply genetically inspired operators to populations of potential solutions in iterative fashion, creating new populations while searching for optimal or nearly optimal solution to problem at hand. Written in Think C.
TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization
2016-11-28
magnitude in computational experiments on portfolio optimization problems. The research on this topic has been published as [CG15a], where details can...AFRL-AFOSR-UK-TR-2017-0001 TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization Horst Hamacher Technische Universität...To) 15 May 2013 to 12 May 2016 4. TITLE AND SUBTITLE TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization 5a. CONTRACT
SNMP Based Network Optimization Technique Using Genetic Algorithms
Directory of Open Access Journals (Sweden)
M. Mohamed Surputheen
2012-03-01
Full Text Available Genetic Algorithms (GAs has innumerable applications through the optimization techniques and network optimization is one of them. SNMP (Simple Network Management Protocol is used as the basic network protocol for monitoring the network activities health of the systems. This paper deals with adding Intelligence to the various aspects of SNMP by adding optimization techniques derived out of genetic algorithms, which enhances the performance of SNMP processes like routing.
Zheng, Wei; Friedman, Alan M; Bailey-Kellogg, Chris
2009-08-01
In engineering protein variants by constructing and screening combinatorial libraries of chimeric proteins, two complementary and competing goals are desired: the new proteins must be similar enough to the evolutionarily-selected wild-type proteins to be stably folded, and they must be different enough to display functional variation. We present here the first method, Staversity, to simultaneously optimize stability and diversity in selecting sets of breakpoint locations for site-directed recombination. Our goal is to uncover all "undominated" breakpoint sets, for which no other breakpoint set is better in both factors. Our first algorithm finds the undominated sets serving as the vertices of the lower envelope of the two-dimensional (stability and diversity) convex hull containing all possible breakpoint sets. Our second algorithm identifies additional breakpoint sets in the concavities that are either undominated or dominated only by undiscovered breakpoint sets within a distance bound computed by the algorithm. Both algorithms are efficient, requiring only time polynomial in the numbers of residues and breakpoints, while characterizing a space defined by an exponential number of possible breakpoint sets. We applied Staversity to identify 2-10 breakpoint plans for different sets of parent proteins taken from the purE family, as well as for parent proteins TEM-1 and PSE-4 from the beta-lactamase family. The average normalized distance between our plans and the lower bound for optimal plans is around 2%. Our plans dominate most (60-90% on average for each parent set) of the plans found by other possible approaches, random sampling or explicit optimization for stability with implicit optimization for diversity. The identified breakpoint sets provide a compact representation of good plans, enabling a protein engineer to understand and account for the trade-offs between two key considerations in combinatorial chimeragenesis.
An ECN-based Optimal Flow Control Algorithm for the Internet
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
According to the Wide Area Network model, we formulate Internet flow control as a constrained convex programming problem, where the objective is to maximize the total utility of all sources over their transmission rates. Based on this formulation, flow control can be converted to a normal unconstrained optimization problem through the barrier function method, so that it can be solved by means of a gradient projection algorithm with properly rate iterations. We prove that the algorithm converges to the global optimal point, which is also a stable proportional fair rate allocation point, provided that the step size is properly chosen. The main difficulty facing the realization of iteration algorithm is the distributed computation of congestion measure. Fortunately, Explicit Congestion Notification (ECN) is likely to be used to improve the performance of TCP in the near future. By using ECN, it is possible to realize the iteration algorithm in IP networks. Our algorithm is divided into two parts, algorithms in the router and in the source. The router marks the ECN bit with a probability that varies as its buffer occupancy varies, so that the congestion measure of links can be communicated to the source when the marked ECN bits are reflected back from its destination. Source rates are then updated by all sessions according to the received congestion measure. The main advantage of our scheme is its fast convergence ability and robustness; it can also provide the network with zero packet loss by properly choosing the queue threshold and provide differentiated service to users by applying different utility functions.
Directory of Open Access Journals (Sweden)
Luís F. P. Silva
2014-01-01
Full Text Available A convex condition in terms of linear matrix inequalities (LMIs is developed for the synthesis of stabilizing fuzzy state feedback controllers for nonlinear discrete-time systems with time-varying delays. A Takagi-Sugeno (T-S fuzzy model is used to represent exactly the nonlinear system in a restricted domain of the state space, called region of validity. The proposed stabilization condition is based on a Lyapunov-Krasovskii (L-K function and it takes into account the region of validity to determine a set of initial conditions for which the actual closed-loop system trajectories are asymptotically stable and do not evolve outside the region of validity. This set of allowable initial conditions is determined from the level set associated to a fuzzy L-K function as a Cartesian product of two subsets: one characterizing the set of states at the initial instant and another for the delayed state sequence necessary to characterize the initial conditions. Finally, we propose a convex programming problem to design a fuzzy controller that maximizes the set of initial conditions taking into account the shape of the region of validity of the T-S fuzzy model. Numerical simulations are given to illustrate this proposal.
Energy Technology Data Exchange (ETDEWEB)
Mehrotra, Sanjay [Northwestern Univ., Evanston, IL (United States)
2016-09-07
The support from this grant resulted in seven published papers and a technical report. Two papers are published in SIAM J. on Optimization [87, 88]; two papers are published in IEEE Transactions on Power Systems [77, 78]; one paper is published in Smart Grid [79]; one paper is published in Computational Optimization and Applications [44] and one in INFORMS J. on Computing [67]). The works in [44, 67, 87, 88] were funded primarily by this DOE grant. The applied papers in [77, 78, 79] were also supported through a subcontract from the Argonne National Lab. We start by presenting our main research results on the scenario generation problem in Sections 1–2. We present our algorithmic results on interior point methods for convex optimization problems in Section 3. We describe a new ‘central’ cutting surface algorithm developed for solving large scale convex programming problems (as is the case with our proposed research) with semi-infinite number of constraints in Section 4. In Sections 5–6 we present our work on two application problems of interest to DOE.
A danger-theory-based immune network optimization algorithm.
Zhang, Ruirui; Li, Tao; Xiao, Xin; Shi, Yuanquan
2013-01-01
Existing artificial immune optimization algorithms reflect a number of shortcomings, such as premature convergence and poor local search ability. This paper proposes a danger-theory-based immune network optimization algorithm, named dt-aiNet. The danger theory emphasizes that danger signals generated from changes of environments will guide different levels of immune responses, and the areas around danger signals are called danger zones. By defining the danger zone to calculate danger signals for each antibody, the algorithm adjusts antibodies' concentrations through its own danger signals and then triggers immune responses of self-regulation. So the population diversity can be maintained. Experimental results show that the algorithm has more advantages in the solution quality and diversity of the population. Compared with influential optimization algorithms, CLONALG, opt-aiNet, and dopt-aiNet, the algorithm has smaller error values and higher success rates and can find solutions to meet the accuracies within the specified function evaluation times.
A New Algorithm for Generalized Optimal Discriminant Vectors
Institute of Scientific and Technical Information of China (English)
吴小俊; 杨静宇; 王士同; 郭跃飞; 曹奇英
2002-01-01
A study has been conducted on the algorithm of solving generalized optimal set of discriminant vectors in this paper. This paper proposes an analytical algorithm of solving generalized optimal set of discriminant vectors theoretically for the first time. A lot of computation time can be saved because all the generalized optimal sets of discriminant vectors can be obtained simultaneously with the proposed algorithm, while it needs no iterative operations. The proposed algorithm can yield a much higher recognition rate. Furthermore,the proposed algorithm overcomes the shortcomings of conventional human face recognition algorithms which were effective for small sample size problems only. These statements are supported by the numerical simulation experiments on facial database of ORL.
Decoherence in optimized quantum random-walk search algorithm
Zhang, Yu-Chao; Bao, Wan-Su; Wang, Xiang; Fu, Xiang-Qun
2015-08-01
This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative. Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).
A Multiobjective Optimization Algorithm Based on Discrete Bacterial Colony Chemotaxis
Directory of Open Access Journals (Sweden)
Zhigang Lu
2014-01-01
Full Text Available Bacterial colony chemotaxis algorithm was originally developed for optimal problem with continuous space. In this paper the discrete bacterial colony chemotaxis (DBCC algorithm is developed to solve multiobjective optimization problems. The basic DBCC algorithm has the disadvantage of being trapped into the local minimum. Therefore, some improvements are adopted in the new algorithm, such as adding chaos transfer mechanism when the bacterium choose their next locations and the crowding distance operation to maintain the population diversity in the Pareto Front. The definition of chaos transfer mechanism is used to retain the elite solution produced during the operation, and the definition of crowding distance is used to guide the bacteria for determinate variation, thus enabling the algorithm obtain well-distributed solution in the Pareto optimal set. The convergence properties of the DBCC strategy are tested on some test functions. At last, some numerical results are given to demonstrate the effectiveness of the results obtained by the new algorithm.
Analog Circuit Design Optimization Based on Evolutionary Algorithms
Directory of Open Access Journals (Sweden)
Mansour Barari
2014-01-01
Full Text Available This paper investigates an evolutionary-based designing system for automated sizing of analog integrated circuits (ICs. Two evolutionary algorithms, genetic algorithm and PSO (Parswal particle swarm optimization algorithm, are proposed to design analog ICs with practical user-defined specifications. On the basis of the combination of HSPICE and MATLAB, the system links circuit performances, evaluated through specific electrical simulation, to the optimization system in the MATLAB environment, for the selected topology. The system has been tested by typical and hard-to-design cases, such as complex analog blocks with stringent design requirements. The results show that the design specifications are closely met. Comparisons with available methods like genetic algorithms show that the proposed algorithm offers important advantages in terms of optimization quality and robustness. Moreover, the algorithm is shown to be efficient.
MAKHA—A New Hybrid Swarm Intelligence Global Optimization Algorithm
Directory of Open Access Journals (Sweden)
Ahmed M.E. Khalil
2015-06-01
Full Text Available The search for efficient and reliable bio-inspired optimization methods continues to be an active topic of research due to the wide application of the developed methods. In this study, we developed a reliable and efficient optimization method via the hybridization of two bio-inspired swarm intelligence optimization algorithms, namely, the Monkey Algorithm (MA and the Krill Herd Algorithm (KHA. The hybridization made use of the efficient steps in each of the two original algorithms and provided a better balance between the exploration/diversification steps and the exploitation/intensification steps. The new hybrid algorithm, MAKHA, was rigorously tested with 27 benchmark problems and its results were compared with the results of the two original algorithms. MAKHA proved to be considerably more reliable and more efficient in tested problems.
When do evolutionary algorithms optimize separable functions in parallel?
DEFF Research Database (Denmark)
Doerr, Benjamin; Sudholt, Dirk; Witt, Carsten
2013-01-01
is that evolutionary algorithms make progress on all subfunctions in parallel, so that optimizing a separable function does not take not much longer than optimizing the hardest subfunction-subfunctions are optimized "in parallel." We show that this is only partially true, already for the simple (1+1) evolutionary...... algorithm ((1+1) EA). For separable functions composed of k Boolean functions indeed the optimization time is the maximum optimization time of these functions times a small O(log k) overhead. More generally, for sums of weighted subfunctions that each attain non-negative integer values less than r = o(log1...
Optimal design of steel portal frames based on genetic algorithms
Institute of Scientific and Technical Information of China (English)
Yue CHEN; Kai HU
2008-01-01
As for the optimal design of steel portal frames, due to both the complexity of cross selections of beams and columns and the discreteness of design variables, it is difficult to obtain satisfactory results by traditional optimization. Based on a set of constraints of the Technical Specification for Light-weighted Steel Portal Frames of China, a genetic algorithm (GA) optimization program for portal frames, written in MATLAB code, was proposed in this paper. The graph user interface (GUI) is also developed for this optimal program, so that it can be used much more conveniently. Finally, some examples illustrate the effectiveness and efficiency of the genetic-algorithm-based optimal program.
Accuracy Analysis of Attitude Computation Based on Optimal Coning Algorithm
Directory of Open Access Journals (Sweden)
Jianfeng Chen
2012-09-01
Full Text Available To accurately evaluate the applicability of optimal coning algorithms, the direct influence of their periodic components on attitude accuracy is investigated. The true value of the change of the rotation vector is derived from the classical coning motion for analytic comparison. The analytic results show that the influence of periodic components is mostly dominant in two types of optimal coning algorithms. Considering that the errors of periodic components cannot be simply neglected, these algorithms are categorized with simplified forms. A variety of simulations are done under the classical coning motion. The numerical results are in good agreement with the analytic deductions. Considering their attitude accuracy, optimal coning algorithms of the 4-subinterval and 5-subinterval algorithms optimized with angular increments are not recommended for use for real application.
Accuracy Analysis of Attitude Computation Based on Optimal Coning Algorithm
Directory of Open Access Journals (Sweden)
Xiyuan Chen
2012-11-01
Full Text Available To accurately evaluate the applicability of optimal coning algorithms, the direct influence of their periodic components on attitude accuracy is investigated. The true value of the change of the rotation vector is derived from the classical coning motion for analytic comparison. The analytic results show that the influence of periodic components is mostly dominant in two types of optimal coning algorithms. Considering that the errors of periodic components cannot be simply neglected, these algorithms are categorized with simplified forms. A variety of simulations are done under the classical coning motion. The numerical results are in good agreement with the analytic deductions. Considering their attitude accuracy, optimal coning algorithms of the 4-subinterval and 5-subinterval algorithms optimized with angular increments are not recommended for use for real application.Defence Science Journal, 2012, 62(6, pp.361-368, DOI:http://dx.doi.org/10.14429/dsj.62.1430
Genetic Algorithms Applied to Multi-Objective Aerodynamic Shape Optimization
Holst, Terry L.
2005-01-01
A genetic algorithm approach suitable for solving multi-objective problems is described and evaluated using a series of aerodynamic shape optimization problems. Several new features including two variations of a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding Pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. A new masking array capability is included allowing any gene or gene subset to be eliminated as decision variables from the design space. This allows determination of the effect of a single gene or gene subset on the Pareto optimal solution. Results indicate that the genetic algorithm optimization approach is flexible in application and reliable. The binning selection algorithms generally provide Pareto front quality enhancements and moderate convergence efficiency improvements for most of the problems solved.
Optimization of Shallow Foundation Using Gravitational Search Algorithm
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Mohammad Khajehzadeh
2012-01-01
Full Text Available In this study an effective method for nonlinear constrained optimization of shallow foundation is presented. A newly developed heuristic global optimization algorithm called Gravitational Search Algorithm (GSA is introduced and applied for the optimization of foundation. The algorithm is classified as random search algorithm and does not require initial values and uses a random search instead of a gradient search, so derivative information is unnecessary. The optimization procedure controls all geotechnical and structural design constraints while reducing the overall cost of the foundation. To verify the efficiency of the proposed method, two design examples of spread footing are illustrated. To further validate the effectiveness and robustness of the GSA, these examples are solved using genetic algorithm. The results indicate that the proposed method could provide solutions of high quality, accuracy and efficiency for optimum design of foundation.
A convex optimization approach for path tracking of robot manipulators%基于凸规划的机械臂轨迹规划方法
Institute of Scientific and Technical Information of China (English)
赵建军; 魏毅; 朱登明; 夏时洪; 王兆其
2014-01-01
The problem of fast solving a robot manipulator’s path tracking with time constraints was studied, and a novel path tracking approach based on convex optimization was presented. To overcome the difficulties in dealing with the strong nonlinear dynamic constraints and time constraints in path tracking, the presented approach converts the nonlinear constraints into linear constraints by replacement of variables, and then adds new constraints to convert the original non convex optimization problem into a convex optimization problem, furthermore, converts it into a second order cone program (SOCP), and uses the optimization tools such as the SeDuMi to conduct the real time solving. This approach has several advantages. Firstly, SOCP problems can be solved in polynomial time by the interior point methods. Secondly, the convex optimization is globally stable and the solution is globally optimal. Besides, there is no need to provide initial values for the optimization. Thirdly, this approach has great flexibility and can be applied to the more complicated circumstances where some other types of constraints and objective functions can be taken into account, such as acceleration constraints, minimum energy objective function and minimum jerk objective function. The simulations on a six degrees of freedom robot manipulator show the better efficiency and effectiveness of the proposed approach.%研究了快速求解具有时间约束的机械臂轨迹规划问题，提出了一种基于凸规划的轨迹规划方法。该方法针对机械臂轨迹规划中动力学约束非线性强、时间约束不易处理的问题，首先通过变量替换，将非线性约束转化为线性约束，然后添加新的约束，将原始非凸优化问题转化为凸规划问题，在此基础上，将其写作二阶锥规划（SOCP）形式，使用SeDuMi等优化工具包近似实时求解。该方法具有以下优点：计算高效，凸规划问题能够在多项式时间内得到
Optimization Algorithms in School Scheduling Programs: Study, Analysis and Results
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Lina PUPEIKIENE
2009-04-01
Full Text Available To create good and optimal school schedule is very important and practical task. Currently in Lithuania schools are using two programs for making the school schedule at the moment. But none of these programs is very effective. Optimization Department of Lithuanian Institute of Mathematics and Informatics (IMI has created ``School schedule optimization program''. It has three optimization algorithms for making best school schedule. A user can choose not only few optimization options and get few optimal schedules, but some subjective and objectives parameters. The making of initial data file is advanced in this program. XML format is used for creating initial data file and getting all optimal results files. The purpose of this study is to analyze used optimization algorithms used in ``School schedule optimization program'' and to compare results with two most popular commercial school scheduling programs in Lithuania.
A Novel and Robust Evolution Algorithm for Optimizing Complicated Functions
Gao, Yifeng; Zhao, Ge
2011-01-01
In this paper, a novel mutation operator of differential evolution algorithm is proposed. A new algorithm called divergence differential evolution algorithm (DDEA) is developed by combining the new mutation operator with divergence operator and assimilation operator (divergence operator divides population, and, assimilation operator combines population), which can detect multiple solutions and robustness in noisy environment. The new algorithm is applied to optimize Michalewicz Function and to track changing of rain-induced-attenuation process. The results based on DDEA are compared with those based on Differential Evolution Algorithm (DEA). It shows that DDEA algorithm gets better results than DEA does in the same premise. The new algorithm is significant for optimizing and tracking the characteristics of MIMO (Multiple Input Multiple Output) channel at millimeter waves.
Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.
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Gonglin Yuan
Full Text Available Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1 βk ≥ 0 2 the search direction has the trust region property without the use of any line search method 3 the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.
Optimal Parallel Algorithm for the Knapsack Problem Without Memory Conflicts
Institute of Scientific and Technical Information of China (English)
Ken-Li Li; Ren-Fa Li; Qing-Hua Li
2004-01-01
The knapsack problem is well known to be NP-complete. Due to its importance in cryptosystem and in number theory, in the past two decades, much effort has been made in order to find techniques that could lead to practical algorithms with reasonable running time. This paper proposes a new parallel algorithm for the knapsack problem where the optimal merging algorithm is adopted. The proposed algorithm is based on an EREW-SIMD machine with shared memory. It is proved that the proposed algorithm is both optimal and the first without memory conflicts algorithm for the knapsack problem. The comparisons of algorithm performance show that it is an improvement over the past researches.
An Adaptive Unified Differential Evolution Algorithm for Global Optimization
Energy Technology Data Exchange (ETDEWEB)
Qiang, Ji; Mitchell, Chad
2014-11-03
In this paper, we propose a new adaptive unified differential evolution algorithm for single-objective global optimization. Instead of the multiple mutation strate- gies proposed in conventional differential evolution algorithms, this algorithm employs a single equation unifying multiple strategies into one expression. It has the virtue of mathematical simplicity and also provides users the flexibility for broader exploration of the space of mutation operators. By making all control parameters in the proposed algorithm self-adaptively evolve during the process of optimization, it frees the application users from the burden of choosing appro- priate control parameters and also improves the performance of the algorithm. In numerical tests using thirteen basic unimodal and multimodal functions, the proposed adaptive unified algorithm shows promising performance in compari- son to several conventional differential evolution algorithms.
On algorithm for building of optimal α-decision trees
Alkhalid, Abdulaziz
2010-01-01
The paper describes an algorithm that constructs approximate decision trees (α-decision trees), which are optimal relatively to one of the following complexity measures: depth, total path length or number of nodes. The algorithm uses dynamic programming and extends methods described in [4] to constructing approximate decision trees. Adjustable approximation rate allows controlling algorithm complexity. The algorithm is applied to build optimal α-decision trees for two data sets from UCI Machine Learning Repository [1]. © 2010 Springer-Verlag Berlin Heidelberg.
A New Class of Hybrid Particle Swarm Optimization Algorithm
Institute of Scientific and Technical Information of China (English)
Da-Qing Guo; Yong-Jin Zhao; Hui Xiong; Xiao Li
2007-01-01
A new class of hybrid particle swarm optimization (PSO) algorithm is developed for solving the premature convergence caused by some particles in standard PSO fall into stagnation. In this algorithm, the linearly decreasing inertia weight technique (LDIW) and the mutative scale chaos optimization algorithm (MSCOA) are combined with standard PSO, which are used to balance the global and local exploration abilities and enhance the local searching abilities, respectively. In order to evaluate the performance of the new method, three benchmark functions are used. The simulation results confirm the proposed algorithm can greatly enhance the searching ability and effectively improve the premature convergence.
Generalized convexity, generalized monotonicity recent results
Martinez-Legaz, Juan-Enrique; Volle, Michel
1998-01-01
A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized conve...
Flower pollination algorithm: A novel approach for multiobjective optimization
Yang, Xin-She; Karamanoglu, Mehmet; He, Xingshi
2014-09-01
Multiobjective design optimization problems require multiobjective optimization techniques to solve, and it is often very challenging to obtain high-quality Pareto fronts accurately. In this article, the recently developed flower pollination algorithm (FPA) is extended to solve multiobjective optimization problems. The proposed method is used to solve a set of multiobjective test functions and two bi-objective design benchmarks, and a comparison of the proposed algorithm with other algorithms has been made, which shows that the FPA is efficient with a good convergence rate. Finally, the importance for further parametric studies and theoretical analysis is highlighted and discussed.
Support Vector Machine Optimized by Improved Genetic Algorithm
Directory of Open Access Journals (Sweden)
Xiang Chang Sheng
2013-07-01
Full Text Available Parameters of support vector machines (SVM which is optimized by standard genetic algorithm is easy to trap into the local minimum, in order to get the optimal parameters of support vector machine, this paper proposed a parameters optimization method for support vector machines based on improved genetic algorithm, the simulation experiment is carried out on 5 benchmark datasets. The simulation show that the proposed method not only can assure the classification precision, but also can reduce training time markedly compared with standard genetic algorithm.
Directory of Open Access Journals (Sweden)
M. Balasubbareddy
2015-12-01
Full Text Available A novel optimization algorithm is proposed to solve single and multi-objective optimization problems with generation fuel cost, emission, and total power losses as objectives. The proposed method is a hybridization of the conventional cuckoo search algorithm and arithmetic crossover operations. Thus, the non-linear, non-convex objective function can be solved under practical constraints. The effectiveness of the proposed algorithm is analyzed for various cases to illustrate the effect of practical constraints on the objectives' optimization. Two and three objective multi-objective optimization problems are formulated and solved using the proposed non-dominated sorting-based hybrid cuckoo search algorithm. The effectiveness of the proposed method in confining the Pareto front solutions in the solution region is analyzed. The results for single and multi-objective optimization problems are physically interpreted on standard test functions as well as the IEEE-30 bus test system with supporting numerical and graphical results and also validated against existing methods.
Genetic algorithms for multicriteria shape optimization of induction furnace
Kůs, Pavel; Mach, František; Karban, Pavel; Doležel, Ivo
2012-09-01
In this contribution we deal with a multi-criteria shape optimization of an induction furnace. We want to find shape parameters of the furnace in such a way, that two different criteria are optimized. Since they cannot be optimized simultaneously, instead of one optimum we find set of partially optimal designs, so called Pareto front. We compare two different approaches to the optimization, one using nonlinear conjugate gradient method and second using variation of genetic algorithm. As can be seen from the numerical results, genetic algorithm seems to be the right choice for this problem. Solution of direct problem (coupled problem consisting of magnetic and heat field) is done using our own code Agros2D. It uses finite elements of higher order leading to fast and accurate solution of relatively complicated coupled problem. It also provides advanced scripting support, allowing us to prepare parametric model of the furnace and simply incorporate various types of optimization algorithms.
A Cooperative Harmony Search Algorithm for Function Optimization
Directory of Open Access Journals (Sweden)
Gang Li
2014-01-01
Full Text Available Harmony search algorithm (HS is a new metaheuristic algorithm which is inspired by a process involving musical improvisation. HS is a stochastic optimization technique that is similar to genetic algorithms (GAs and particle swarm optimizers (PSOs. It has been widely applied in order to solve many complex optimization problems, including continuous and discrete problems, such as structure design, and function optimization. A cooperative harmony search algorithm (CHS is developed in this paper, with cooperative behavior being employed as a significant improvement to the performance of the original algorithm. Standard HS just uses one harmony memory and all the variables of the object function are improvised within the harmony memory, while the proposed algorithm CHS uses multiple harmony memories, so that each harmony memory can optimize different components of the solution vector. The CHS was then applied to function optimization problems. The results of the experiment show that CHS is capable of finding better solutions when compared to HS and a number of other algorithms, especially in high-dimensional problems.
A GLOBALLY AND SUPERLINEARLY CONVERGENT TRUST REGION METHOD FOR LC1 OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
ZhangLiping; LaiYanlian
2001-01-01
Abstract. A new trust region algorithm for solving convex LC1 optimization problem is present-ed. It is proved that the algorithm is globally convergent and the rate of convergence is superlin-ear under some reasonable assumptions.
Kidney-inspired algorithm for optimization problems
Jaddi, Najmeh Sadat; Alvankarian, Jafar; Abdullah, Salwani
2017-01-01
In this paper, a population-based algorithm inspired by the kidney process in the human body is proposed. In this algorithm the solutions are filtered in a rate that is calculated based on the mean of objective functions of all solutions in the current population of each iteration. The filtered solutions as the better solutions are moved to filtered blood and the rest are transferred to waste representing the worse solutions. This is a simulation of the glomerular filtration process in the kidney. The waste solutions are reconsidered in the iterations if after applying a defined movement operator they satisfy the filtration rate, otherwise it is expelled from the waste solutions, simulating the reabsorption and excretion functions of the kidney. In addition, a solution assigned as better solution is secreted if it is not better than the worst solutions simulating the secreting process of blood in the kidney. After placement of all the solutions in the population, the best of them is ranked, the waste and filtered blood are merged to become a new population and the filtration rate is updated. Filtration provides the required exploitation while generating a new solution and reabsorption gives the necessary exploration for the algorithm. The algorithm is assessed by applying it on eight well-known benchmark test functions and compares the results with other algorithms in the literature. The performance of the proposed algorithm is better on seven out of eight test functions when it is compared with the most recent researches in literature. The proposed kidney-inspired algorithm is able to find the global optimum with less function evaluations on six out of eight test functions. A statistical analysis further confirms the ability of this algorithm to produce good-quality results.
Davidon's optimally conditioned algorithms for unconstrained optimization
Energy Technology Data Exchange (ETDEWEB)
Nazareth, L.
1976-01-01
Recently, Davidon (Math. Prog., 9, 1-30) has published some new and very promising algorithms for minimizing unconstrained functionals. A particular perspective on these algorithms is presented, and extensions of some of the theory underlying them are developed in this paper.
An Improved Particle Swarm Optimization Algorithm Based on Ensemble Technique
Institute of Scientific and Technical Information of China (English)
SHI Yan; HUANG Cong-ming
2006-01-01
An improved particle swarm optimization (PSO) algorithm based on ensemble technique is presented. The algorithm combines some previous best positions (pbest) of the particles to get an ensemble position (Epbest), which is used to replace the global best position (gbest). It is compared with the standard PSO algorithm invented by Kennedy and Eberhart and some improved PSO algorithms based on three different benchmark functions. The simulation results show that the improved PSO based on ensemble technique can get better solutions than the standard PSO and some other improved algorithms under all test cases.
A Unified Differential Evolution Algorithm for Global Optimization
Energy Technology Data Exchange (ETDEWEB)
Qiang, Ji; Mitchell, Chad
2014-06-24
Abstract?In this paper, we propose a new unified differential evolution (uDE) algorithm for single objective global optimization. Instead of selecting among multiple mutation strategies as in the conventional differential evolution algorithm, this algorithm employs a single equation as the mutation strategy. It has the virtue of mathematical simplicity and also provides users the flexbility for broader exploration of different mutation strategies. Numerical tests using twelve basic unimodal and multimodal functions show promising performance of the proposed algorithm in comparison to convential differential evolution algorithms.
Wolf Search Algorithm for Solving Optimal Reactive Power Dispatch Problem
Directory of Open Access Journals (Sweden)
Kanagasabai Lenin
2015-03-01
Full Text Available This paper presents a new bio-inspired heuristic optimization algorithm called the Wolf Search Algorithm (WSA for solving the multi-objective reactive power dispatch problem. Wolf Search algorithm is a new bio – inspired heuristic algorithm which based on wolf preying behaviour. The way wolves search for food and survive by avoiding their enemies has been imitated to formulate the algorithm for solving the reactive power dispatches. And the speciality of wolf is possessing both individual local searching ability and autonomous flocking movement and this special property has been utilized to formulate the search algorithm .The proposed (WSA algorithm has been tested on standard IEEE 30 bus test system and simulation results shows clearly about the good performance of the proposed algorithm .
Model-based multiobjective evolutionary algorithm optimization for HCCI engines
Ma, He; Xu, Hongming; Wang, Jihong; Schnier, Thorsten; Neaves, Ben; Tan, Cheng; Wang, Zhi
2014-01-01
Modern engines feature a considerable number of adjustable control parameters. With this increasing number of Degrees of Freedom (DoF) for engines, and the consequent considerable calibration effort required to optimize engine performance, traditional manual engine calibration or optimization methods are reaching their limits. An automated engine optimization approach is desired. In this paper, a self-learning evolutionary algorithm based multi-objective globally optimization approach for a H...
A Hamiltonian Algorithm for Singular Optimal LQ Control Systems
Delgado-Tellez, M
2012-01-01
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the well-known Rabier-Rheinhboldt constraints algorithm used to solve differential-algebraic equations. Its geometrical content is exploited fully by implementing a Hamiltonian extension of it which is closer to Gotay-Nester presymplectic constraint algorithm used to solve singular Hamiltonian systems. Thus, given an optimal control problem whose optimal feedback is given in implicit form, a consistent set of equations is obtained describing the first order differential conditions of Pontryaguine's Maximum Principle. Such equations are shown to be Hamiltonian and the set of first class constraints corresponding to controls that are not determined, are obtained explicitly. The strength of the algorithm is shown by exhibiting a numerical implementation with partial feedback on the c...
Application of an Evolutionary Algorithm for Parameter Optimization in a Gully Erosion Model
Energy Technology Data Exchange (ETDEWEB)
Rengers, Francis; Lunacek, Monte; Tucker, Gregory
2016-06-01
Herein we demonstrate how to use model optimization to determine a set of best-fit parameters for a landform model simulating gully incision and headcut retreat. To achieve this result we employed the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), an iterative process in which samples are created based on a distribution of parameter values that evolve over time to better fit an objective function. CMA-ES efficiently finds optimal parameters, even with high-dimensional objective functions that are non-convex, multimodal, and non-separable. We ran model instances in parallel on a high-performance cluster, and from hundreds of model runs we obtained the best parameter choices. This method is far superior to brute-force search algorithms, and has great potential for many applications in earth science modeling. We found that parameters representing boundary conditions tended to converge toward an optimal single value, whereas parameters controlling geomorphic processes are defined by a range of optimal values.
Multiphase Return Trajectory Optimization Based on Hybrid Algorithm
Directory of Open Access Journals (Sweden)
Yi Yang
2016-01-01
Full Text Available A hybrid trajectory optimization method consisting of Gauss pseudospectral method (GPM and natural computation algorithm has been developed and utilized to solve multiphase return trajectory optimization problem, where a phase is defined as a subinterval in which the right-hand side of the differential equation is continuous. GPM converts the optimal control problem to a nonlinear programming problem (NLP, which helps to improve calculation accuracy and speed of natural computation algorithm. Through numerical simulations, it is found that the multiphase optimal control problem could be solved perfectly.
Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem
Chen, Wei
2015-07-01
In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.
Directory of Open Access Journals (Sweden)
Sukanta Nama
2016-04-01
Full Text Available Differential evolution (DE is an effective and powerful approach and it has been widely used in different environments. However, the performance of DE is sensitive to the choice of control parameters. Thus, to obtain optimal performance, time-consuming parameter tuning is necessary. Backtracking Search Optimization Algorithm (BSA is a new evolutionary algorithm (EA for solving real-valued numerical optimization problems. An ensemble algorithm called E-BSADE is proposed which incorporates concepts from DE and BSA. The performance of E-BSADE is evaluated on several benchmark functions and is compared with basic DE, BSA and conventional DE mutation strategy.
Salcedo-Sanz, S.; Del Ser, J.; Landa-Torres, I.; Gil-López, S.; Portilla-Figueras, J. A.
2014-01-01
This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems. PMID:25147860
Directory of Open Access Journals (Sweden)
A. Hajnoori
2013-07-01
Full Text Available Portfolio optimization problem follows the calculation of investment income per share, based on return and risk criteria. Since stock risk is achieved by calculating its return, which is itself computed based on stock price, it is essential to forecast the stock price, efficiently. In this paper, in order to predict the stock price, grey fuzzy technique with high efficiency is employed. The proposed study of this paper calculates the return and risk of each asset and portfolio optimization model is developed based on cardinality constraint and investment income per share. To solve the resulted model, Invasive Weed Optimization (IWO algorithm is applied. In an example this algorithm is compared with other metaheuristic algorithms such as Imperialist Competitive Algorithm (ICA, Genetic Algorithm (GA and Particle Swarm Optimization (PSO. The results show that the applied algorithm performs significantly better than other algorithms.
Salcedo-Sanz, S; Del Ser, J; Landa-Torres, I; Gil-López, S; Portilla-Figueras, J A
2014-01-01
This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems.
Hybrid Algorithm for the Optimization of Training Convolutional Neural Network
Directory of Open Access Journals (Sweden)
Hayder M. Albeahdili
2015-10-01
Full Text Available The training optimization processes and efficient fast classification are vital elements in the development of a convolution neural network (CNN. Although stochastic gradient descend (SGD is a Prevalence algorithm used by many researchers for the optimization of training CNNs, it has vast limitations. In this paper, it is endeavor to diminish and tackle drawbacks inherited from SGD by proposing an alternate algorithm for CNN training optimization. A hybrid of genetic algorithm (GA and particle swarm optimization (PSO is deployed in this work. In addition to SGD, PSO and genetic algorithm (PSO-GA are also incorporated as a combined and efficient mechanism in achieving non trivial solutions. The proposed unified method achieves state-of-the-art classification results on the different challenge benchmark datasets such as MNIST, CIFAR-10, and SVHN. Experimental results showed that the results outperform and achieve superior results to most contemporary approaches.
PCB Drill Path Optimization by Combinatorial Cuckoo Search Algorithm
Directory of Open Access Journals (Sweden)
Wei Chen Esmonde Lim
2014-01-01
Full Text Available Optimization of drill path can lead to significant reduction in machining time which directly improves productivity of manufacturing systems. In a batch production of a large number of items to be drilled such as printed circuit boards (PCB, the travel time of the drilling device is a significant portion of the overall manufacturing process. To increase PCB manufacturing productivity and to reduce production costs, a good option is to minimize the drill path route using an optimization algorithm. This paper reports a combinatorial cuckoo search algorithm for solving drill path optimization problem. The performance of the proposed algorithm is tested and verified with three case studies from the literature. The computational experience conducted in this research indicates that the proposed algorithm is capable of efficiently finding the optimal path for PCB holes drilling process.
PCB drill path optimization by combinatorial cuckoo search algorithm.
Lim, Wei Chen Esmonde; Kanagaraj, G; Ponnambalam, S G
2014-01-01
Optimization of drill path can lead to significant reduction in machining time which directly improves productivity of manufacturing systems. In a batch production of a large number of items to be drilled such as printed circuit boards (PCB), the travel time of the drilling device is a significant portion of the overall manufacturing process. To increase PCB manufacturing productivity and to reduce production costs, a good option is to minimize the drill path route using an optimization algorithm. This paper reports a combinatorial cuckoo search algorithm for solving drill path optimization problem. The performance of the proposed algorithm is tested and verified with three case studies from the literature. The computational experience conducted in this research indicates that the proposed algorithm is capable of efficiently finding the optimal path for PCB holes drilling process.
A Hierachical Evolutionary Algorithm for Multiobjective Optimization in IMRT
Holdsworth, Clay; Liao, Jay; Phillips, Mark H
2012-01-01
Purpose: Current inverse planning methods for IMRT are limited because they are not designed to explore the trade-offs between the competing objectives between the tumor and normal tissues. Our goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans. Methods: We developed a hierarchical evolutionary multiobjective algorithm designed to quickly generate a diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the trade-offs in the plans. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then...
Research on particle swarm optimization algorithm based on optimal movement probability
Ma, Jianhong; Zhang, Han; He, Baofeng
2017-01-01
The particle swarm optimization algorithm to improve the control precision, and has great application value training neural network and fuzzy system control fields etc.The traditional particle swarm algorithm is used for the training of feed forward neural networks,the search efficiency is low, and easy to fall into local convergence.An improved particle swarm optimization algorithm is proposed based on error back propagation gradient descent. Particle swarm optimization for Solving Least Squares Problems to meme group, the particles in the fitness ranking, optimization problem of the overall consideration, the error back propagation gradient descent training BP neural network, particle to update the velocity and position according to their individual optimal and global optimization, make the particles more to the social optimal learning and less to its optimal learning, it can avoid the particles fall into local optimum, by using gradient information can accelerate the PSO local search ability, improve the multi beam particle swarm depth zero less trajectory information search efficiency, the realization of improved particle swarm optimization algorithm. Simulation results show that the algorithm in the initial stage of rapid convergence to the global optimal solution can be near to the global optimal solution and keep close to the trend, the algorithm has faster convergence speed and search performance in the same running time, it can improve the convergence speed of the algorithm, especially the later search efficiency.
Directory of Open Access Journals (Sweden)
Yuksel Celik
2013-01-01
Full Text Available Marriage in honey bees optimization (MBO is a metaheuristic optimization algorithm developed by inspiration of the mating and fertilization process of honey bees and is a kind of swarm intelligence optimizations. In this study we propose improved marriage in honey bees optimization (IMBO by adding Levy flight algorithm for queen mating flight and neighboring for worker drone improving. The IMBO algorithm’s performance and its success are tested on the well-known six unconstrained test functions and compared with other metaheuristic optimization algorithms.
Path following algorithm for the graph matching problem
Zaslavskiy, Mikhail; Vert, Jean-Philippe
2008-01-01
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore to perform labeled graph matching. The algorithm is compared with some of t...
Optimal Design of Materials for DJMP Based on Genetic Algorithm
Institute of Scientific and Technical Information of China (English)
FENG Zhong-ren; WANG Xiong-jiang
2004-01-01
The genetic algorithm was used in optimal design of deep jet method pile. The cost of deep jetmethod pile in one unit area of foundation was taken as the objective function. All the restrains were listed followingthe corresponding specification. Suggestions were proposed and the modified. The real-coded Genetic Algorithm wasgiven to deal with the problems of excessive computational cost and premature convergence. Software system of opti-mal design of deep jet method pile was developed.
Institute of Scientific and Technical Information of China (English)
张艺
2002-01-01
In this paper,a primal-dual interior point algorithm for convex quadratic progromming problem with box constrains is presented.It can be started at any primal-dual interior feasible point.If the initial point is close to the central path,it becomes a central path-following alogorithm and requires a total of O(√nL)number of iterations,where L is the input length.
Differential evolution algorithm for global optimizations in nuclear physics
Qi, Chong
2017-04-01
We explore the applicability of the differential evolution algorithm in finding the global minima of three typical nuclear structure physics problems: the global deformation minimum in the nuclear potential energy surface, the optimization of mass model parameters and the lowest eigenvalue of a nuclear Hamiltonian. The algorithm works very effectively and efficiently in identifying the minima in all problems we have tested. We also show that the algorithm can be parallelized in a straightforward way.
A TRUST-REGION ALGORITHM FOR NONLINEAR INEQUALITY CONSTRAINED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Xiaojiao Tong; Shuzi Zhou
2003-01-01
This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived,which is the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps, local quadratic convergence theorem is proved for nondegenerate minimizer point. Numerical experiment is presented to show the effectiveness of our approach.
QOS-BASED MULTICAST ROUTING OPTIMIZATION ALGORITHMS FOR INTERNET
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Most of the multimedia applications require strict Quality-of-Service (QoS) guarantee during the communication between a single source and multiple destinations. The paper mainly presents a QoS Multicast Routing algorithms based on Genetic Algorithm (QMRGA). Simulation results demonstrate that the algorithm is capable of discovering a set of QoS-based near optimized, non-dominated multicast routes within a few iterations, even for the networks environment with uncertain parameters.
A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization
Directory of Open Access Journals (Sweden)
Zhijun Luo
2014-01-01
Full Text Available A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.
The study of cuckoo optimization algorithm for production planning problem
Akbarzadeh, Afsane; Shadkam, Elham
2015-01-01
Constrained Nonlinear programming problems are hard problems, and one of the most widely used and common problems for production planning problem to optimize. In this study, one of the mathematical models of production planning is survey and the problem solved by cuckoo algorithm. Cuckoo Algorithm is efficient method to solve continues non linear problem. Moreover, mentioned models of production planning solved with Genetic algorithm and Lingo software and the results will compared. The Cucko...
Gradient Gene Algorithm: a Fast Optimization Method to MST Problem
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The extension of Minimum Spanning Tree(MST) problem is an NP hardproblem which does not exit a polynomial time algorithm. In this paper, a fast optimizat ion method on MST problem--the Gradient Gene Algorithm is introduced. Compar ed with other evolutionary algorithms on MST problem, it is more advanced: firstly, very simple and easy to realize; then, efficient and accurate; finally general on other combination optimization problems.
Advanced optimization of permanent magnet wigglers using a genetic algorithm
Energy Technology Data Exchange (ETDEWEB)
Hajima, Ryoichi [Univ. of Tokyo (Japan)
1995-12-31
In permanent magnet wigglers, magnetic imperfection of each magnet piece causes field error. This field error can be reduced or compensated by sorting magnet pieces in proper order. We showed a genetic algorithm has good property for this sorting scheme. In this paper, this optimization scheme is applied to the case of permanent magnets which have errors in the direction of field. The result shows the genetic algorithm is superior to other algorithms.
Parallel optimization algorithms and their implementation in VLSI design
Lee, G.; Feeley, J. J.
1991-01-01
Two new parallel optimization algorithms based on the simplex method are described. They may be executed by a SIMD parallel processor architecture and be implemented in VLSI design. Several VLSI design implementations are introduced. An application example is reported to demonstrate that the algorithms are effective.
Bio Inspired Algorithms in Single and Multiobjective Reliability Optimization
DEFF Research Database (Denmark)
Madsen, Henrik; Albeanu, Grigore; Burtschy, Bernard
2014-01-01
Non-traditional search and optimization methods based on natural phenomena have been proposed recently in order to avoid local or unstable behavior when run towards an optimum state. This paper describes the principles of bio inspired algorithms and reports on Migration Algorithms and Bees...
Genetic algorithm for neural networks optimization
Setyawati, Bina R.; Creese, Robert C.; Sahirman, Sidharta
2004-11-01
This paper examines the forecasting performance of multi-layer feed forward neural networks in modeling a particular foreign exchange rates, i.e. Japanese Yen/US Dollar. The effects of two learning methods, Back Propagation and Genetic Algorithm, in which the neural network topology and other parameters fixed, were investigated. The early results indicate that the application of this hybrid system seems to be well suited for the forecasting of foreign exchange rates. The Neural Networks and Genetic Algorithm were programmed using MATLAB«.
Niche Genetic Algorithm with Accurate Optimization Performance
Institute of Scientific and Technical Information of China (English)
LIU Jian-hua; YAN De-kun
2005-01-01
Based on crowding mechanism, a novel niche genetic algorithm was proposed which can record evolutionary direction dynamically during evolution. After evolution, the solutions's precision can be greatly improved by means of the local searching along the recorded direction. Simulation shows that this algorithm can not only keep population diversity but also find accurate solutions. Although using this method has to take more time compared with the standard GA, it is really worth applying to some cases that have to meet a demand for high solution precision.
Uniformly convex and strictly convex Orlicz spaces
Masta, Al Azhary
2016-02-01
In this paper we define the new norm of Orlicz spaces on ℝn through a multiplication operator on an old Orlicz spaces. We obtain some necessary and sufficient conditions that the new norm to be a uniformly convex and strictly convex spaces.
DEFF Research Database (Denmark)
Dollerup, Niels; Jepsen, Michael S.; Frier, Christian;
2014-01-01
A robust and effective finite element based implementation of lower bound limit state analysis applying an interior point formulation is presented in this paper. The lower bound formulation results in a convex optimization problem consisting of a number of linear constraints from the equilibrium...... equations and a number of convex non-linear constraints from the yield criteria. The computational robustness has been improved by eliminating a large number of the equilibrium equations a priori leaving only the statical redundant variables as free optimization variables. The elimination of equilibrium...... equations is based on a optimized numbering of elements and stress variables based on the frontal method approach used in the standard finite element method. The optimized numbering secures sparsity in the formulation. The convex non-linear yield criteria are treated directly in the interior point...
MPC Toolbox with GPU Accelerated Optimization Algorithms
DEFF Research Database (Denmark)
Gade-Nielsen, Nicolai Fog; Jørgensen, John Bagterp; Dammann, Bernd
2012-01-01
The introduction of Graphical Processing Units (GPUs) in scientific computing has shown great promise in many different fields. While GPUs are capable of very high floating point performance and memory bandwidth, its massively parallel architecture requires algorithms to be reimplemented to suit...
A Hybrid Mutation Chemical Reaction Optimization Algorithm for Global Numerical Optimization
Directory of Open Access Journals (Sweden)
Ransikarn Ngambusabongsopa
2015-01-01
Full Text Available This paper proposes a hybrid metaheuristic approach that improves global numerical optimization by increasing optimal quality and accelerating convergence. This algorithm involves a recently developed process for chemical reaction optimization and two adjustment operators (turning and mutation operators. Three types of mutation operators (uniform, nonuniform, and polynomial were combined with chemical reaction optimization and turning operator to find the most appropriate framework. The best solution among these three options was selected to be a hybrid mutation chemical reaction optimization algorithm for global numerical optimization. The optimal quality, convergence speed, and statistical hypothesis testing of our algorithm are superior to those previous high performance algorithms such as RCCRO, HP-CRO2, and OCRO.
OPTIMIZATION BASED ON LMPROVED REAL—CODED GENETIC ALGORITHM
Institute of Scientific and Technical Information of China (English)
ShiYu; YuShenglin
2002-01-01
An improved real-coded genetic algorithm is pro-posed for global optimization of functionsl.The new algo-rithm is based om the judgement of the searching perfor-mance of basic real-coded genetic algorithm.The opera-tions of basic real-coded genetic algorithm are briefly dis-cussed and selected.A kind of chaos sequence is described in detail and added in the new algorithm ad a disturbance factor.The strategy of field partition is also used to im-prove the strcture of the new algorithm.Numerical ex-periment shows that the mew genetic algorithm can find the global optimum of complex funtions with satistaiting precision.
Adaptive symbiotic organisms search (SOS algorithm for structural design optimization
Directory of Open Access Journals (Sweden)
Ghanshyam G. Tejani
2016-07-01
Full Text Available The symbiotic organisms search (SOS algorithm is an effective metaheuristic developed in 2014, which mimics the symbiotic relationship among the living beings, such as mutualism, commensalism, and parasitism, to survive in the ecosystem. In this study, three modified versions of the SOS algorithm are proposed by introducing adaptive benefit factors in the basic SOS algorithm to improve its efficiency. The basic SOS algorithm only considers benefit factors, whereas the proposed variants of the SOS algorithm, consider effective combinations of adaptive benefit factors and benefit factors to study their competence to lay down a good balance between exploration and exploitation of the search space. The proposed algorithms are tested to suit its applications to the engineering structures subjected to dynamic excitation, which may lead to undesirable vibrations. Structure optimization problems become more challenging if the shape and size variables are taken into account along with the frequency. To check the feasibility and effectiveness of the proposed algorithms, six different planar and space trusses are subjected to experimental analysis. The results obtained using the proposed methods are compared with those obtained using other optimization methods well established in the literature. The results reveal that the adaptive SOS algorithm is more reliable and efficient than the basic SOS algorithm and other state-of-the-art algorithms.
Implementation and Optimization of A Fast Inter Prediction Algorithm
Directory of Open Access Journals (Sweden)
Xiaoyu Li
2013-07-01
Full Text Available Audio Video coding Standard is the second generation Source Coding-Decoding standards of China, especially for embedded audio/video platform. This paper proposes an efficient and fast inter prediction algorithm, which is one of the key techniques of Audio Video coding Standard.Reducing of the redundancy in source sequence inter prediction, it could improve the picture quality. The optimization schemes include two aspects,which are the algorithm framework, variables and data structure. Optimized results demonstrate that our algorithm has a notable improvement of the clockcycle efficiency. Furthermore, this research also gives a valuable insight of the combination with quantum information.
Optimal Path Planning for Mobile Robot Using Tailored Genetic Algorithm
Directory of Open Access Journals (Sweden)
Dong Xiao Xian
2013-07-01
Full Text Available During routine inspecting, mobile robot may be requested to visit multiple locations to execute special tasks occasionally. This study aims at optimal path planning for multiple goals visiting task based on tailored genetic algorithm. The proposed algorithm will generate an optimal path that has the least idle time, which is proven to be more effective on evaluating a path in our previous work. In proposed algorithm, customized chromosome representing a path and genetic operators including repair and cut are developed and implemented. Afterwards, simulations are carried out to verify the effectiveness and applicability. Finally, analysis of simulation results is conducted and future work is addressed.
NONMONOTONE PRECONDITIONAL CURVILINEAR PATH ALGORITHMS FOR UNCONSTRAINED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
朱德通
2003-01-01
This paper presents nonmonotonic quasi-Newton algorithms via two pre-conditional curvilinear paths, the preconditional modified gradient path and the precon-ditional optimal path, for unconstrained optimization problem. We employ the stableBunch-Parlett factorization method to form two curvilinear paths very easily. Thenonmonotone criterion is used to speed up the convergence progress in the contoursof objective function with large curvature. Theoretical analyses are given which provethat the proposed algorithms are globally convergent and have a local superlinear con-vergence rate under some reasonable conditions. The results of numerical experimentsare reported to show the effectiveness of the proposed algorithms.
Optimization of deep learning algorithms for object classification
Horváth, András.
2017-02-01
Deep learning is currently the state of the art algorithm for image classification. The complexity of these feedforward neural networks have overcome a critical point, resulting algorithmic breakthroughs in various fields. On the other hand their complexity makes them executable in tasks, where High-throughput computing powers are available. The optimization of these networks -considering computational complexity and applicability on embedded systems- has not yet been studied and investigated in details. In this paper I show some examples how this algorithms can be optimized and accelerated on embedded systems.
Imperialist competitive algorithm combined with chaos for global optimization
Talatahari, S.; Farahmand Azar, B.; Sheikholeslami, R.; Gandomi, A. H.
2012-03-01
A novel chaotic improved imperialist competitive algorithm (CICA) is presented for global optimization. The ICA is a new meta-heuristic optimization developed based on a socio-politically motivated strategy and contains two main steps: the movement of the colonies and the imperialistic competition. Here different chaotic maps are utilized to improve the movement step of the algorithm. Seven different chaotic maps are investigated and the Logistic and Sinusoidal maps are found as the best choices. Comparing the new algorithm with the other ICA-based methods demonstrates the superiority of the CICA for the benchmark functions.
Multi-class DTI Segmentation: A Convex Approach.
Xie, Yuchen; Chen, Ting; Ho, Jeffrey; Vemuri, Baba C
2012-10-01
In this paper, we propose a novel variational framework for multi-class DTI segmentation based on global convex optimization. The existing variational approaches to the DTI segmentation problem have mainly used gradient-descent type optimization techniques which are slow in convergence and sensitive to the initialization. This paper on the other hand provides a new perspective on the often difficult optimization problem in DTI segmentation by providing a reasonably tight convex approximation (relaxation) of the original problem, and the relaxed convex problem can then be efficiently solved using various methods such as primal-dual type algorithms. To the best of our knowledge, such a DTI segmentation technique has never been reported in literature. We also show that a variety of tensor metrics (similarity measures) can be easily incorporated in the proposed framework. Experimental results on both synthetic and real diffusion tensor images clearly demonstrate the advantages of our method in terms of segmentation accuracy and robustness. In particular, when compared with existing state-of-the-art methods, our results demonstrate convincingly the importance as well as the benefit of using more refined and elaborated optimization method in diffusion tensor MR image segmentation.
On Quasi E-Convex Bilevel Programming Problem
Directory of Open Access Journals (Sweden)
E. A. Youness
2005-01-01
Full Text Available Bilevel programming problems involve two optimization problems where the data of the first one is implicity determined by the solution of the second. This study introduces the notions of E-convexity and quasi E-convexity in bilevel programming problems to generalize quasi convex bilevel programming problems.
PRECONDITIONED SPECTRAL PROJECTED GRADIENT METHOD ON CONVEX SETS
Institute of Scientific and Technical Information of China (English)
Lenys Bello; Marcos Raydan
2005-01-01
The spectral gradient method has proved to be effective for solving large-scale unconstrained optimization problems. It has been recently extended and combined with the projected gradient method for solving optimization problems on convex sets. This combination includes the use of nonmonotone line search techniques to preserve the fast local convergence. In this work we further extend the spectral choice of steplength to accept preconditioned directions when a good preconditioner is available. We present an algorithm that combines the spectral projected gradient method with preconditioning strategies to increase the local speed of convergence while keeping the global properties. We discuss implementation details for solving large-scale problems.
Concrete Plant Operations Optimization Using Combined Simulation and Genetic Algorithms
Cao, Ming; Lu, Ming; Zhang, Jian-Ping
2004-01-01
This work presents a new approach for concrete plant operations optimization by combining a ready mixed concrete (RMC) production simulation tool (called HKCONSIM) with a genetic algorithm (GA) based optimization procedure. A revamped HKCONSIM computer system can be used to automate the simulation m