The Team Orienteering Arc Routing Problem
Archetti, Claudia; Speranza, M. Grazia; Corberan, Angel; Sanchís Llopis, José María; Plana, Isaac
2014-01-01
The team orienteering arc routing problem (TOARP) is the extension to the arc routing setting of the team orienteering problem. In the TOARP, in addition to a possible set of regular customers that have to be serviced, another set of potential customers is available. Each customer is associated with an arc of a directed graph. Each potential customer has a profit that is collected when it is serviced, that is, when the associated arc is traversed. A fleet of vehicles with a given maximum trav...
The time-dependent prize-collecting arc routing problem
DEFF Research Database (Denmark)
Black, Dan; Eglese, Richard; Wøhlk, Sanne
2013-01-01
A new problem is introduced named the Time-Dependent Prize-Collecting Arc Routing Problem (TD-PARP). It is particularly relevant to situations where a transport manager has to choose between a number of full truck load pick-ups and deliveries on a road network where travel times change with the t......A new problem is introduced named the Time-Dependent Prize-Collecting Arc Routing Problem (TD-PARP). It is particularly relevant to situations where a transport manager has to choose between a number of full truck load pick-ups and deliveries on a road network where travel times change...
An Approximation Algorithm for the Capacitated Arc Routing Problem
DEFF Research Database (Denmark)
Wøhlk, Sanne
2008-01-01
In this paper we consider approximation of the Capacitated Arc Routing Problem, which is the problem of servicing a set of edges in a graph using a fleet of capacity constrained vehicles. We present a 7/2 - 3/W-approximation algorithm for the problem and prove that this algorithm outperforms...
Capacitated arc routing problem and its extensions in waste collection
Energy Technology Data Exchange (ETDEWEB)
Fadzli, Mohammad; Najwa, Nurul [Institut Matematik Kejuruteraan, Universiti Malaysia Perlis, Kampus Pauh Putra, 02600 Arau, Perlis (Malaysia); Luis, Martino [Othman Yeop Abdullah Graduate School of Business, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia)
2015-05-15
Capacitated arc routing problem (CARP) is the youngest generation of graph theory that focuses on solving the edge/arc routing for optimality. Since many years, operational research devoted to CARP counterpart, known as vehicle routing problem (VRP), which does not fit to several real cases such like waste collection problem and road maintenance. In this paper, we highlighted several extensions of capacitated arc routing problem (CARP) that represents the real-life problem of vehicle operation in waste collection. By purpose, CARP is designed to find a set of routes for vehicles that satisfies all pre-setting constraints in such that all vehicles must start and end at a depot, service a set of demands on edges (or arcs) exactly once without exceeding the capacity, thus the total fleet cost is minimized. We also addressed the differentiation between CARP and VRP in waste collection. Several issues have been discussed including stochastic demands and time window problems in order to show the complexity and importance of CARP in the related industry. A mathematical model of CARP and its new version is presented by considering several factors such like delivery cost, lateness penalty and delivery time.
Capacitated arc routing problem and its extensions in waste collection
Fadzli, Mohammad; Najwa, Nurul; Luis, Martino
2015-05-01
Capacitated arc routing problem (CARP) is the youngest generation of graph theory that focuses on solving the edge/arc routing for optimality. Since many years, operational research devoted to CARP counterpart, known as vehicle routing problem (VRP), which does not fit to several real cases such like waste collection problem and road maintenance. In this paper, we highlighted several extensions of capacitated arc routing problem (CARP) that represents the real-life problem of vehicle operation in waste collection. By purpose, CARP is designed to find a set of routes for vehicles that satisfies all pre-setting constraints in such that all vehicles must start and end at a depot, service a set of demands on edges (or arcs) exactly once without exceeding the capacity, thus the total fleet cost is minimized. We also addressed the differentiation between CARP and VRP in waste collection. Several issues have been discussed including stochastic demands and time window problems in order to show the complexity and importance of CARP in the related industry. A mathematical model of CARP and its new version is presented by considering several factors such like delivery cost, lateness penalty and delivery time.
Solving Arc Routing Problems Using the Lin-Kernighan-Helsgaun Algorithm
DEFF Research Database (Denmark)
Helsgaun, Keld
It is well known that many arc routing problems can be transformed into the Equality Generalized Traveling Salesman Problem (E-GTSP), which in turn can be transformed into a standard Asymmetric Traveling Salesman Problem (TSP). This opens up the possibility of solving arc routing problems using...... and general routing problem instances....
Periodic capacitated arc routing problem applied in a real context
Directory of Open Access Journals (Sweden)
Guilherme Vinicyus Batista
2015-09-01
Full Text Available A good inspection and maintenance planning in railways is essential to ensure the flow of trains and avoid possible accidents. This inspection should be performed periodically by vehicle traveling on rails collecting data and identifying gaps that need to be corrected. The aim of this paper is to present a mathematical model based on binary linear programming, capable of solving this problem, which is a real application of Periodic Capacitated Arc Routing Problem (PCARP. In the PCARP each arc of a network has a demand over a well-defined time horizon and routes must be created for each car so that it covers all the requests in the best way possible without exceeding the vehicles capacity at service. The proposed application has different characteristics to those already proposed in the literature because the vehicle does not need to come back to the depot at the end of the day and the service can be delayed if necessary. The result is satisfactory, covering the demands with a synchronized movement of vehicles.
General heuristics algorithms for solving capacitated arc routing problem
Fadzli, Mohammad; Najwa, Nurul; Masran, Hafiz
2015-05-01
In this paper, we try to determine the near-optimum solution for the capacitated arc routing problem (CARP). In general, NP-hard CARP is a special graph theory specifically arises from street services such as residential waste collection and road maintenance. By purpose, the design of the CARP model and its solution techniques is to find optimum (or near-optimum) routing cost for a fleet of vehicles involved in operation. In other words, finding minimum-cost routing is compulsory in order to reduce overall operation cost that related with vehicles. In this article, we provide a combination of various heuristics algorithm to solve a real case of CARP in waste collection and benchmark instances. These heuristics work as a central engine in finding initial solutions or near-optimum in search space without violating the pre-setting constraints. The results clearly show that these heuristics algorithms could provide good initial solutions in both real-life and benchmark instances.
A Branch-and-Price Algorithm for the Capacitated Arc Routing Problem with Stochastic Demands
DEFF Research Database (Denmark)
Christiansen, Christian Holk; Lysgaard, Jens; Wøhlk, Sanne
2009-01-01
We address the Capacitated Arc Routing Problem with Stochastic Demands (CARPSD), which we formulate as a Set Partitioning Problem. The CARPSD is solved by a Branch-and-Price algorithm, which we apply without graph transformation. The demand's stochastic nature is incorporated into the pricing...... problem. Computational results are reported....
A mathematical modeling proposal for a Multiple Tasks Periodic Capacitated Arc Routing Problem
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Cleverson Gonçalves dos Santos
2015-12-01
Full Text Available The countless accidents and incidents occurred at dams at the last years, propelled the development of politics related with dams safety. One of the strategies is related to the plan for instrumentation and monitoring of dams. The monitoring demands from the technical team the reading of the auscultation data, in order to periodically monitor the dam. The monitoring plan of the dam can be modeled as a problem of mathematical program of the periodical capacitated arcs routing program (PCARP. The PCARP is considered as a generalization of the classic problem of routing in capacitated arcs (CARP due to two characteristics: 1 Planning period larger than a time unity, as that vehicle make several travels and; 2 frequency of associated visits to the arcs to be serviced over the planning horizon. For the dam's monitoring problem studied in this work, the frequent visits, along the time horizon, it is not associated to the arc, but to the instrument with which is intended to collect the data. Shows a new problem of Multiple tasks Periodic Capacitated Arc Routing Problem and its elaboration as an exact mathematical model. The new main characteristics presented are: multiple tasks to be performed on each edge or edges; different frequencies to accomplish each of the tasks; heterogeneous fleet; and flexibility for more than one vehicle passing through the same edge at the same day. The mathematical model was implemented and examples were generated randomly for the proposed model's validation.
The Time-Dependent Multiple-Vehicle Prize-Collecting Arc Routing Problem
DEFF Research Database (Denmark)
Black, Daniel; Eglese, Richard; Wøhlk, Sanne
2015-01-01
In this paper, we introduce a multi vehicle version of the Time-Dependent Prize-Collecting Arc Routing Problem (TD-MPARP). It is inspired by a situation where a transport manager has to choose between a number of full truck load pick-ups and deliveries to be performed by a fleet of vehicles. Real...
Lower and Upper Bounds for the Node, Edge, and Arc Routing Problem
DEFF Research Database (Denmark)
Bach, Lukas; Wøhlk, Sanne; Hasle, Geir
The Node, Edge, and Arc Routing Problem (NEARP) was defined by Prins and Bouchenoua in 2004. They also proposed a memetic algorithm procedure and defined a set of test instances: the so-called CBMix benchmark. The NEARP generalizes the classical CVRP, the CARP, and the General Routing Problem....... It captures important aspects of real-life routing problems that were not adequately modeled in previous VRP variants. Hence, its definition and investigation contribute to the development of rich VRPs. In this paper we present the first lower bound for the NEARP. It is a further development of lower bounds...... for the CARP. We also define two novel sets of test instances to complement the CBMix benchmark. The first is based on well-known CARP instances; the second consists of real life cases of newspaper delivery routing. We provide numerical results in the form 1 of lower and best known upper bounds for all...
THE PERIODIC CAPACITATED ARC ROUTING PROBLEM LINEAR PROGRAMMING MODEL,METAHEURISTIC AND LOWER BOUNDS
Institute of Scientific and Technical Information of China (English)
Feng CHU; Nacima LABADI; Christian PRINS
2004-01-01
The Periodic Capacitated Arc Routing Problem (PCARP) generalizes the well known NP-hard Capacitated Arc Routing Problem (CARP) by extending the single period to multi-period horizon.The Capacitated Arc Routing Problem (CARP) is defined on an undirected network in which a fleet of identical vehicles is based at a depot node. A subset of edges, called tasks, must be serviced by a vehicle. The CARP consists of determining a set of feasible vehicle trips that minimizes the total cost of traversed edges. The PCARP involves the assignment of tasks to periods and the determination of vehicles trips in each period, to minimize the total cost on the whole horizon. This new problem arises in various real life applications such as waste collection, mail delivery, etc. In this paper, a new linear programming model and preliminary lower bounds based on graph transformation are proposed. A meta-heuristic approach - Scatter Search (SS) is developed for the PCARP and evaluated on a large variety of instances.
Implementation Weather-Type Models of Capacitated Arc Routing Problem via Heuristics
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Zuhaimy Ismail
2011-01-01
Full Text Available Problem statement: In this study, we introduced a new and real-life condition of Capacitated Arc Routing Problem (CARP, a model that represents vehicles operation in waste collection. In general, we studied the element of rain drops that affected the collected waste weight in total by imposed a new variable namely rainy weight age. In rainy days, the household refusals did not increase in volumes, but in weights due to rain drops. Consequently, this matter thus burdened vehicles capacity and prolonged its operation time. This dynamic variable thus changes the initial CARP model where the existing model did not consider other external elements that have effected onto the model. Approach: Then we developed and enhanced CARP by integrating stochastic demand and time windows to suit the models with our specific case. Results: Objectively, CARP with stochastic demand (CARPSD and CARP with time windows (CARPTW were designed to minimize the total routing cost and number of trips for a vehicle. Our approach is to design CARP models in almost likely to road layout in residential area and graphically this model is called mesh network. We also developed a constructive heuristic that is called nearest procedure based on highest demand/cost (NPHDC and work in conjunction with switching rules to search the feasible solution. Conclusion: Our preliminary results show a higher cost and more trips are needed when the vehicle operates in rainy day compared to normal day operation.
Cumulative Vehicle Routing Problems
Kara, &#;mdat; Kara, Bahar Yeti&#;; Yeti&#;, M. Kadri
2008-01-01
This paper proposes a new objective function and corresponding formulations for the vehicle routing problem. The new cost function defined as the product of the distance of the arc and the flow on that arc. We call a vehicle routing problem with this new objective function as the Cumulative Vehicle Routing Problem (CumVRP). Integer programming formulations with O(n2) binary variables and O(n2) constraints are developed for both collection and delivery cases. We show that the CumVRP is a gener...
A lower bound for the node, edge, and arc routing problem
DEFF Research Database (Denmark)
Bach, Lukas; Hasle, Geir; Wøhlk, Sanne
2013-01-01
called the CBMix benchmark. The NEARP definition and investigation contribute to the development of rich VRPs. In this paper we present the first lower bound procedure for the NEARP. It is a further development of lower bounds for the CARP. We also define two novel sets of test instances to complement...... the CBMix benchmark. The first is based on well-known CARP instances; the second consists of real life cases of newspaper delivery routing. We provide numerical results in the form of lower and best known upper bounds for all instances of all three benchmarks. For three of the instances, the gap between...
Routing and scheduling problems
DEFF Research Database (Denmark)
Reinhardt, Line Blander
be that the objects routed have an availability time window and a delivery time window or that locations on the path have a service time window. When routing moving transportation objects such as vehicles and vessels schedules are made in connection with the routing. Such schedules represent the time for the presence...... to a destination on a predefined network, the routing and scheduling of vessels in a liner shipping network given a demand forecast to be covered, the routing of manpower and vehicles transporting disabled passengers in an airport and the vehicle routing with time windows where one version studied includes edge...... of a connection between two locations. This could be an urban bus schedule where busses are routed and this routing creates a bus schedule which the passengers between locations use. In this thesis various routing and scheduling problems will be presented. The topics covered will be routing from an origin...
Energy Technology Data Exchange (ETDEWEB)
Laporte, G.
1987-01-01
Location-routing problems involve simultaneously locating a number of facilities among candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. This paper presents a survey of such problems. It includes some applications and examples of location-routing problems, a description of the main heuristics that have been developed for such problems, and reviews of various formulations and algorithms used in solving these problems. A more detailed review is given of exact algorithms for the vehicle routing problem, three-index vehicle flow formulations, and two-index vehicle flow formulations and algorithms for symmetrical and non-symmetrical problems. It is concluded that location-routing problem research is a fast-growing area, with most developments occurring over the past few years; however, research is relatively fragmented, often addresses problems which are too specific and contains several voids which have yet to be filled. A number of promising research areas are identified. 137 refs., 3 figs.
Vehicle Routing Problem Models
Directory of Open Access Journals (Sweden)
Tonči Carić
2004-01-01
Full Text Available The Vehicle Routing Problem cannot always be solved exactly,so that in actual application this problem is solved heuristically.The work describes the concept of several concrete VRPmodels with simplified initial conditions (all vehicles are ofequal capacity and start from a single warehouse, suitable tosolve problems in cases with up to 50 users.
A branch-and-cut-and-price algorithm for the mixed capacitated general routing problem
DEFF Research Database (Denmark)
Bach, Lukas; Wøhlk, Sanne; Lysgaard, Jens
2016-01-01
In this paper, we consider the Mixed Capacitated General Routing Problem which is a combination of the Capacitated Vehicle Routing Problem and the Capacitated Arc Routing Problem. The problem is also known as the Node, Edge, and Arc Routing Problem. We propose a Branch-and-Cut-and-Price algorithm...
Routing and scheduling problems
DEFF Research Database (Denmark)
Reinhardt, Line Blander
In today’s globalized society, transport contributes to our daily life in many different ways. The production of the parts for a shelf ready product may take place on several continents and our travel between home and work, vacation travel and business trips has increased in distance the last......, the effectiveness of the network is of importance aiming at satisfying as many costumer demands as possible at a low cost. Routing represent a path between locations such as an origin and destination for the object routed. Sometimes routing has a time dimension as well as the physical paths. This may...... to a destination on a predefined network, the routing and scheduling of vessels in a liner shipping network given a demand forecast to be covered, the routing of manpower and vehicles transporting disabled passengers in an airport and the vehicle routing with time windows where one version studied includes edge...
Waste Collection Vehicle Routing Problem: Literature Review
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Hui Han
2015-08-01
Full Text Available Waste generation is an issue which has caused wide public concern in modern societies, not only for the quantitative rise of the amount of waste generated, but also for the increasing complexity of some products and components. Waste collection is a highly relevant activity in the reverse logistics system and how to collect waste in an efficient way is an area that needs to be improved. This paper analyzes the major contribution about Waste Collection Vehicle Routing Problem (WCVRP in literature. Based on a classification of waste collection (residential, commercial and industrial, firstly the key findings for these three types of waste collection are presented. Therefore, according to the model (Node Routing Problems and Arc Routing problems used to represent WCVRP, different methods and techniques are analyzed in this paper to solve WCVRP. This paper attempts to serve as a roadmap of research literature produced in the field of WCVRP.
Heuristic methods for a refuse collection vehicle routing problem
Energy Technology Data Exchange (ETDEWEB)
Mourao, M.C.; Almeida, M.T.
1994-12-31
The problem of generating the set of routes that minimizes the total time required to collect the household refuse in a particular quarter of Lisbon can be formulated as a Capacitated Arc Routing Problem with some side constraints. Our aim is to obtain approximate solutions, as the problem is known to be NP-hard. We present heuristic methods to generate feasible solutions and report their performance over a set of test problems.
The Consistent Vehicle Routing Problem
Energy Technology Data Exchange (ETDEWEB)
Groer, Christopher S [ORNL; Golden, Bruce [University of Maryland; Edward, Wasil [American University
2009-01-01
In the small package shipping industry (as in other industries), companies try to differentiate themselves by providing high levels of customer service. This can be accomplished in several ways, including online tracking of packages, ensuring on-time delivery, and offering residential pickups. Some companies want their drivers to develop relationships with customers on a route and have the same drivers visit the same customers at roughly the same time on each day that the customers need service. These service requirements, together with traditional constraints on vehicle capacity and route length, define a variant of the classical capacitated vehicle routing problem, which we call the consistent VRP (ConVRP). In this paper, we formulate the problem as a mixed-integer program and develop an algorithm to solve the ConVRP that is based on the record-to-record travel algorithm. We compare the performance of our algorithm to the optimal mixed-integer program solutions for a set of small problems and then apply our algorithm to five simulated data sets with 1,000 customers and a real-world data set with more than 3,700 customers. We provide a technique for generating ConVRP benchmark problems from vehicle routing problem instances given in the literature and provide our solutions to these instances. The solutions produced by our algorithm on all problems do a very good job of meeting customer service objectives with routes that have a low total travel time.
Adaptive Memory Procedure to solve the Profitable Arc Tour Problem
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Jalel Euchi
2010-05-01
Full Text Available In this paper we propose an Adaptive memory procedure to solve the Profitable Arc Tour Problem (PATP. The PATP is a variant of the well-known Vehicle Routing Problems in which a set of vehicle tours are constructed. The objective is to find a set of cycles in the vehicle tours that maximize the collection of profits minus travel costs, subject to constraints limiting the length of cycles that profit is available on arcs. Computational experiments show that our algorithms provide good results in terms of quality of solution and running times.
The pyramidal capacitated vehicle routing problem
DEFF Research Database (Denmark)
Lysgaard, Jens
2010-01-01
This paper introduces the pyramidal capacitated vehicle routing problem (PCVRP) as a restricted version of the capacitated vehicle routing problem (CVRP). In the PCVRP each route is required to be pyramidal in a sense generalized from the pyramidal traveling salesman problem (PTSP). A pyramidal...
A Genetic Algorithm on Inventory Routing Problem
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Nevin Aydın
2014-03-01
Full Text Available Inventory routing problem can be defined as forming the routes to serve to the retailers from the manufacturer, deciding on the quantity of the shipment to the retailers and deciding on the timing of the replenishments. The difference of inventory routing problems from vehicle routing problems is the consideration of the inventory positions of retailers and supplier, and making the decision accordingly. Inventory routing problems are complex in nature and they can be solved either theoretically or using a heuristics method. Metaheuristics is an emerging class of heuristics that can be applied to combinatorial optimization problems. In this paper, we provide the relationship between vendor-managed inventory and inventory routing problem. The proposed genetic for solving vehicle routing problem is described in detail.
Route Elimination Heuristic for Vehicle Routing Problem with Time Windows
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Sándor Csiszár
2005-11-01
Full Text Available The paper deals with the design of a route elimination (RE algorithm for thevehicle routing problem with time windows (VRPTW. The problem has two objectives, oneof them is the minimal number of routes the other is the minimal cost. To cope with theseobjectives effectively two-phase solutions are often suggested in the relevant literature. Inthe first phase the main focus is the route elimination, in the second one it is the costreduction. The algorithm described here is a part of a complete VRPWT study. The methodwas developed by studying the graph behaviour during the route elimination. For thispurpose a model -called “Magic Bricks” was developed. The computation results on theSolomon problem set show that the developed algorithm is competitive with the best ones.
Vehicle routing problem in investment fund allocation
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita; Mohd, Ismail
2013-04-01
Since its introduction by Dantzig and Ramser in 1959, vehicle routing problem keeps evolving in theories, applications and variability. The evolution in computing and technology are also important contributors to research in solving vehicle routing problem. The main sectors of interests among researchers and practitioners for vehicle routing problem are transportation, distribution and logistics. However, literature found that concept and benefits of vehicle routing problem are not taken advantages of by researchers in the field of investment. Other methods found used in investment include multi-objective programming, linear programming, goal programming and integer programming. Yet the application of vehicle routing problem is not fully explored. A proposal on a framework of the fund allocation optimization using vehicle routing problem is presented here. Preliminary results using FTSE Bursa Malaysia data testing the framework are also given.
On green routing and scheduling problem
Touati, Nora
2012-01-01
The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools.
On green routing and scheduling problem
Touati, Nora; Jost, Vincent
2011-01-01
The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools.
The Pyramidal Capacitated Vehicle Routing Problem
DEFF Research Database (Denmark)
Lysgaard, Jens
This paper introduces the Pyramidal Capacitated Vehicle Routing Problem (PCVRP) as a restricted version of the Capacitated Vehicle Routing Problem (CVRP). In the PCVRP each route is required to be pyramidal in a sense generalized from the Pyramidal Traveling Salesman Problem (PTSP). A pyramidal...... found in many optimal solutions to CVRP instances. An optimal solution to the PCVRP may therefore be useful in itself as a heuristic solution to the CVRP. Further, an attempt can be made to find an even better CVRP solution by solving a TSP, possibly leading to a non-pyramidal route, for each...... of the routes in the PCVRP solution. This paper develops an exact branch-and-cut-and-price (BCP) algorithm for the PCVRP. At the pricing stage, elementary routes can be computed in pseudo-polynomial time in the PCVRP, unlike in the CVRP. We have therefore implemented pricing algorithms that generate only...
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah@Rozita
2016-11-01
Two new methods adopted from methods commonly used in the field of transportation and logistics are proposed to solve a specific issue of investment allocation problem. Vehicle routing problem and capacitated vehicle routing methods are applied to optimize the fund allocation of a portfolio of investment assets. This is done by determining the sequence of the assets. As a result, total investment risk is minimized by this sequence.
A model for routing problem in quay management problem
Zirour, Mourad; Oughalime, Ahmed; Liong, Choong-Yeun; Ismail, Wan Rosmanira; Omar, Khairuddin
2014-06-01
Quadratic Assignment Problem (QAP), like Vehicle Routing Problem, is one of those optimization problems that interests many researchers in the last decades. The Quay Management Problem is a specific problem which could be presented as a QAP which involves a double assignment of customers and products toward loading positions using lifting trucks. This study focuses on the routing problem while delivering the customers' demands. In this problem, lifting trucks will route around the storage sections to collect the products then deliver to the customers who are assigned to specific loading positions. The objective of minimizing the residence time for each customer is sought. This paper presents the problem and the proposed model.
Subset-row inequalities applied to the vehicle routing problem with time windows
DEFF Research Database (Denmark)
Jepsen, Mads Kehlet; Petersen, Bjørn; Spoorendonk, Simon;
2008-01-01
This paper presents a branch-and-cut-and-price algorithm for the vehicle-routing problem with time windows. The standard Dantzig-Wolfe decomposition of the arc flow formulation leads to a set-partitioning problem as the master problem and an elementary shortest-path problem with resource...
Rich Vehicle Routing Problems and Applications
DEFF Research Database (Denmark)
Wen, Min
the company’s solution in terms of all the objectives, including the travel time, customer waiting and daily workload balances, under the given constraints considered in the work. Finally, we address an integrated vehicle routing and driver scheduling problem, in which a large number of practical constraints......The Vehicle Routing Problem (VRP) is one of the most important and challenging optimization problems in the field of Operations Research. It was introduced by Dantzig and Ramser (1959) and defined as the problem of designing the optimal set of routes for a fleet of vehicles in order to serve...... given to various extensions of the VRP that arise in real life. These extensions are often called Rich Vehicle Routing Problems (RVRPs). In contrast to the research of classical VRP that focuses on the idealized models with unrealistic assumptions, the research of RVRPs considers those complicated...
Routing problems based on hils system platform
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Andrzej Adamski
2015-03-01
Full Text Available Background: The logistic systems are very complex socio-technical systems. In this paper the proposal of application of the hierarchical multi-layers system platform HILS approach for the solution of the complex vehicle routing problems is presented. The interactive system functional structure was proposed which by intelligent dedicated inter-layers interactions enables the professional solutions of these practical problems. To illustrate these capabilities the complex example of the real-time VRP-SPD-TW routing problem was presented in which upper layers offers the context-related real-time updating network specifications that stimulates the adequate routing parameters and specifications updating for problem solution in optimization layer. At the bottom dispatching control layer the DISCON (Dispatching CONtrol method from public transport was adopted to logistics applications in which the actual routing is treated as obligatory reference schedule to be stabilized. The intelligence aspects are related among others to HILS based decomposition, context-related trade-offs between routing modifications and corrective dispatching control capabilities e.g. priority or route guidance actions. Methods: Decomposition of the vehicle routing problem for the HILS layers tasks creating the ILS system hierarchical structure. Dedicated solution method for the VRP-SPD-TW routing problem. The recognition of the control preferences structure by AHP-Entropy methods. DISCON and PIACON multi-criteria interacting control methods. Results: Original formulation and solution of the vehicle routing problem by system-wide approach with essential practical advantages: consistency, lack of redundancy, essential reduction of dimension, dedicated formulation, multi-criteria approach, exploration of the integration and intelligence features supported by the intelligent PIACON-DISCON methods control activities Conclusions: The presented proposal creates the professional
Genetic algorithms for the vehicle routing problem
Volna, Eva
2016-06-01
The Vehicle Routing Problem (VRP) is one of the most challenging combinatorial optimization tasks. This problem consists in designing the optimal set of routes for fleet of vehicles in order to serve a given set of customers. Evolutionary algorithms are general iterative algorithms for combinatorial optimization. These algorithms have been found to be very effective and robust in solving numerous problems from a wide range of application domains. This problem is known to be NP-hard; hence many heuristic procedures for its solution have been suggested. For such problems it is often desirable to obtain approximate solutions, so they can be found fast enough and are sufficiently accurate for the purpose. In this paper we have performed an experimental study that indicates the suitable use of genetic algorithms for the vehicle routing problem.
Integrating routing decisions in public transportation problems
Schmidt, Marie E
2014-01-01
This book treats three planning problems arising in public railway transportation planning: line planning, timetabling, and delay management, with the objective to minimize passengers’ travel time. While many optimization approaches simplify these problems by assuming that passengers’ route choice is independent of the solution, this book focuses on models which take into account that passengers will adapt their travel route to the implemented planning solution. That is, a planning solution and passengers’ routes are determined and evaluated simultaneously. This work is technically deep, with insightful findings regarding complexity and algorithmic approaches to public transportation problems with integrated passenger routing. It is intended for researchers in the fields of mathematics, computer science, or operations research, working in the field of public transportation from an optimization standpoint. It is also ideal for students who want to gain intuition and experience in doing complexity proofs ...
Analytical Analysis of Vehicle Routing and Inventory Routing Problems
2007-11-02
The objective of the project is to perform analytical analyses of heuristics for the Vehicle Routing Problem ( VRP ) and apply the results in models...asymptotic optimal solution value of the VRP with capacity and time window constraints and used it to develop a new and efficient algorithm. (2) Obtained a...characterization of the effectiveness of set partitioning formulations for VRPs . (3) Characterized the worst case behavior of the linear programming
The Balanced Billing Cycle Vehicle Routing Problem
Energy Technology Data Exchange (ETDEWEB)
Groer, Christopher S [ORNL; Golden, Bruce [University of Maryland; Edward, Wasil [American University
2009-01-01
Utility companies typically send their meter readers out each day of the billing cycle in order to determine each customer s usage for the period. Customer churn requires the utility company to periodically remove some customer locations from its meter-reading routes. On the other hand, the addition of new customers and locations requires the utility company to add newstops to the existing routes. A utility that does not adjust its meter-reading routes over time can find itself with inefficient routes and, subsequently, higher meter-reading costs. Furthermore, the utility can end up with certain billing days that require substantially larger meter-reading resources than others. However, remedying this problem is not as simple as it may initially seem. Certain regulatory and customer service considerations can prevent the utility from shifting a customer s billing day by more than a few days in either direction. Thus, the problem of reducing the meterreading costs and balancing the workload can become quite difficult. We describe this Balanced Billing Cycle Vehicle Routing Problem in more detail and develop an algorithm for providing solutions to a slightly simplified version of the problem. Our algorithm uses a combination of heuristics and integer programming via a three-stage algorithm. We discuss the performance of our procedure on a real-world data set.
A Survey of Vehicle Routing Problem
Directory of Open Access Journals (Sweden)
Cao Wujun
2017-01-01
Full Text Available In recent years, vehicle routing problem (VRP has become an important content in logistics management research, and has been widely used in transportation system, logistics distribution system and express delivery system. In this paper, we discuss the classification of VRP, and summarize the common constraints of VRP, model algorithm and the main research results in recent years. Finally, we analyzes the future of VRP, and it is considered that the intelligent vehicle routing problem and intelligent heuristic algorithm will be an important field of future research.
Overview of Stochastic Vehicle Routing Problems
Institute of Scientific and Technical Information of China (English)
郭耀煌; 谢秉磊; 郭强
2002-01-01
Stochastic vehicle routing problems (VRPs) play important roles in logistics, though they have not been studied systematically yet. The paper summaries the definition, properties and classification of stochastic VRPs, makes further discussion about two strategies in stochastic VRPs, and at last overviews dynamic and stochastic VRPs.
Fund allocation using capacitated vehicle routing problem
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita; Darus, Maslina
2014-09-01
In investment fund allocation, it is unwise for an investor to distribute his fund into several assets simultaneously due to economic reasons. One solution is to allocate the fund into a particular asset at a time in a sequence that will either maximize returns or minimize risks depending on the investor's objective. The vehicle routing problem (VRP) provides an avenue to this issue. VRP answers the question on how to efficiently use the available fleet of vehicles to meet a given service demand, subjected to a set of operational requirements. This paper proposes an idea of using capacitated vehicle routing problem (CVRP) to optimize investment fund allocation by employing data of selected stocks in the FTSE Bursa Malaysia. Results suggest that CRVP can be applied to solve the issue of investment fund allocation and increase the investor's profit.
Full truckload vehicle routing problem with profits
Directory of Open Access Journals (Sweden)
Jian Li
2014-04-01
Full Text Available A new variant of the full truckload vehicle routing problem is studied. In this problem there are more than one delivery points corresponding to the same pickup point, and one order is allowed to be served several times by the same vehicle or different vehicles. For the orders which cannot be assigned because of resource constraint, the logistics company outsources them to other logistics companies at a certain cost. To maximize its profits, logistics company decides which to be transported by private fleet and which to be outsourced. The mathematical model is constructed for the problem. Since the problem is NP-hard and it is difficult to solve the large-scale problems with an exact algorithm, a hybrid genetic algorithm is proposed. Computational results show the effectiveness of the hybrid genetic algorithm.
Use of Interactive Computer Graphics to Solve Routing Problems.
Gillett, B. E.; Lawrence, J. L.
1981-01-01
Discusses vehicle routing problems and solutions. Describes testing of an interactive computer graphics package combining several types of solutions that allows users with little or no experience to work out routing problems. (Author/RW)
The vehicle routing problem with backhauls
Energy Technology Data Exchange (ETDEWEB)
Goetschalckx, M.; Jacobs-Blecha, C.
1989-09-05
The Vehicle Routing Problem with Backhauls is a pickup/delivery problem where on each route all deliveries must be made before any pickups. A two-phased solution methodology is proposed. In the first phase, a high quality initial feasible solution is generated based on spacefilling curves. In the second phase, this solution is improved based on optimization of the subproblems identified in a mathematical model of the problem. An extensive computational analysis of several initial solution algorithms is presented, which identifies the tradeoffs between solution quality and computational requirements. The class of greedy algorithms is capacity oriented, while K-median algorithms focus on distance. It is concluded that the greedy and K-median algorithms generate equivalent tour lengths, but that the greedy procedure reduces the required number of trucks and increases the truck utilization. The effect of exchange improvement procedures as well as optimal procedures on solution quality and run time is demonstrated. Comparisons with the Clark-Wright method adapted to backhauls are also given. 4 figs., 26 refs.
Approximation algorithms for some vehicle routing problems
Bazgan, Cristina; Hassin, Refael; Monnot, Jérôme
2005-01-01
We study vehicle routing problems with constraints on the distance traveled by each vehicle or on the number of vehicles. The objective is either to minimize the total distance traveled by vehicles or to minimize the number of vehicles used. We design constant differential approximation algorithms for kVRP. Note that, using the differential bound for METRIC 3VRP, we obtain the randomized standard ratio . This is an improvement of the best-known bound of 2 given by Haimovich et al. (Vehicle Ro...
Improved Ant Colony Optimization for Seafood Product Delivery Routing Problem
Directory of Open Access Journals (Sweden)
Baozhen Yao
2014-02-01
Full Text Available This paper deals with a real-life vehicle delivery routing problem, which is a seafood product delivery routing problem. Considering the features of the seafood product delivery routing problem, this paper formulated this problem as a multi-depot open vehicle routing problem. Since the multi-depot open vehicle routing problem is a very complex problem, a method is used to reduce the complexity of the problem by changing the multi-depot open vehicle routing problem into an open vehicle routing problem with a dummy central depot in this paper. Then, ant colony optimization is used to solve the problem. To improve the performance of the algorithm, crossover operation and some adaptive strategies are used. Finally, the computational results for the benchmark problems of the multi-depot vehicle routing problem indicate that the proposed ant colony optimization is an effective method to solve the multi-depot vehicle routing problem. Furthermore, the computation results of the seafood product delivery problem from Dalian, China also suggest that the proposed ant colony optimization is feasible to solve the seafood product delivery routing problem.
Disruption management of the vehicle routing problem with vehicle breakdown
DEFF Research Database (Denmark)
Mu, Q; Fu, Z; Lysgaard, Jens
2011-01-01
This paper introduces a new class of problem, the disrupted vehicle routing problem (VRP), which deals with the disruptions that occur at the execution stage of a VRP plan. The paper then focuses on one type of such problem, in which a vehicle breaks down during the delivery and a new routing sol...
The vehicle routing problem with time windows and temporal dependencies
DEFF Research Database (Denmark)
Dohn, Anders Høeg; Rasmussen, Matias Sevel; Larsen, Jesper
2011-01-01
In this article, we formulate the vehicle routing problem with time windows and temporal dependencies. The problem is an extension of the well studied vehicle routing problem with time windows. In addition to the usual constraints, a scheduled time of one visit may restrain the scheduling options...
An approximate algorithm for solving the watchman route problem
Li, Fajie; Klette, Reinhard; Sommer, G; Klette, R
2008-01-01
The watchman route problem (WRP) was first introduced in 1988 and is defined as follows: How to calculate a shortest route completely contained inside a simple polygon such that any point inside this polygon is visible from at least one point on the route? So far the best known result for the WRP is
Solving Segment Routing Problems with Hybrid Constraint Programming Techniques
Hartert, Renaud; Schaus, Pierre; Vissicchio, Stefano; Bonaventure, Olivier; International Conference on Principles and Practice of Constraint Programming (CP2014)
2015-01-01
Segment routing is an emerging network technology that exploits the existence of several paths between a source and a destination to spread the traffic in a simple and elegant way. The major commercial network vendors already support segment routing, and several Internet actors are ready to use segment routing in their network. Unfortunately, by changing the way paths are computed, segment routing poses new op- timization problems which cannot be addressed with previous research contributions...
A Tabu Search Heuristic for the Vehicle Routing Problem
1994-01-01
The purpose of this paper is to describe TABUROUTE, a new tabu search heuristic for the vehicle routing problem with capacity and route length restrictions. The algorithm considers a sequence of adjacent solutions obtained by repeatedly removing a vertex from its current route and reinserting it into another route. This is done by means of a generalized insertion procedure previously developed by the authors. During the course of the algorithm, infeasible solutions are allowed. Numerical test...
OPTIMIZATION OF CAPACITATED VEHICLE ROUTING PROBLEM USING PSO
Directory of Open Access Journals (Sweden)
S.R.VENKATESAN
2011-10-01
Full Text Available This paper presents solution techniques for Capacitated Vehicle Routing Problem (CVRP using metaheuristics. Capacitated Vehicle Routing Problem is divided into set of customers called cluster, and find optimum travel distance of vehicle route. The CVRP is a combinatorial optimization problem; particle swarm optimization(PSO technique is adapted in this paper to solve this problem. The main problem is divided into subprograms/clusters and each subprogram is treated as travelling salesman problem and solved by usingparticle swarm optimization techniques (PSO. This paper presents a sweep, Clark and wright algorithm to form the clusters. This model is then solved by using a particle swarm optimization (PSO method to find optimum travel distance of vehicle route. Our analysis suggests that the proposed model enables users to establish route to serve all given customers with minimum distance of vehicles and maximum capacity.
About some types of constraints in problems of routing
Petunin, A. A.; Polishuk, E. G.; Chentsov, A. G.; Chentsov, P. A.; Ukolov, S. S.
2016-12-01
Many routing problems arising in different applications can be interpreted as a discrete optimization problem with additional constraints. The latter include generalized travelling salesman problem (GTSP), to which task of tool routing for CNC thermal cutting machines is sometimes reduced. Technological requirements bound to thermal fields distribution during cutting process are of great importance when developing algorithms for this task solution. These requirements give rise to some specific constraints for GTSP. This paper provides a mathematical formulation for the problem of thermal fields calculating during metal sheet thermal cutting. Corresponding algorithm with its programmatic implementation is considered. The mathematical model allowing taking such constraints into account considering other routing problems is discussed either.
Genetic algorithm to solve constrained routing problem with applications for cruise missile routing
Latourell, James L.; Wallet, Bradley C.; Copeland, Bruce
1998-03-01
In this paper the use of a Genetic Algorithm to solve a constrained vehicle routing problem is explored. The problem is two-dimensional with obstacles represented as ellipses of uncertainty surrounding each obstacle point. A route is defined as a series of points through which the vehicle sequentially travels from the starting point to the ending point. The physical constraints of total route length and maximum turn angle are included and appear in the fitness function. In order to be valid, a route must go from start to finish without violating any constraint. The effects that different mutation rates and population sizes have on the algorithm's computation speed and ability to find a high quality route are also explored. Finally, possible applications of this algorithm to the problem of route planning for cruise missiles are discussed.
Open Vehicle Routing Problem by Ant Colony Optimization
Directory of Open Access Journals (Sweden)
Er. Gurpreet Singh
2014-01-01
Full Text Available Vehicle routing problem (VRP is real-world combinatorial optimization problem which determine the optimal route of a vehicle. Generally, toprovide the efficientvehicle serving to the customer through different services by visiting the number of cities or stops. The VRP follows the Travelling Salesman Problem (TSP, in which each of vehicle visiting a set of cities such that every city is visited by exactly one vehicle only once. This work proposes the Ant Colony Optimization (ACO-TSP algorithm to eliminate the tour loop for Open Vehicle routing Problem (OVRP. A key aspect of this algorithm is to plan the routes of buses that must pick up and deliver the school students from various bus stops on time, especially in the case of far distance covered by the vehicle in a rural area and find out the efficient and safe vehicle route.
Directory of Open Access Journals (Sweden)
Yan Sun
2015-01-01
Full Text Available We explore a freight routing problem wherein the aim is to assign optimal routes to move commodities through a multimodal transportation network. This problem belongs to the operational level of service network planning. The following formulation characteristics will be comprehensively considered: (1 multicommodity flow routing; (2 a capacitated multimodal transportation network with schedule-based rail services and time-flexible road services; (3 carbon dioxide emissions consideration; and (4 a generalized costs optimum oriented to customer demands. The specific planning of freight routing is thus defined as a capacitated time-sensitive multicommodity multimodal generalized shortest path problem. To solve this problem systematically, we first establish a node-arc-based mixed integer nonlinear programming model that combines the above formulation characteristics in a comprehensive manner. Then, we develop a linearization method to transform the proposed model into a linear one. Finally, a computational experiment from the Chinese inland container export business is presented to demonstrate the feasibility of the model and linearization method. The computational results indicate that implementing the proposed model and linearization method in the mathematical programming software Lingo can effectively solve the large-scale practical multicommodity multimodal transportation routing problem.
The Vehicle Routing Problem with Time Windows and Temporal Dependencies
DEFF Research Database (Denmark)
Rasmussen, Matias Sevel; Dohn, Anders Høeg; Larsen, Jesper
assignment and routing problem with synchronization constraints. The problem has been solved by column generation. The synchronized vehicle dispatching problem (SVDP), which is a dynamic vehicle routing problem with synchronization between vehicles. Constraint programming and local search are applied...... to be scheduled with a certain slack between them. They refer to the vehicle problem as having interdependent time windows. Temporal dependencies have been modeled for a home care routing problem in a mixed integer programming model (MIP) which was solved with a standard MIP solver. An application with general...... temporal dependencies is also found in machine scheduling. Column generation is used to solve the problem. The pricing problem is primarily solved heuristically by local search and occasionally to optimality using a standard solver on an integer programming formulation of the pricing problem. Two compact...
Cobweb heuristic for multi-objective vehicle routing problem
Joseph Okitonyumbe Y. F; Berthold Ulungu E.-L; Joel Kapiamba Nt.
2015-01-01
Solving a classical vehicle routing problem (VRP) by exact methods presents many difficulties for large dimension problem. Consequently, in multi-objective framework, heuristic or metaheuristic methods are required. Due to particular VRP structure, it seems that a dedicated heuristicis more suitable than a metaheuristic. The aim of this article is to collapse different heuristics solving classical VRP and adapt them for to solve the multi-objective vehicle routing problem (MOVRP). The so-call...
Cobweb Heuristic for solving Multi-Objective Vehicle Routing Problem
Okitonyumbe Y.F., Joseph; Ulungu, Berthold E.-L.; Kapiamba Nt., Joel
2015-01-01
Abstract Solving a classical vehicle routing problem (VRP) by exact methods presents many difficulties for large dimension problem. Consequently, in multi-objective framework, heuristic or metaheuristic methods are required. Due to particular VRP structure, it seems that a dedicated heuristic is more suitable than a metaheuristic. The aim of this article is to collapse different heuristics solving classical VRP and adapt them for to solve the multi-objective vehicle routing problem (MOVRP)...
Optimizing investment fund allocation using vehicle routing problem framework
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita
2014-07-01
The objective of investment is to maximize total returns or minimize total risks. To determine the optimum order of investment, vehicle routing problem method is used. The method which is widely used in the field of resource distribution shares almost similar characteristics with the problem of investment fund allocation. In this paper we describe and elucidate the concept of using vehicle routing problem framework in optimizing the allocation of investment fund. To better illustrate these similarities, sectorial data from FTSE Bursa Malaysia is used. Results show that different values of utility for risk-averse investors generate the same investment routes.
Polynomial Size Formulations for the Distance and Capacity Constrained Vehicle Routing Problem
Kara, Imdat; Derya, Tusan
2011-09-01
The Distance and Capacity Constrained Vehicle Routing Problem (DCVRP) is an extension of the well known Traveling Salesman Problem (TSP). DCVRP arises in distribution and logistics problems. It would be beneficial to construct new formulations, which is the main motivation and contribution of this paper. We focused on two indexed integer programming formulations for DCVRP. One node based and one arc (flow) based formulation for DCVRP are presented. Both formulations have O(n2) binary variables and O(n2) constraints, i.e., the number of the decision variables and constraints grows with a polynomial function of the nodes of the underlying graph. It is shown that proposed arc based formulation produces better lower bound than the existing one (this refers to the Water's formulation in the paper). Finally, various problems from literature are solved with the node based and arc based formulations by using CPLEX 8.0. Preliminary computational analysis shows that, arc based formulation outperforms the node based formulation in terms of linear programming relaxation.
Tawanda’s non- iterative optimal tree algorithm for shortest route problems
Directory of Open Access Journals (Sweden)
Trust Tawanda
2013-03-01
Full Text Available So many algorithms have been proposed to solve the shortest path in road networks, in this paper, an algorithm is developed to solve shortest route problems. The algorithm is being demonstrated through solving of various network problems. The principle of the algorithm consist in transforming the graph into a tree by means of arc and node replication, thereby expanding outwards from the source node considering all possible paths up to the destination node. The objective is to develop a method that can be applied in directed and non-directed graphs.
Study on model and algorithm of inventory routing problem
Wan, Fengjiao
Vehicle routing problem(VRP) is one of important research in the logistics system. Nowadays, there are many researches on the VRP, but their don't consider the cost of inventory. Thus, the conclusion doesn't meet reality. This paper studies on the inventory routing problem (IRP)and uses one target function to describe these two conflicting problems, which are very important in the logistics optimization. The paper establishes the model of single client and many clients' inventory routing problem. An optimizing iterative algorithm is presented to solve the model. According to the model we can confirm the best quantity, efficiency and route of delivery. Finally, an example is given to illustrate the efficiency of model and algorithm.
A Sweep Coverage Scheme Based on Vehicle Routing Problem
Directory of Open Access Journals (Sweden)
Li Shu
2013-04-01
Full Text Available As an emerging coverage problem in wireless sensor networks, sweep coverage which introducing mobile sensors to cover points of interest within certain time interval can satisfy monitoring request in some particular application scenarios with less number of nodes than the conventional static coverage approach. In this work, aiming to support dynamical POI coverage and data delivery simultaneously, a novel sweep coverage scheme, named VRPSC(Vehicle Routing Problem based Sweep Coverage, is proposed by modeling the minimum number of required sensors problem in sweep coverage as a Vehicle Routing Problem (VRP. In VRPSC, an insertion algorithm is first introduced to create the initial scanning routes for POIs, and then the Simulated Annealing is employed to optimize these routes. The simulation results show that the VRPSC scheme achieves better performance than existing schemes.
Solving the Vehicle Routing Problem using Genetic Algorithm
Directory of Open Access Journals (Sweden)
Abdul Kadar Muhammad Masum
2011-08-01
Full Text Available The main goal of this research is to find a solution of Vehicle Routing Problem using genetic algorithms. The Vehicle Routing Problem (VRP is a complex combinatorial optimization problem that belongs to the NP-complete class. Due to the nature of the problem it is not possible to use exact methods for large instances of the VRP. Genetic algorithms provide a search technique used in computing to find true or approximate solution to optimization and search problems. However we used some heuristic in addition during crossover or mutation for tuning the system to obtain better result.
Branch and price for the time-dependent vehicle routing problem with time windows
DEFF Research Database (Denmark)
Dabia, Said; Van Woensel, Tom; De Kok, Ton
2013-01-01
solution methods to the DM-TDVRPTW are based on (meta-)heuristics. The decomposition of an arc-based formulation leads to a setpartitioning problem as the master problem, and a time-dependent shortest path problem with resource constraints as the pricing problem. The master problem is solved by means...... of column generation, and a tailored labeling algorithm is used to solve the pricing problem. We introduce new dominance criteria that allow more label dominance. For our numerical results, we modified Solomon's data sets by adding time dependency. Our algorithm is able to solve about 63% of the instances......This paper presents a branch-and-price algorithm for the time-dependent vehicle routing problem with time windows (TDVRPTW). We capture road congestion by considering time-dependent travel times, i.e., depending on the departure time to a customer, a different travel time is incurred. We consider...
A survey on multi trip vehicle routing problem
2008-01-01
The vehicle routing problem (VRP) and its variants are well known and greatly explored in the transportation literature. The vehicle routing problem can be considered as the scheduling of vehicles (trucks) to a set of customers under various side constraints. In most studies, a fundamental assumption is that a vehicle dispatched for service finishes its duty in that scheduling period after it returns back to the depot. Clearly, in many cases this assumption may not hold. Thus, in the last dec...
A matheuristic approach for the Pollution-Routing Problem
Kramer, Raphael; Subramanian, Anand; Vidal, Thibaut; Cabral, Lucídio dos Anjos Formiga
2014-01-01
This paper deals with the Pollution-Routing Problem (PRP), a Vehicle Routing Problem (VRP) with environmental considerations, recently introduced in the literature by [Bektas and Laporte (2011), Transport. Res. B-Meth. 45 (8), 1232-1250]. The objective is to minimize operational and environmental costs while respecting capacity constraints and service time windows. Costs are based on driver wages and fuel consumption, which depends on many factors, such as travel distance and vehicle load. Th...
Heuristic for vehicle routing problem with release and due dates
Johar, Farhana; Potts, Chris; Bennell, Julia
2014-06-01
This research is classifies as non-classical Vehicle Routing Problem (VRP) where the maximum release date of customer's demand of the route determine the vehicle departure time. Thus, there could be lateness on the delivery process from awaiting all customers' demand of the route to be released. A mathematical formulation is developed to represent the problem studied. Insertion method based on the cheapest cost is used to generate an initial solution. Then, Local Search technique is applied to improve the solution in term of minimization of total traveling and tardiness cost.
The Service-Time Restricted Capacitated Arc Routing Problem
DEFF Research Database (Denmark)
Lystlund, Lise; Wøhlk, Sanne
, it may be sensible to make reservations for the order in the inventory system, thereby preventing later arriving orders from getting access to the inventory before this particular order. We propose various reservation policies and study their impact on the performance of the inventory system....
Multicast Routing Problem Using Tree-Based Cuckoo Optimization Algorithm
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Mahmood Sardarpour
2016-06-01
Full Text Available The problem of QoS multicast routing is to find a multicast tree with the least expense/cost which would meet the limitations such as band width, delay and loss rate. This is a NP-Complete problem. To solve the problem of multicast routing, the entire routes from the source node to every destination node are often recognized. Then the routes are integrated and changed into a single multicast tree. But they are slow and complicated methods. The present paper introduces a new tree-based optimization method to overcome such weaknesses. The recommended method directly optimizes the multicast tree. Therefore a tree-based typology including several spanning trees is created which combines the trees two by two. For this purpose, the Cuckoo Algorithm is used which is proved to be well converged and makes quick calculations. The simulation conducted on different types of network typologies proved that it is a practical and influential algorithm.
Investigation of Voltage Unbalance Problems In Electric Arc Furnace Operation Model
Yacine DJEGHADER; Hocine LABAR
2013-01-01
In modern steel industry, Electric Arc Furnaces are widely used for iron and scarp melting. The operation of electric arc furnace causes many power quality problems such as harmonics, unbalanced voltage and flicker. The factors that affect Electric arc furnace operation are the melting or refining materials, melting stage, electrodes position (arc length), electrode arm control and short circuit power of the feeder, so, arc voltages, current and power are defined as a nonlinear function of ar...
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.
Partial Path Column Generation for the Vehicle Routing Problem
DEFF Research Database (Denmark)
Jepsen, Mads Kehlet; Petersen, Bjørn
This paper presents a column generation algorithm for the Capacitated Vehicle Routing Problem (CVRP) and the Vehicle Routing Problem with Time Windows (VRPTW). Traditionally, column generation models of the CVRP and VRPTW have consisted of a Set Partitioning master problem with each column repres...... of the giant tour’; a so-called partial path, i.e., not necessarily starting and ending in the depot. This way, the length of the partial path can be bounded and a better control of the size of the solution space for the pricing problem can be obtained....
Ant Colony Algorithm for Solving QoS Routing Problem
Institute of Scientific and Technical Information of China (English)
SUN Li-juan; WANG Liang-jun; WANG Ru-chuan
2004-01-01
Based on the state transition rule, the local updating rule and the global updating rule of ant colony algorithm, we propose an improved ant colony algorithm of the least-cost quality of service (QoS) unicast routing. The algorithm is used for solving the routing problem with delay, delay jitter, bandwidth, and packet loss-constrained. In the simulation, about 52.33% ants find the successful QoS routing , and converge to the best. It is proved that the algorithm is efficient and effective.
Multicriteria vehicle routing problem solved by artificial immune system
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Bogna MRÓWCZYŃSKA
2015-09-01
Full Text Available Vehicles route planning in large transportation companies, where drivers are workers, usually takes place on the basis of experience or intuition of the employees. Because of the cost and environmental protection, it is important to save fuel, thus planning routes in an optimal way. In this article an example of the problem is presented solving delivery vans route planning taking into account the distance and travel time within the constraints of vehicle capacities, restrictions on working time of drivers and having varying degrees of movement. An artificial immune system was used for the calculations.
A Subpath Ejection Method for the Vehicle Routing Problem
1998-01-01
Generically, ejection chains are methods conceived to allow solution transformations to be efficiently carried out by modifying a variable number of their components at each step of a local search algorithm. We consider a subpath ejection chain method for the vehicle routing problem (VRP) under capacity and route length restrictions. The method undertakes the identification of a substructure named the flower reference structure which, besides coordinating moves during an ejection chain constr...
Path inequalities for the vehicle routing problem with time windows
DEFF Research Database (Denmark)
Kallehauge, Brian; Boland, Natashia; Madsen, Oli B.G.
2007-01-01
In this paper we introduce a new formulation of the vehicle routing problem with time windows (VRPTW) involving only binary variables. The new formulation is based on the formulation of the asymmetric traveling salesman problem with time windows by Ascheuer et al. (Networks 36 (2000) 69-79) and has...
Reachability cuts for the vehicle routing problem with time windows
DEFF Research Database (Denmark)
Lysgaard, Jens
2004-01-01
This paper introduces a class of cuts, called reachability cuts, for the Vehicle Routing Problem with Time Windows (VRPTW). Reachability cuts are closely related to cuts derived from precedence constraints in the Asymmetric Traveling Salesman Problem with Time Windows and to k-path cuts...
Bula, Gustavo Alfredo; Prodhon, Caroline; Gonzalez, Fabio Augusto; Afsar, H Murat; Velasco, Nubia
2017-02-15
This work focuses on the Heterogeneous Fleet Vehicle Routing problem (HFVRP) in the context of hazardous materials (HazMat) transportation. The objective is to determine a set of routes that minimizes the total expected routing risk. This is a nonlinear function, and it depends on the vehicle load and the population exposed when an incident occurs. Thus, a piecewise linear approximation is used to estimate it. For solving the problem, a variant of the Variable Neighborhood Search (VNS) algorithm is employed. To improve its performance, a post-optimization procedure is implemented via a Set Partitioning (SP) problem. The SP is solved on a pool of routes obtained from executions of the local search procedure embedded on the VNS. The algorithm is tested on two sets of HFVRP instances based on literature with up to 100 nodes, these instances are modified to include vehicle and arc risk parameters. The results are competitive in terms of computational efficiency and quality attested by a comparison with Mixed Integer Linear Programming (MILP) previously proposed.
On the vehicle routing problem with time windows
DEFF Research Database (Denmark)
Kallehauge, Brian
2006-01-01
by examining possible future lines of research in the area of the VRPTW. In the second paper ‘Lagrangian duality applied to the vehicle routing problem with time windows’ (Kallehauge, Larsen, and Madsen, Computers & Operations Research, 33:1464-1487, 2006) we consider the Lagrangian relaxation...... formulation is based on a formulation of the asymmetric traveling salesman problem with time windows and has the advantage of avoiding additional variables and linking constraints. In the new formulation of the VRPTW time windows aremodeled using path inequalities. The path inequalities eliminate time......The vehicle routing problem with time windows is concerned with the optimal routing of a fleet of vehicles between a depot and a number of customers that must be visited within a specified time interval, called a time window. The purpose of this thesis is to develop new and efficient solution...
A Study of Urgency Vehicle Routing Disruption Management Problem
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Xuping Wang
2010-12-01
Full Text Available If a transit vehicle breaks down on a schedule trip, there are some vehicles in the system need to serve this trip and the former plan must be changed. For solving the urgency vehicle routing problem with disruption that may be vehicle breakdowns or traffic accidents in the logistics distribution system, through the analysis of the problem and the disruption measurement, the mathematics model is given based on the thought of disruption management. For the characteristics of the problem, a Lagrangian relaxation is given to simplify the model, and decompose the problem into two parts. The Lagrangian multiplier is given by subgradient method and the subproblems are solved by saving approach to gain the initial solution. A fast insertion algorithm is given to obtain a feasible solution for the primal problem. The results show that the algorithm designed in this paper performs very well for solving the urgency vehicle routing disruption management problem.
Dispersal routes reconstruction and the minimum cost arborescence problem.
Hordijk, Wim; Broennimann, Olivier
2012-09-01
We show that the dispersal routes reconstruction problem can be stated as an instance of a graph theoretical problem known as the minimum cost arborescence problem, for which there exist efficient algorithms. Furthermore, we derive some theoretical results, in a simplified setting, on the possible optimal values that can be obtained for this problem. With this, we place the dispersal routes reconstruction problem on solid theoretical grounds, establishing it as a tractable problem that also lends itself to formal mathematical and computational analysis. Finally, we present an insightful example of how this framework can be applied to real data. We propose that our computational method can be used to define the most parsimonious dispersal (or invasion) scenarios, which can then be tested using complementary methods such as genetic analysis.
FUNDAMENTAL PROBLEMS IN PULSED-BIAS ARC DEPOSITION
Institute of Scientific and Technical Information of China (English)
G.Q.Lin; Z.F.Ding; D.Qi; N.H.Wang; M.D.Huang; D.Z.Wang; Y.N.Wang; C.Dong; L.S.Wen
2002-01-01
Arc deposition, a widely used surface coating technique, has disadvantages such aslarge droplet size and high deposition temperature. Recent trend in its renovation isthe introduction of pulsed bias at the substrate. The present paper attempts to describethe deposition process of TiN films using this technique with emphasis laid on theunderstanding of the basic problems such as discharge plasma properties, temperaturecalculation, and droplet size reduction. We show that this technique improves thefilm microstructure and quality, lowers deposition temperature, and allows coatingson insulating substrates. After analyzing load current oscillation behaviors, we havedetermined that the plasma load is of capacitance nature due to plasma sheath and thatit is equivalent to a circuit element consisting of parallel capacitance and resistance.At last, we point out the remaining problems and future development of the pulsed-biasarc deposition technique.
Applying Soft Arc Consistency to Distributed Constraint Optimization Problems
Matsui, Toshihiro; Silaghi, Marius C.; Hirayama, Katsutoshi; Yokoo, Makot; Matsuo, Hiroshi
The Distributed Constraint Optimization Problem (DCOP) is a fundamental framework of multi-agent systems. With DCOPs a multi-agent system is represented as a set of variables and a set of constraints/cost functions. Distributed task scheduling and distributed resource allocation can be formalized as DCOPs. In this paper, we propose an efficient method that applies directed soft arc consistency to a DCOP. In particular, we focus on DCOP solvers that employ pseudo-trees. A pseudo-tree is a graph structure for a constraint network that represents a partial ordering of variables. Some pseudo-tree-based search algorithms perform optimistic searches using explicit/implicit backtracking in parallel. However, for cost functions taking a wide range of cost values, such exact algorithms require many search iterations. Therefore additional improvements are necessary to reduce the number of search iterations. A previous study used a dynamic programming-based preprocessing technique that estimates the lower bound values of costs. However, there are opportunities for further improvements of efficiency. In addition, modifications of the search algorithm are necessary to use the estimated lower bounds. The proposed method applies soft arc consistency (soft AC) enforcement to DCOP. In the proposed method, directed soft AC is performed based on a pseudo-tree in a bottom up manner. Using the directed soft AC, the global lower bound value of cost functions is passed up to the root node of the pseudo-tree. It also totally reduces values of binary cost functions. As a result, the original problem is converted to an equivalent problem. The equivalent problem is efficiently solved using common search algorithms. Therefore, no major modifications are necessary in search algorithms. The performance of the proposed method is evaluated by experimentation. The results show that it is more efficient than previous methods.
A Parallel Algorithm for the Vehicle Routing Problem
Energy Technology Data Exchange (ETDEWEB)
Groer, Christopher S [ORNL; Golden, Bruce [University of Maryland; Edward, Wasil [American University
2011-01-01
The vehicle routing problem (VRP) is a dicult and well-studied combinatorial optimization problem. We develop a parallel algorithm for the VRP that combines a heuristic local search improvement procedure with integer programming. We run our parallel algorithm with as many as 129 processors and are able to quickly nd high-quality solutions to standard benchmark problems. We assess the impact of parallelism by analyzing our procedure's performance under a number of dierent scenarios.
Parallelization of the Vehicle Routing Problem with Time Windows
1999-01-01
This dissertation presents a number of algorithms for solving the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW is a generalization of the well known capacity constrained Vehicle Routing Problem (VRP). In the VRP a fleet of vehicles based at a central depot must service a set of customers. In the VRPTW each customer has a time window. Service of a customer must begin within the interval given by the time window. The objective is to minimize some aspect of operating costs (e.g. ...
Particle Swarm Optimization with Genetic Operators for Vehicle Routing Problem
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P. V. PURANIK
2012-07-01
Full Text Available Vehicle Routing Problem (VRP is to find shortest route thereby minimizing total cost. VRP is a NP-hard and Combinatorial optimization problem. Such problems increase exponentially with the problem size. Various derivative based optimization techniques are employed for optimization. Derivative based optimization techniques are difficult to evaluate. Therefore parallel search algorithm emerged to solve VRP. In this work, a particle swarm optimization (PSO algorithm and Genetic algorithm (GA with crossover and mutation operator are applied to two typical functions to deal with the problem of VRP efficiently using MATLAB software. Before solving VRP, optimization of functions using PSO and GA are checked. In this paper capacitate VRP with time window (CVRPTW is proposed. The computational result shows generation of input for VRP, optimization of Rastrigin function, Rosenbrock function using PSO and GA.
A novel heuristic algorithm for capacitated vehicle routing problem
Kır, Sena; Yazgan, Harun Reşit; Tüncel, Emre
2017-02-01
The vehicle routing problem with the capacity constraints was considered in this paper. It is quite difficult to achieve an optimal solution with traditional optimization methods by reason of the high computational complexity for large-scale problems. Consequently, new heuristic or metaheuristic approaches have been developed to solve this problem. In this paper, we constructed a new heuristic algorithm based on the tabu search and adaptive large neighborhood search (ALNS) with several specifically designed operators and features to solve the capacitated vehicle routing problem (CVRP). The effectiveness of the proposed algorithm was illustrated on the benchmark problems. The algorithm provides a better performance on large-scaled instances and gained advantage in terms of CPU time. In addition, we solved a real-life CVRP using the proposed algorithm and found the encouraging results by comparison with the current situation that the company is in.
New exact algorithms for the vehicle routing problem
Energy Technology Data Exchange (ETDEWEB)
Mingozzi, A.; Galdacci, R.; Christofides, N.; Hadjiconstantinou, E.
1994-12-31
We consider the problem in which a fleet of M vehicles stationed at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. This problem is referred as the Vehicle Routing Problem (VRP). In this paper we present two exact branch and bound algorithms for solving the VRP based on a Set Partitioning formulation of the problem. The first algorithm is based on a bounding procedure that finds a heuristic solution of the dual of the LP-relaxation of the Set Partitioning formulation without generating the entire set partitioning matrix. The dual solution obtained is then used to limit the set of the feasible routes containing the optimal VRP solution. The resulting Set Partitioning problem is solved by using a branch and bound method. The second algorithm is based on a lower bound that makes use of a new surrogate relaxation of the Set Partitioning problem. The two algorithms can solve both symmetric and asymmetric VRPS. Computational results are presented for a number of problems derived from the literature.
Meta Heuristic Algorithms for Vehicle Routing Problem with Stochastic Demands
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Geetha Shanmugam
2011-01-01
Full Text Available Problem statement: The shipment of goods from manufacturer to the consumer is a focal point of distribution logistics. In reality, the demand of consumers is not known a priori. This kind of distribution is dealt by Stochastic Vehicle Routing Problem (SVRP which is a NP-hard problem. In this proposed work, VRP with stochastic demand is considered. A probability distribution is considered as a random variable for stochastic demand of a customer. Approach: In this study, VRPSD is resolved using Meta heuristic algorithms such as Genetic Algorithm (GA, Particle Swarm Optimization (PSO and Hybrid PSO (HPSO. Dynamic Programming (DP is used to find the expected cost of each route generated by GA, PSO and HPSO. Results: The objective is to minimize the total expected cost of a priori route. The fitness value of a priori route is calculated using DP. In proposed HPSO, the initial particles are generated based Nearest Neighbor Heuristic (NNH. Elitism is used in HPSO for updating the particles. The algorithm is implemented using MATLAB7.0 and tested with problems having different number of customers. The results obtained are competitive in terms of execution time and memory usage. Conclusion: The computational time is reduced as polynomial time as O(nKQ time and the memory required is O(nQ. The ANOVA test is performed to compare the proposed HPSO with other heuristic algorithms.
The Military Inventory Routing Problem with Direct Delivery
2014-03-27
Unmanned Aircraft Systems (UAS). General Dynamics Information Technology. [13] Kleywegt, Anton J, Nori , Vijay S, & Savelsbergh, Martin WP. 2002. The...stochas- tic inventory routing problem with direct deliveries. Transportation Science, 36(1), 94–118. 55 [14] Kleywegt, Anton J, Nori , Vijay S
Genetic Algorithm for Vehicle Routing Problem with Backhauls
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W.Nurfahizul Ifwah. WA
2012-07-01
Full Text Available The Vehicle Routing Problem with Backhauls (VRPB is an extension of the classical Vehicle Routing Problem (VRP that includes both a set of customers to whom products are to be delivered and a set of suppliers whose goods need to be transported back to the distribution center. In addition, on each route all deliveries have to be made before any goods can be picked up to avoid rearranging the loads on the vehicle. The main objective for VRPB is to determine the network route to minimize the total cost, distance or time. There are a few methods that can be identified to solve this VRPB. The objective of this research is to present a heuristic method, called Genetic Algorithm (GA, for the VRPB. In brief, GA is a system developing methods that use the natural principle of a genetic population and involved three main processes that is crossover, mutation and inversion. GA implementation on the 68 nodes problems taken from Goetschalckx and Jacobs- Blecha is done by using Microsoft C++ Programming. Solutions to the problem are presented and performance comparison is conducted with the existing best solution. Several parameters in GA will be tested such as population size, crossover point and also the choice of operators used.
Periodic Sweep Coverage Scheme Based on Periodic Vehicle Routing Problem
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Li Shu
2014-03-01
Full Text Available We provide a sweep coverage algorithm for routing mobile sensors that communicate with a central data sink. This algorithm improves on its predecessors by reducing the number of unnecessary scans when different points of interest (POIs have different requirements for the time interval within which they must be scanned (sweep period. Most sweep coverage algorithms seek to minimize the number of sensors required to cover a given collection of POIs. When POIs have different sweep period requirements, existing algorithms will produce solutions in which sensors visit some POIs much more frequently than is necessary. We define this as the POI Over-Coverage problem. In order to address this problem we develop a Periodic Sweep Coverage (PSC scheme based on a well-known solution to the Periodic Vehicle Routing Problem (PVRP. Our algorithm seeks a route for the mobile sensors that minimizes the number of unnecessary visits to each POI. To verify and test the proposed scheme we implemented a C++ simulation and ran scenarios with a variety of POI topologies (number and distribution of the POIs and the speed at which sensors could travel. The simulation results show that the PSC algorithm outperforms other sweep coverage algorithms such as CSweep and Vehicle Routing Problem Sweep Coverage (VRPSC on both the average number of sensors in a solution and in the computational time required to find a solution. Our results also demonstrate that the PSC scheme is more suitable for the sweep coverage scenarios in which higher speed mobile sensors are used.
Dynamic vehicle routing problems: Three decades and counting
DEFF Research Database (Denmark)
Psaraftis, Harilaos N.; Wen, Min; Kontovas, Christos A.
2016-01-01
Since the late 70s, much research activity has taken place on the class of dynamic vehicle routing problems (DVRP), with the time period after year 2000 witnessing a real explosion in related papers. Our paper sheds more light into work in this area over more than 3 decades by developing a taxonomy...
Practical inventory routing: A problem definition and an optimization method
Geiger, Martin Josef
2011-01-01
The global objective of this work is to provide practical optimization methods to companies involved in inventory routing problems, taking into account this new type of data. Also, companies are sometimes not able to deal with changing plans every period and would like to adopt regular structures for serving customers.
STUDI TENTANG TRAVELLING SALESMAN DAN VEHICLE ROUTING PROBLEM DENGAN TIME WINDOWS
I Nyoman Sutapa; I Gede Agus Widyadana; Christine Christine
2003-01-01
The article shows the study of model development of travelling salesman problem. Three models are studied, i.e. travelling salesman problem with time windows, vehicle routing problem, and vehicle routing problem with time windows. Abstract in Bahasa Indonesia : Dalam artikel ini dipaparkan kajian mengenai pengembangan model travelling salesman problem. Ada tiga model yang dikaji yaitu travelling salesman problem dengan time windows, vehicle routing problem, serta vehicle routing problem denga...
Modeling a four-layer location-routing problem
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Mohsen Hamidi
2012-01-01
Full Text Available Distribution is an indispensable component of logistics and supply chain management. Location-Routing Problem (LRP is an NP-hard problem that simultaneously takes into consideration location, allocation, and vehicle routing decisions to design an optimal distribution network. Multi-layer and multi-product LRP is even more complex as it deals with the decisions at multiple layers of a distribution network where multiple products are transported within and between layers of the network. This paper focuses on modeling a complicated four-layer and multi-product LRP which has not been tackled yet. The distribution network consists of plants, central depots, regional depots, and customers. In this study, the structure, assumptions, and limitations of the distribution network are defined and the mathematical optimization programming model that can be used to obtain the optimal solution is developed. Presented by a mixed-integer programming model, the LRP considers the location problem at two layers, the allocation problem at three layers, the vehicle routing problem at three layers, and a transshipment problem. The mathematical model locates central and regional depots, allocates customers to plants, central depots, and regional depots, constructs tours from each plant or open depot to customers, and constructs transshipment paths from plants to depots and from depots to other depots. Considering realistic assumptions and limitations such as producing multiple products, limited production capacity, limited depot and vehicle capacity, and limited traveling distances enables the user to capture the real world situations.
Mass Transport Vehicle Routing Problem (MTVRP) and the Associated Network Design Problem (MTNDP)
2005-01-01
This research studies a new class of dynamic problem MTVRP where n vehicles are routed in real time in a fast varying environment to pickup and deliver m passengers when both n and m are big. The problem is very relevant to future transportation options involving large scale real-time routing of shared-ride fleet transit vehicles. Traditionally, dynamic routing solutions were found as static approximations for smaller-scale problems or using local heuristics for the larger-scale ones. General...
The Vehicle Routing Problem with Limited Vehicle Capacities
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Fernando Taracena Sanz
2013-09-01
Full Text Available The vehicle routing problem (VRP has been an important research topic during the last decades because of his vital role in the productive systems efficiency. Most of the work done in this area has been directed to solve large scale problems which may not apply for small companies which are a very important engine of the world economy. This paper approaches the problem when limited vehicle resources are present and road transportation is used. This study assumes variable customer orders. Variable volume and weight vehicle capacities are considered and the proposed algorithm develops the vehicle delivery routes and the set of customer orders to deliver per vehicle minimizing a cost objective function. In sampling small company’s logistics costs, big cost savings are found when using the proposed method.
Vehicle routing problem with time-varying speed
Institute of Scientific and Technical Information of China (English)
LIU Yun-zhong
2010-01-01
Vehicle routing problem with time-varying speed(VRPTS)is a generalization of vehicle routing problem in which the travel speed between two locations depends on the passing areas and the time of a day.This paper proposes a simple model for estimating time-varying travel speeds in VRPTS that relieves much bur den to the data-related problems.The study further presents three heuristics(saving technique,proximity priority searching technique,and insertion technique)for VRPTS,developed by extending and modifying the existing heuristics for conventional VRP.The results of computational experiments demonstrate that the proposed estimation model performs well and the saving technique is the best among the three heuristics.
Investigation of Voltage Unbalance Problems In Electric Arc Furnace Operation Model
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Yacine DJEGHADER
2013-06-01
Full Text Available In modern steel industry, Electric Arc Furnaces are widely used for iron and scarp melting. The operation of electric arc furnace causes many power quality problems such as harmonics, unbalanced voltage and flicker. The factors that affect Electric arc furnace operation are the melting or refining materials, melting stage, electrodes position (arc length, electrode arm control and short circuit power of the feeder, so, arc voltages, current and power are defined as a nonlinear function of arc length. This study focuses on investigation of unbalanced voltage due to Electrics Arc Furnace operation mode. The simulation results show the major problem of unbalanced voltage affecting secondary of furnace transformer is caused by the different continues movement of electrodes.
Ant colony optimization for the real-time train routing selection problem
SAMA, Marcella; Pellegrini, Paola; D'Ariano, Andrea; Rodriguez, Joaquin; Pacciarelli, Dario
2016-01-01
This paper deals with the real-time problem of scheduling and routing trains in a railway network. In the related literature, this problem is usually solved starting from a subset of routing alternatives and computing the near-optimal solution of the simplified routing problem. We study how to select the best subset of routing alternatives for each train among all possible alternatives. The real-time train routing selection problem is formulated as an integer linear programming formulation an...
STUDI TENTANG TRAVELLING SALESMAN DAN VEHICLE ROUTING PROBLEM DENGAN TIME WINDOWS
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I Nyoman Sutapa
2003-01-01
Full Text Available The article shows the study of model development of travelling salesman problem. Three models are studied, i.e. travelling salesman problem with time windows, vehicle routing problem, and vehicle routing problem with time windows. Abstract in Bahasa Indonesia : Dalam artikel ini dipaparkan kajian mengenai pengembangan model travelling salesman problem. Ada tiga model yang dikaji yaitu travelling salesman problem dengan time windows, vehicle routing problem, serta vehicle routing problem dengan time windows. Kata-kunci: travelling salesman problem, vehicle routing problem, time windows.
Optimization of Multiple Vehicle Routing Problems Using Approximation Algorithms
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R. Nallusamy
2009-12-01
Full Text Available This paper deals with generating of an optimized route for multiple Vehicle routing Problems (mVRP. We used a methodology of clustering the given cities depending upon the number of vehicles and eachcluster is allotted to a vehicle. k- Means clustering algorithm has been used for easy clustering of the cities. In this way the mVRP has been converted into VRP which is simple in computation compared to mVRP. After clustering, an optimized route is generated for each vehicle in its allotted cluster. Once the clustering had been done and after the cities were allocated to the various vehicles, each cluster/tour was taken as an individual Vehicle Routing problem and the steps of Genetic Algorithm were applied to the cluster and iterated to obtain the most optimal value of the distance after convergence takes place. After the application of the variousheuristic techniques, it was found that the Genetic algorithm gave a better result and a more optimal tour for mVRPs in short computational time than other Algorithms due to the extensive search and constructive nature of the algorithm.
Optimization of Multiple Vehicle Routing Problems using Approximation Algorithms
Nallusamy, R; Dhanalaksmi, R; Parthiban, P
2010-01-01
This paper deals with generating of an optimized route for multiple Vehicle routing Problems (mVRP). We used a methodology of clustering the given cities depending upon the number of vehicles and each cluster is allotted to a vehicle. k- Means clustering algorithm has been used for easy clustering of the cities. In this way the mVRP has been converted into VRP which is simple in computation compared to mVRP. After clustering, an optimized route is generated for each vehicle in its allotted cluster. Once the clustering had been done and after the cities were allocated to the various vehicles, each cluster/tour was taken as an individual Vehicle Routing problem and the steps of Genetic Algorithm were applied to the cluster and iterated to obtain the most optimal value of the distance after convergence takes place. After the application of the various heuristic techniques, it was found that the Genetic algorithm gave a better result and a more optimal tour for mVRPs in short computational time than other Algorit...
Dynamic Air Route Open-Close Problem for Airspace Management
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Dynamic airspace management plans and assigns airspace resources to airspace users on demand to increase airspace capacity. Although many studies of air traffic flow management (ATFM) have sought to optimally allocate air traffic to get the best use of given airspace resources, few studies have focused on how to build an efficient air traffic network or how to adjust the current network in real time. This paper presents an integer program model named the dynamic air route open-close problem (DROP). DROP has a cost-based objective function which takes into account constraints such as the shortest occupancy time of routes, which are not considered in ATFM models. The aim of DROP is to determine which routes will be opened to a certain user during a given time period. Simulation results show that DROP can facilitate utilization of air routes. DROP, a simplified version of an air traffic network constructing problem, is the first step towards realizing dynamic airspace management. The combination of ATFM and DROP can facilitate decisions toward more reasonable, efficient use of limited airspace resources.
ACTIVITY-BASED COSTING FOR VEHICLE ROUTING PROBLEMS
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A. J. Moolman
2012-01-01
Full Text Available
ENGLISH ABSTRACT:Activity-based costing (ABC is a costing model that identifies activity costs in an organisation. It assigns the cost of activity resources to generate the actual cost of products in order to eliminateunprofitable products and to lowerthe prices of overpriced ones. The vehicle routing problem (VRP is a combinatorial optimisation and nonlinear programming problem that seeks to service a number of customers with a fleet of vehicles in a cost-effective manner. In this article we propose a new approach to determine costing for vehicle routing type problems. The methodology incorporates the predictive sharing of a resource by clustering producers.
AFRIKAANSE OPSOMMING: ‘Activity-based costing’ (ABC is ’n kostemodel wat die aktiwiteitskoste in ’n organisasie identifiseer. Dit allokeer die koste van die bronne sodat die ware koste van die vervaardiging en dienste van die produk bereken kan word om winsgewendheid te bepaal. Die ‘vehicle routing problem’ (VRP is ’n kombinatoriese optimisering en nie-lineêre programmeringsprobleem wat verskeie kliënte met ’n vloot voertuie in die mees koste- effektiewe manier bedien. Die artikel bespreek ’n nuwe metode om die kombinasie van probleme op te los. Die metode maak gebruik van groeperingsalgoritmes om meer akkurate voertuig deling te voorspel.
Performansi Algoritma CODEQ dalam Penyelesaian Vehicle Routing Problem
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Annisa Kesy Garside
2014-01-01
Full Text Available Genetic Algorithm, Tabu Search, Simulated Annealing, and Ant Colony Optimization showed a good performance in solving vehicle routing problem. However, the generated solution of those algorithms was changeable regarding on the input parameter of each algorithm. CODEQ is a new, parameter free meta-heuristic algorithm that had been successfully used to solve constrained optimization problems, integer programming, and feed-forward neural network. The purpose of this research are improving CODEQ algorithm to solve vehicle routing problem and testing the performance of the improved algorithm. CODEQ algorithm is started with population initiation as initial solution, generated of mutant vector for each parent in every iteration, replacement of parent by mutant when fitness function value of mutant is better than parent’s, generated of new vector for each iteration based on opposition value or chaos principle, replacement of worst solution by new vector when fitness function value of new vector is better, iteration ceasing when stooping criterion is achieved, and sub-tour determination based on vehicle capacity constraint. The result showed that the average deviation of the best-known and the best-test value is 6.35%. Therefore, CODEQ algorithm is good in solving vehicle routing problem.
Enhanced ant colony optimization for inventory routing problem
Wong, Lily; Moin, Noor Hasnah
2015-10-01
The inventory routing problem (IRP) integrates and coordinates two important components of supply chain management which are transportation and inventory management. We consider a one-to-many IRP network for a finite planning horizon. The demand for each product is deterministic and time varying as well as a fleet of capacitated homogeneous vehicles, housed at a depot/warehouse, delivers the products from the warehouse to meet the demand specified by the customers in each period. The inventory holding cost is product specific and is incurred at the customer sites. The objective is to determine the amount of inventory and to construct a delivery routing that minimizes both the total transportation and inventory holding cost while ensuring each customer's demand is met over the planning horizon. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (best integer) for each instance considered. We propose an enhanced ant colony optimization (ACO) to solve the problem and the built route is improved by using local search. The computational experiments demonstrating the effectiveness of our approach is presented.
Analysis of the single-vehicle cyclic inventory routing problem
Aghezzaf, El-Houssaine; Zhong, Yiqing; Raa, Birger; Mateo, Manel
2012-11-01
The single-vehicle cyclic inventory routing problem (SV-CIRP) consists of a repetitive distribution of a product from a single depot to a selected subset of customers. For each customer, selected for replenishments, the supplier collects a corresponding fixed reward. The objective is to determine the subset of customers to replenish, the quantity of the product to be delivered to each and to design the vehicle route so that the resulting profit (difference between the total reward and the total logistical cost) is maximised while preventing stockouts at each of the selected customers. This problem appears often as a sub-problem in many logistical problems. In this article, the SV-CIRP is formulated as a mixed-integer program with a nonlinear objective function. After a thorough analysis of the structure of the problem and its features, an exact algorithm for its solution is proposed. This exact algorithm requires only solutions of linear mixed-integer programs. Values of a savings-based heuristic for this problem are compared to the optimal values obtained for a set of some test problems. In general, the gap may get as large as 25%, which justifies the effort to continue exploring and developing exact and approximation algorithms for the SV-CIRP.
Parallelization of the Vehicle Routing Problem with Time Windows
DEFF Research Database (Denmark)
Larsen, Jesper
1999-01-01
of customers. In the VRPTW each customer has a time window. Service of a customer must begin within the interval given by the time window. The objective is to minimize some aspect of operating costs (e.g. total distance traveled, number of vehicles needed or a combination of parameters). Since the late 80's......This dissertation presents a number of algorithms for solving the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW is a generalization of the well known capacity constrained Vehicle Routing Problem (VRP). In the VRP a fleet of vehicles based at a central depot must service a set...... obtained using Lagrange relaxation. This dissertation is divided into three parts. First the theoretical framework is described. Thereafter a number of techniques to improve the performance of the column-generation framework are proposed and analyzed. Finally a parallel algorithm based on the sequential...
A Memetic Algorithm for the Capacitated Location-Routing Problem
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Laila KECHMANE
2016-06-01
Full Text Available In this paper, a hybrid genetic algorithm is proposed to solve a Capacitated Location-Routing Problem. The objective is to minimize the total cost of the distribution in a network composed of depots and customers, both depots and vehicles have limited capacities, each depot has a homogenous vehicle fleet and customers’ demands are known and must be satisfied. Solving this problem involves making strategic decisions such as the location of depots, as well as tactical and operational decisions which include assigning customers to the opened depots and organization of the vehicle routing. To evaluate the performance of the proposed algorithm, its results are compared to those obtained by a greedy randomized adaptive search procedure, computational results shows that the algorithm gave good quality solutions.
Vehicle Coordinated Strategy for Vehicle Routing Problem with Fuzzy Demands
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Chang-shi Liu
2016-01-01
Full Text Available The vehicle routing problem with fuzzy demands (VRPFD is considered. A fuzzy reasoning constrained program model is formulated for VRPFD, and a hybrid ant colony algorithm is proposed to minimize total travel distance. Specifically, the two-vehicle-paired loop coordinated strategy is presented to reduce the additional distance, unloading times, and waste capacity caused by the service failure due to the uncertain demands. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed approaches.
Electric Vehicle Routing Problems : models and solution approaches
Montoya, Jose-Alejandro
2016-01-01
Electric vehicles (evs) are one of the most promising technologies to reduce the greenhouse gas emissions. For this reason, the use of evs in service operations has dramatically increased in recent years. Despite their environmental benefits, evs still face technical constraints such as short autonomy and long charging times. Taking into account these constraints when planning ev operations leads to a new breed of vehicle routing problems (vrps), known as electricVrps (evrps). In addition, to...
Two Multivehicle Routing Problems with Unit-Time Windows
Frederickson, Greg N
2011-01-01
Two multivehicle routing problems are considered in the framework that a visit to a location must take place during a specific time window in order to be counted and all time windows are the same length. In the first problem, the goal is to visit as many locations as possible using a fixed number of vehicles. In the second, the goal is to visit all locations using the smallest number of vehicles possible. For the first problem, we present an approximation algorithm whose output path collects a reward within a constant factor of optimal for any fixed number of vehicles. For the second problem, our algorithm finds a 6-approximation to the problem on a tree metric, whenever a single vehicle could visit all locations during their time windows.
Dynamic vehicle routing problems: Three decades and counting
DEFF Research Database (Denmark)
Psaraftis, Harilaos N.; Wen, Min; Kontovas, Christos A.
2016-01-01
Since the late 70s, much research activity has taken place on the class of dynamic vehicle routing problems (DVRP), with the time period after year 2000 witnessing a real explosion in related papers. Our paper sheds more light into work in this area over more than 3 decades by developing a taxonomy...... of DVRP papers according to 11 criteria. These are (1) type of problem, (2) logistical context, (3) transportation mode, (4) objective function, (5) fleet size, (6) time constraints, (7) vehicle capacity constraints, (8) the ability to reject customers, (9) the nature of the dynamic element, (10...
Robust Optimisation Approach for Vehicle Routing Problems with Uncertainty
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Liang Sun
2015-01-01
Full Text Available We formulated a solution procedure for vehicle routing problems with uncertainty (VRPU for short with regard to future demand and transportation cost. Unlike E-SDROA (expectation semideviation robust optimisation approach for solving the proposed problem, the formulation focuses on robust optimisation considering situations possibly related to bidding and capital budgets. Besides, numerical experiments showed significant increments in the robustness of the solutions without much loss in solution quality. The differences and similarities of the robust optimisation model and existing robust optimisation approaches were also compared.
Solving the time dependent vehicle routing problem by metaheuristic algorithms
Johar, Farhana; Potts, Chris; Bennell, Julia
2015-02-01
The problem we consider in this study is Time Dependent Vehicle Routing Problem (TDVRP) which has been categorized as non-classical VRP. It is motivated by the fact that multinational companies are currently not only manufacturing the demanded products but also distributing them to the customer location. This implies an efficient synchronization of production and distribution activities. Hence, this study will look into the routing of vehicles which departs from the depot at varies time due to the variation in manufacturing process. We consider a single production line where demanded products are being process one at a time once orders have been received from the customers. It is assumed that order released from the production line will be loaded into scheduled vehicle which ready to be delivered. However, the delivery could only be done once all orders scheduled in the vehicle have been released from the production line. Therefore, there could be lateness on the delivery process from awaiting all customers' order of the route to be released. Our objective is to determine a schedule for vehicle routing that minimizes the solution cost including the travelling and tardiness cost. A mathematical formulation is developed to represent the problem and will be solved by two metaheuristics; Variable Neighborhood Search (VNS) and Tabu Search (TS). These algorithms will be coded in C ++ programming and run using 56's Solomon instances with some modification. The outcome of this experiment can be interpreted as the quality criteria of the different approximation methods. The comparison done shown that VNS gave the better results while consuming reasonable computational efforts.
TSP based Evolutionary optimization approach for the Vehicle Routing Problem
Kouki, Zoulel; Chaar, Besma Fayech; Ksouri, Mekki
2009-03-01
Vehicle Routing and Flexible Job Shop Scheduling Problems (VRP and FJSSP) are two common hard combinatorial optimization problems that show many similarities in their conceptual level [2, 4]. It was proved for both problems that solving techniques like exact methods fail to provide good quality solutions in a reasonable amount of time when dealing with large scale instances [1, 5, 14]. In order to overcome this weakness, we decide in the favour of meta heuristics and we focalize on evolutionary algorithms that have been successfully used in scheduling problems [1, 5, 9]. In this paper we investigate the common properties of the VRP and the FJSSP in order to provide a new controlled evolutionary approach for the CVRP optimization inspired by the FJSSP evolutionary optimization algorithms introduced in [10].
SOLVING THE PROBLEM OF VEHICLE ROUTING BY EVOLUTIONARY ALGORITHM
Directory of Open Access Journals (Sweden)
Remigiusz Romuald Iwańkowicz
2016-03-01
Full Text Available In the presented work the vehicle routing problem is formulated, which concerns planning the collection of wastes by one garbage truck from a certain number of collection points. The garbage truck begins its route in the base point, collects the load in subsequent collection points, then drives the wastes to the disposal site (landfill or sorting plant and returns to the another visited collection points. The filled garbage truck each time goes to the disposal site. It returns to the base after driving wastes from all collection points. Optimization model is based on genetic algorithm where individual is the whole garbage collection plan. Permutation is proposed as the code of the individual.
Optimization of location routing inventory problem with transshipment
Ghani, Nor Edayu Abd; Shariff, S. Sarifah Radiah; Zahari, Siti Meriam
2015-05-01
Location Routing Inventory Problem (LRIP) is a collaboration of the three components in the supply chain. It is confined by location-allocation, vehicle routing and inventory management. The aim of the study is to minimize the total system cost in the supply chain. Transshipment is introduced in order to allow the products to be shipped to a customer who experiences a shortage, either directly from the supplier or from another customer. In the study, LRIP is introduced with the transshipment (LRIPT) and customers act as the transshipment points. We select the transshipment point by using the p-center and we present the results in two divisions of cases. Based on the analysis, the results indicated that LRIPT performed well compared to LRIP.
Ant Colony Optimization for Capacitated Vehicle Routing Problem
Directory of Open Access Journals (Sweden)
H. V. Seow
2012-01-01
Full Text Available Problem statement: The Capacitated Vehicle Routing Problem (CVRP is a well-known combinatorial optimization problem which is concerned with the distribution of goods between the depot and customers. It is of economic importance to businesses as approximately 10-20% of the final cost of the goods is contributed by the transportation process. Approach: This problem was tackled using an Ant Colony Optimization (ACO combined with heuristic approaches that act as the route improvement strategies. The proposed ACO utilized a pheromone evaporation procedure of standard ant algorithm in order to introduce an evaporation rate that depends on the solutions found by the artificial ants. Results: Computational experiments were conducted on benchmark data set and the results obtained from the proposed algorithms shown that the application of combination of two different heuristics in the ACO had the capability to improve the ants solutions better than ACO embedded with only one heuristic. Conclusion: ACO with swap and 3-opt heuristic has the capability to tackle the CVRP with satisfactory solution quality and run time. It is a viable alternative for solving the CVRP.
The dynamic multi-period vehicle routing problem
DEFF Research Database (Denmark)
Wen, Min; Cordeau, Jean-Francois; Laporte, Gilbert
2010-01-01
This paper considers the Dynamic Multi-Period Vehicle Routing Problem which deals with the distribution of orders from a depot to a set of customers over a multi-period time horizon. Customer orders and their feasible service periods are dynamically revealed over time. The objectives...... planning horizon. The multi-objective aspect of the problem is handled through a scalar technique approach. Computational results show that the proposed approach can yield high quality solutions within reasonable running times....... are to minimize total travel costs and customer waiting, and to balance the daily workload over the planning horizon. This problem originates from a large distributor operating in Sweden. It is modeled as a mixed integer linear program, and solved by means of a three-phase heuristic that works over a rolling...
The Dynamic Multi-Period Vehicle Routing Problem
DEFF Research Database (Denmark)
Wen, Min; Cordeau, Jean-Francois; Laporte, Gilbert
This paper considers the Dynamic Multi-Period Vehicle Routing Problem which deals with the distribution of orders from a depot to a set of customers over a multi-period time horizon. Customer orders and their feasible service periods are dynamically revealed over time. The objectives...... are to minimize total travel costs and customer waiting, and to balance the daily workload over the planning horizon. This problem originates from a large distributor operating in Sweden. It is modeled as a mixed integer linear program, and solved by means of a three-phase heuristic that works over a rolling...... planning horizon. The multi-objective aspect of the problem is handled through a scalar technique approach. Computational results show that our solutions improve upon those of the Swedish distributor....
A green vehicle routing problem with customer satisfaction criteria
Afshar-Bakeshloo, M.; Mehrabi, A.; Safari, H.; Maleki, M.; Jolai, F.
2016-08-01
This paper develops an MILP model, named Satisfactory-Green Vehicle Routing Problem. It consists of routing a heterogeneous fleet of vehicles in order to serve a set of customers within predefined time windows. In this model in addition to the traditional objective of the VRP, both the pollution and customers' satisfaction have been taken into account. Meanwhile, the introduced model prepares an effective dashboard for decision-makers that determines appropriate routes, the best mixed fleet, speed and idle time of vehicles. Additionally, some new factors evaluate the greening of each decision based on three criteria. This model applies piecewise linear functions (PLFs) to linearize a nonlinear fuzzy interval for incorporating customers' satisfaction into other linear objectives. We have presented a mixed integer linear programming formulation for the S-GVRP. This model enriches managerial insights by providing trade-offs between customers' satisfaction, total costs and emission levels. Finally, we have provided a numerical study for showing the applicability of the model.
A Cost Assessment of the Dayton Public Schools Vehicle Routing Problem
2009-03-01
A COST ASSESMENT OF THE DAYTON PUBLIC SCHOOLS VEHICLE ROUTING PROBLEM THESIS...PUBLIC SCHOOLS VEHICLE ROUTING PROBLEM THESIS Presented to the Faculty Department of Operational Sciences Graduate School of... VEHICLE ROUTING PROBLEM Frankie L. Woods Jr., BS Captain, USAF Approved: ____________________________________ Dr
Large scale stochastic inventory routing problems with split delivery and service level constraints
Y. Yu (Yugang); C. Chu (Chengbin); H.X. Chen (Haoxun); F. Chu (Feng)
2010-01-01
textabstractA stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. Th
Large scale stochastic inventory routing problems with split delivery and service level constraints
Y. Yu (Yugang); C. Chu (Chengbin); H.X. Chen (Haoxun); F. Chu (Feng)
2012-01-01
textabstractA stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. Th
Y. Yu (Yugang); C. Chu (Chengbin); H.X. Chen (Haoxun); F. Chu (Feng)
2010-01-01
textabstractA stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, for a depot to determine delivery volumes to its customers in each period, and vehicle routes to distribute the delivery volumes. This
A Survey of the Routing and Wavelength Assignment Problem
DEFF Research Database (Denmark)
Gamst, Mette
When transmitting data in an all-optical network, data connections must be established in such a way that two or more connections never share a wavelength on the same fi ber. The NP-hard Routing and Wavelength Assignment (RWA) problem consists of finding paths and wavelengths for a set of data...... connections. This survey introduces the RWA and gives an overview of heuristic, metaheuristic and exact solution methods from the literature. Running times for the heuristic methods are presented and computational results are discussed....
Cooperative vehicle routing problem: an opportunity for cost saving
Zibaei, Sedighe; Hafezalkotob, Ashkan; Ghashami, Seyed Sajad
2016-02-01
In this paper, a novel methodology is proposed to solve a cooperative multi-depot vehicle routing problem. We establish a mathematical model for multi-owner VRP in which each owner (i.e. player) manages single or multiple depots. The basic idea consists of offering an option that owners cooperatively manage the VRP to save their costs. We present cooperative game theory techniques for cost saving allocations which are obtained from various coalitions of owners. The methodology is illustrated with a numerical example in which different coalitions of the players are evaluated along with the results of cooperation and cost saving allocation methods.
Hybrid Ant Algorithm and Applications for Vehicle Routing Problem
Xiao, Zhang; Jiang-qing, Wang
Ant colony optimization (ACO) is a metaheuristic method that inspired by the behavior of real ant colonies. ACO has been successfully applied to several combinatorial optimization problems, but it has some short-comings like its slow computing speed and local-convergence. For solving Vehicle Routing Problem, we proposed Hybrid Ant Algorithm (HAA) in order to improve both the performance of the algorithm and the quality of solutions. The proposed algorithm took the advantages of Nearest Neighbor (NN) heuristic and ACO for solving VRP, it also expanded the scope of solution space and improves the global ability of the algorithm through importing mutation operation, combining 2-opt heuristics and adjusting the configuration of parameters dynamically. Computational results indicate that the hybrid ant algorithm can get optimal resolution of VRP effectively.
An evolutionary algorithm for a real vehicle routing problem
Directory of Open Access Journals (Sweden)
Adamidis, P.
2012-01-01
Full Text Available The NP-hard Vehicle Routing Problem (VRP is central in the optimisation of distribution networks. Its main objective is to determine a set of vehicle trips of minimum total cost. The ideal schedule will efficiently exploit the company's recourses, service all customers and satisfy the given (mainly daily constraints. There have been many attempts to solve this problem with conventional techniques but applied to small-scale simplified problems. This is due to the complexity of the problem and the large volume of data to be processed. Evolutionary Algorithms are search and optimization techniques that are capable of confronting that kind of problems and reach a good feasible solution in a reasonable period of time. In this paper we develop an Evolutionary Algorithm in order to solve the VRP of a specific transportation company in Volos, Greece with different vehicle capacities. The algorithm has been tested with different configurations and constraints, and proved to be effective in reaching a satisfying solution for the company's needs.
Wang, Qian; Li, Xingwen; Song, Haoyong; Rong, Mingzhe
2010-04-01
Non-contact magnetic measurement method is an effective way to study the air arc behavior experimentally One of the crucial techniques is to solve an inverse problem for the electromagnetic field. This study is devoted to investigating different algorithms for this kind of inverse problem preliminarily, including the preconditioned conjugate gradient method, penalty function method and genetic algorithm. The feasibility of each algorithm is analyzed. It is shown that the preconditioned conjugate gradient method is valid only for few arc segments, the estimation accuracy of the penalty function method is dependent on the initial conditions, and the convergence of genetic algorithm should be studied further for more segments in an arc current.
Variable neighbourhood simulated annealing algorithm for capacitated vehicle routing problems
Xiao, Yiyong; Zhao, Qiuhong; Kaku, Ikou; Mladenovic, Nenad
2014-04-01
This article presents the variable neighbourhood simulated annealing (VNSA) algorithm, a variant of the variable neighbourhood search (VNS) combined with simulated annealing (SA), for efficiently solving capacitated vehicle routing problems (CVRPs). In the new algorithm, the deterministic 'Move or not' criterion of the original VNS algorithm regarding the incumbent replacement is replaced by an SA probability, and the neighbourhood shifting of the original VNS (from near to far by k← k+1) is replaced by a neighbourhood shaking procedure following a specified rule. The geographical neighbourhood structure is introduced in constructing the neighbourhood structures for the CVRP of the string model. The proposed algorithm is tested against 39 well-known benchmark CVRP instances of different scales (small/middle, large, very large). The results show that the VNSA algorithm outperforms most existing algorithms in terms of computational effectiveness and efficiency, showing good performance in solving large and very large CVRPs.
Driver's workload comparison in waste collection vehicle routing problem
Benjamin, Aida Mauziah; Abdul-Rahman, Syariza
2016-10-01
This paper compares the workload of the drivers for a waste collection benchmark problem. The problem involves ten data sets with different number of customers to be served and different number of disposal facilities available. Previous studies proposed a heuristic algorithm, namely Different Initial Customer (DIC) to solve the problem by constructing initial vehicles routes for the drivers with two main objectives; to minimize the total distance travelled and to minimize the total number of vehicles needed to collect the waste. The results from DIC compared well with other solutions in the literature. However, the balance of the workload among the vehicle drivers is not considered in the solutions. Thus in this paper, we evaluate the quality of the solutions in terms of the total number of customers served by each driver. Then the computational result is compared in terms of the total distance travelled which have been presented in a previous study. Comparison results show that the workload of the drivers are unbalance in terms of these two factors that may cause dissatisfaction among the drivers as well as to the managament.
Nafezi, Nima
2013-01-01
In this dissertation, we discussed a type of vehicle routing problem called vehicle routing problem with intermediate facilities with consideration of the impact of adding intermediate facilities to the problem. To study how IFs change the result of the problem, we firstly present a simple model based on clustering algorithm along with finding the shortest route between clusters, implementing Clarke and Wright’s algorithm within each cluster. Then we determine a set of design of experiments w...
Damanik, Donna
2016-01-01
Model to choose vehicle route is known as Vehicle Routing Problem (VRP). VRP is related to optimal routing problem that involve more than one vehicle of each capacity to serve costumer’s demand. Capacitated Vehicle Routing Problem is one of VRP form which each of vehicle has finite capacity. Solution in this research use Clarke and Wright’s Savings Algorithm. This algorithm may get a route depand to vehicle capacity and customer’s demand. Data that use in this research is di...
Directory of Open Access Journals (Sweden)
Yu Lin
2015-01-01
Full Text Available High frequency and small lot size are characteristics of milk runs and are often used to implement the just-in-time (JIT strategy in logistical systems. The common frequency problem, which simultaneously involves planning of the route and frequency, has been extensively researched in milk run systems. In addition, vehicle type choice in the milk run system also has a significant influence on the operating cost. Therefore, in this paper, we simultaneously consider vehicle routing planning, frequency planning, and vehicle type choice in order to optimize the sum of the cost of transportation, inventory, and dispatch. To this end, we develop a mathematical model to describe the common frequency problem with vehicle type choice. Since the problem is NP hard, we develop a two-phase heuristic algorithm to solve the model. More specifically, an initial satisfactory solution is first generated through a greedy heuristic algorithm to maximize the ratio of the superior arc frequency to the inferior arc frequency. Following this, a tabu search (TS with limited search scope is used to improve the initial satisfactory solution. Numerical examples with different sizes establish the efficacy of our model and our proposed algorithm.
A Mixed Integer Linear Program for Solving a Multiple Route Taxi Scheduling Problem
Montoya, Justin Vincent; Wood, Zachary Paul; Rathinam, Sivakumar; Malik, Waqar Ahmad
2010-01-01
Aircraft movements on taxiways at busy airports often create bottlenecks. This paper introduces a mixed integer linear program to solve a Multiple Route Aircraft Taxi Scheduling Problem. The outputs of the model are in the form of optimal taxi schedules, which include routing decisions for taxiing aircraft. The model extends an existing single route formulation to include routing decisions. An efficient comparison framework compares the multi-route formulation and the single route formulation. The multi-route model is exercised for east side airport surface traffic at Dallas/Fort Worth International Airport to determine if any arrival taxi time savings can be achieved by allowing arrivals to have two taxi routes: a route that crosses an active departure runway and a perimeter route that avoids the crossing. Results indicate that the multi-route formulation yields reduced arrival taxi times over the single route formulation only when a perimeter taxiway is used. In conditions where the departure aircraft are given an optimal and fixed takeoff sequence, accumulative arrival taxi time savings in the multi-route formulation can be as high as 3.6 hours more than the single route formulation. If the departure sequence is not optimal, the multi-route formulation results in less taxi time savings made over the single route formulation, but the average arrival taxi time is significantly decreased.
A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem
DEFF Research Database (Denmark)
Wøhlk, Sanne; Lysgaard, Jens
2014-01-01
The paper considers the Cumulative Capacitated Vehicle Routing Problem (CCVRP), which is a variation of the well-known Capacitated Vehicle Routing Problem (CVRP). In this problem, the traditional objective of minimizing total distance or time traveled by the vehicles is replaced by minimizing...
Kok, A. Leendert; Meyer, C. Manuel; Kopfer, Herbert; Schutten, J. Marco J.
2009-01-01
In practice, apart from the problem of vehicle routing, schedulers also face the problem of nding feasible driver schedules complying with complex restrictions on drivers' driving and working hours. To address this complex interdependent problem of vehicle routing and break scheduling, we propose a
Kok, A. Leendert; Meyer, C. Manuel; Kopfer, Herbert; Schutten, J. Marco J.
2009-01-01
In practice, apart from the problem of vehicle routing, schedulers also face the problem of finding feasible driver schedules complying with complex restrictions on drivers' driving and working hours. To address this complex interdependent problem of vehicle routing and break scheduling, we propose
Sanjeevi, V; Shahabudeen, P
2016-01-01
Worldwide, about US$410 billion is spent every year to manage four billion tonnes of municipal solid wastes (MSW). Transport cost alone constitutes more than 50% of the total expenditure on solid waste management (SWM) in major cities of the developed world and the collection and transport cost is about 85% in the developing world. There is a need to improve the ability of the city administrators to manage the municipal solid wastes with least cost. Since 2000, new technologies such as geographical information system (GIS) and related optimization software have been used to optimize the haul route distances. The city limits of Chennai were extended from 175 to 426 km(2) in 2011, leading to sub-optimum levels in solid waste transportation of 4840 tonnes per day. After developing a spatial database for the whole of Chennai with 200 wards, the route optimization procedures have been run for the transport of solid wastes from 13 wards (generating nodes) to one transfer station (intermediary before landfill), using ArcGIS. The optimization process reduced the distances travelled by 9.93%. The annual total cost incurred for this segment alone is Indian Rupees (INR) 226.1 million. Savings in terms of time taken for both the current and shortest paths have also been computed, considering traffic conditions. The overall savings are thus very meaningful and call for optimization of the haul routes for the entire Chennai.
Capacitated vehicle routing problem with sequence-based pallet loading and axle weight constraints
2016-01-01
In this paper, we introduce and study the capacitated vehicle routing problem with sequence-based pallet loading and axle weight constraints. To the best of our knowledge, it is the first time that axle weight restrictions are incorporated in a vehicle routing model. The aim of this paper is to demonstrate that incorporating axle weight restrictions in a vehicle routing model is possible and necessary for a feasible route planning. Axle weight limits impose a great challenge for transportatio...
Solving the Generalized Vehicle Routing Problem with an ACS-based Algorithm
Pop, Petrica Claudiu; Pintea, Camelia; Zelina, Ioana; Dumitrescu, Dan
2009-04-01
Ant colony system is a metaheuristic algorithm inspired by the behavior of real ants and was proposed by Dorigo et al. as a method for solving hard combinatorial optimization problems. In this paper we show its successful application to solving a network design problem: Generalized Vehicle Routing Problem. The Generalized Vehicle Routing Problem (GVRP) is the problem of designing optimal delivery or collection routes, subject to capacity restrictions, from a given depot to a number of predefined, mutually exclusive and exhaustive clusters. Computational results for several benchmark problems are reported.
Fast 3D route-planning approach for air vehicle
Tu, Jilin; Ding, Mingyue; Zhou, Chengping; Ai, Haojun
1997-06-01
A fast 3-D route planning method for unmanned air vehicle is proposed which can generate physically realizable 3-D route within a reasonable time. Our method includes two steps: First, 2-D route planning generates a route which satisfies turning radius constraint(abbreviated as R-constrained below); second, 3-D route planning generates 3-D route in vertical profile of the 2-D route. To make 2-D route R-constrained, a method is proposed by supposing 2-D route of air vehicle is composed of a sequence of arc route segments and tangential points between neighboring arcs are searching nodes. 3 -D route planning is considered as optimal control problem, and its route can be determined by applying motion equations of air vehicle. The experiments show that our method can produce feasible 3-D routes within a reasonable time, and ensure the planned 3-D routes satisfy aerodynamics constraints of air vehicle.
Combining Nearest Neighbor Search with Tabu Search for Large-Scale Vehicle Routing Problem
Du, Lingling; He, Ruhan
The vehicle routing problem is a classical problem in operations research, where the objective is to design least cost routes for a fleet of identical capacitated vehicles to service geographically scattered customers. In this paper, we present a new and effective hybrid metaheuristic algorithm for large-scale vehicle routing problem. The algorithm combines the strengths of the well-known Nearest Neighbor Search and Tabu Search into a two-stage procedure. More precisely, Nearest Neighbor Search is used to construct initial routes in the first stage and the Tabu Search is utilized to optimize the intra-route and the inter-route in the second stage. The presented algorithm is specifically designed for large-scale problems. The computational experiments were carried out on a standard benchmark and a real dataset with 6772 tobacco customers. The results demonstrate that the suggested method is highly competitive.
A branch-and-cut algorithm for the capacitated open vehicle routing problem
DEFF Research Database (Denmark)
Letchford, A.N.; Lysgaard, Jens; Eglese, R.W.
2007-01-01
In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The algorithm is based on branch-and...
A Branch-and-Price Algorithm for Two Multi-Compartment Vehicle Routing Problems
DEFF Research Database (Denmark)
Mirzaei, Samira; Wøhlk, Sanne
2016-01-01
Despite the vast body of literature on vehicle routing problems, little attention has been paid to multi-compartment vehicle routing problems that investigate transportation of different commodities on the same vehicle, but in different compartments. In this project, we present two strategically...
DEFF Research Database (Denmark)
Larsen, Jesper
2002-01-01
Two ideas for using structural information for solving the Vehicle Routing Problem with Time Windows (VRPTW) is presented. The VRPTW is a generalization of the well known capacity constrained Vehicle Routing Problem (VRP). Both techniques are based on solving the VRPTW using a Branch...
Ardema, M. D.
1979-01-01
Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.
An Endosymbiotic Evolutionary Algorithm for the Hub Location-Routing Problem
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Ji Ung Sun
2015-01-01
Full Text Available We consider a capacitated hub location-routing problem (HLRP which combines the hub location problem and multihub vehicle routing decisions. The HLRP not only determines the locations of the capacitated p-hubs within a set of potential hubs but also deals with the routes of the vehicles to meet the demands of customers. This problem is formulated as a 0-1 mixed integer programming model with the objective of the minimum total cost including routing cost, fixed hub cost, and fixed vehicle cost. As the HLRP has impractically demanding for the large sized problems, we develop a solution method based on the endosymbiotic evolutionary algorithm (EEA which solves hub location and vehicle routing problem simultaneously. The performance of the proposed algorithm is examined through a comparative study. The experimental results show that the proposed EEA can be a viable solution method for the supply chain network planning.
A Hybrid TCNN Optimization Approach for the Capacity Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A novel approximation algorithm was proposed for the problem of finding the minimum total cost of all routes in Capacity Vehicle Routing Problem (CVRP). CVRP can be partitioned into three parts: the selection of vehicles among the available vehicles, the initial routing of the selected fleet and the routing optimization. Fuzzy Cmeans (FCM) can group the customers with close Euclidean distance into the same vehicle according to the principle of similar feature partition. Transiently chaotic neural network (TCNN) combines local search and global search, possessing high search efficiency. It will solve the routes to near optimality. A simple tabu search (TS)procedure can improve the routes to more optimality. The computations on benchmark problems and comparisons with other results in literatures show that the proposed algorithm is a viable and effective approach for CVRP.
Goal-programming model of the stochastic vehicle-routing problem
Energy Technology Data Exchange (ETDEWEB)
Zare-Mehrjerdi, Y.
1986-01-01
This research proposes a Goal Programming (GP) model of the Stochastic Vehicle Routing Problem (SVRP). The SVRP examined considers the multiple-vehicle, single-depot-node routing problem in which customer demand and travel and unload times are random variables having known distribution functions. The problem formulation of the SVRP is divided into two major stages which are referred to as Route Construction Stage (RCS) and Route Improvement Stage (RIS). The RCS of the SVRP is required in order to partition a set of stations into feasible sets of routes, one for each vehicle, using an appropriate heuristic approach. The RIS of the problem is required in order to sequence the stations on each vehicle route to meet the customer's and decision maker's requirements by applying a GP method. Two problems discuss the GP formulation of the RIS, which is used for improving the arrangement of stations on each vehicle route based on the customer's and decision maker's criteria. The formulation of the RCS of the problem is divided into two sections according to the type of criteria that is to be minimized. A substantial improvement in the results of the SVRP can be obtained by integrating the customer's and decision maker's requirements with the SVRP in order to determine the final arrangement of stations for each vehicle route.
A Problem-Reduction Evolutionary Algorithm for Solving the Capacitated Vehicle Routing Problem
Directory of Open Access Journals (Sweden)
Wanfeng Liu
2015-01-01
Full Text Available Assessment of the components of a solution helps provide useful information for an optimization problem. This paper presents a new population-based problem-reduction evolutionary algorithm (PREA based on the solution components assessment. An individual solution is regarded as being constructed by basic elements, and the concept of acceptability is introduced to evaluate them. The PREA consists of a searching phase and an evaluation phase. The acceptability of basic elements is calculated in the evaluation phase and passed to the searching phase. In the searching phase, for each individual solution, the original optimization problem is reduced to a new smaller-size problem. With the evolution of the algorithm, the number of common basic elements in the population increases until all individual solutions are exactly the same which is supposed to be the near-optimal solution of the optimization problem. The new algorithm is applied to a large variety of capacitated vehicle routing problems (CVRP with customers up to nearly 500. Experimental results show that the proposed algorithm has the advantages of fast convergence and robustness in solution quality over the comparative algorithms.
What Is the Best Route? Route-Finding Strategies of Middle School Students Using GIS
Wigglesivorth, John C.
2003-01-01
This paper summarizes a research project conducted to investigate the strategies developed by middle school students to solve a route-finding problem using Arc View GIS software. Three different types of route-finding strategies were identified. Some students were visual route-finders and used a highly visual strategy; others were logical route…
Problems in the Information Dissemination of the Internet Routing
Institute of Scientific and Technical Information of China (English)
ZHAO YiXin(赵邑新); YIN Xia(尹霞); WU JianPing(吴建平)
2003-01-01
Internet routing is achieved by a set of nodes running distributed algorithms -routing protocols. However, many nodes are resistless to wrong messages or improper operations,unable to detect or correct them. Thus a wrong message or an improper operation can easilysweep almost the whole Internet. Such a fragile Internet routing comes from the features of thesealgorithms and protocols. Besides, the strategies taken by the network equipment manufacturersand administrators also are of important influence. When determining the options or selectionsin the implementation/operation, they always pay more attention to the expense of a single nodeor a single area and make some simplifications in implementations and configurations while caringless about the influence on the whole network. This paper tries to illustrate such a scheme is notreasonable at all and suggests the consideration from the view of the overall optimization. Fromthree typical cases involved in the Internet routing, a general model is abstracted, which makes theresults signiflcative for more Internet related aspects. This paper evaluates the complexity of thetheoretical analysis, then acquires the effect of error information on the whole network through thesimulation on the Internet topology. It is shown that even very little error information can incursevere impact on the Internet. And it will take much more efforts of downstream nodes to makeremedies. This result is intuitively revealed through the comparisons in the charts and the visualpresentations. Then a hierarchical solution to establish the upgrade plan is given, which helps toupgrade the nodes of the network in a most efficient and economical way.
A Learning Automata Based Algorithm For Solving Capacitated Vehicle Routing Problem
Directory of Open Access Journals (Sweden)
Mir Mohammad Alipour
2012-03-01
Full Text Available This paper presents an approximate algorithm based on distributed learning automata for solving capacitated vehicle routing problem. The vehicle routing problem (VRP is an NP-hard problem and capacitated vehicle routing problem variant (CVRP is considered here. This problem is one of the NP-hard problems and for this reason many approximate algorithms have been designed for solving it. Distributed learning automata that is a general searching tool and is a solving tool for variety of NP-complete problems, is used to solve this problem and tested on fourteen benchmark problems. Our results were compared to the best known results. The results of comparison have shown the efficiency of the proposed algorithm.
Sarwono, A. A.; Ai, T. J.; Wigati, S. S.
2017-01-01
Vehicle Routing Problem (VRP) is a method for determining the optimal route of vehicles in order to serve customers starting from depot. Combination of the two most important problems in distribution logistics, which is called the two dimensional loading vehicle routing problem, is considered in this paper. This problem combines the loading of the freight into the vehicles and the successive routing of the vehicles along the route. Moreover, an additional feature of last-in-first-out loading sequencesis also considered. In the sequential two dimensional loading capacitated vehicle routing problem (sequential 2L-CVRP), the loading must be compatible with the trip sequence: when the vehicle arrives at a customer i, there must be no obstacle (items for other customers) between the item of i and the loading door (rear part) of the vehicle. In other words, it is not necessary to move non-i’s items whenever the unloading process of the items of i. According with aforementioned conditions, a program to solve sequential 2L-CVRP is required. A nearest neighbor algorithm for solving the routing problem is presented, in which the loading component of the problem is solved through a collection of 5 packing heuristics.
Solving the vehicle routing problem by a hybrid meta-heuristic algorithm
Yousefikhoshbakht, Majid; Khorram, Esmaile
2012-01-01
The vehicle routing problem (VRP) is one of the most important combinational optimization problems that has nowadays received much attention because of its real application in industrial and service problems. The VRP involves routing a fleet of vehicles, each of them visiting a set of nodes such that every node is visited by exactly one vehicle only once. So, the objective is to minimize the total distance traveled by all the vehicles. This paper presents a hybrid two-phase algorithm called s...
Layered Formulation for the Robust Vehicle Routing Problem with Time Windows
2012-01-01
International audience; This paper studies the vehicle routing problem with time windows where travel times are uncertain and belong to a predetermined polytope. The objective of the problem is to find a set of routes that services all nodes of the graph and that are feasible for all values of the travel times in the uncertainty polytope. The problem is motivated by maritime transportation where delays are frequent and must be taken into account. We present an extended formulation for the veh...
An Adaptable Variable Neighborhood Search for the Vehicle Routing Problem with Order Outsourcing
2014-01-01
In practice, many package transportation companies lower their costs by hiring outside carriers to serve orders that cannot be served efficiently by their own trucks. The problem which takes the order outsource option into account is the Vehicle Routing Problem with Private Fleet and Common Carrier. In this variant of the Vehicle Routing Problem, orders are either delivered by an outside carrier, the common carrier, which receives an order specific price for this or by the own fleet, the priv...
A Cluster Based Scatter Search Heuristic for the Vehicle Routing Problem
Wendolsky, Rolf; Scheuerer, Stephan
2006-01-01
The Vehicle Routing Problem (VRP) is one of the most studied problems in the field of Operations Research. Closely related to the VRP is the Capacitated Clustering Problem (CCP). The VRP can be considered as an 'extension' of the CCP in the way that for each cluster in the CCP solution, additionally a route through all cluster customers and the depot has to be constructed to generate the routing information. In a previous study the Scatter Search methodology was used to solve the CCP. This al...
The Linehaul-Feeder Vehicle Routing Problem with Virtual Depots and Time Windows
Directory of Open Access Journals (Sweden)
Huey-Kuo Chen
2011-01-01
Full Text Available This paper addresses the linehaul-feeder vehicle routing problem with virtual depots and time windows (LFVRPTW. Small and large vehicles deliver services to customers within time constraints; small vehicles en route may reload commodities from either the physical depot or from the larger vehicle at a virtual depot before continuing onward. A two-stage solution heuristic involving Tabu search is proposed to solve this problem. The test results show that the LFVRPTW performs better than the vehicle routing problem with time windows in terms of both objective value and the number of small vehicles dispatched.
DEFF Research Database (Denmark)
Cetin, Bilge Kartal; Prasad, Neeli R.; Prasad, Ramjee
2011-01-01
of the maximum lifetime routing problem that considers the operation modes of the node. Solution of the linear programming gives the upper analytical bound for the network lifetime. In order to illustrate teh application of the optimization model, we solved teh problem for different parameter settings...... protocols, and the energy model for transmission. In this paper, we tackle the routing challenge for maximum lifetime of the sensor network. We introduce a novel linear programming approach to the maximum lifetime routing problem. To the best of our knowledge, this is the first mathematical programming...
Refinements of the column generation process for the Vehicle Routing Problem with Time Windows
DEFF Research Database (Denmark)
Larsen, Jesper
2004-01-01
The Vehicle Routing Problem with Time Windows is a generalization of the well known capacity constrained Vehicle Routing Problem. A homogeneous fleet of vehicles has to service a set of the customers and fulfill their demands. The service of the customers can only start within a well-defined time......-and-Bound, also known as Branch-and-Price. This paper presents two ideas for run-time improvements of the Branch-and-Price framework for the Vehicle Routing Problem with Time Windows. Both ideas reveal a significant potential for using run-time refinements when speeding up an exact approach without compromising...
Hybrid discrete particle swarm 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 NP-hard problem. For large-scale problems, it is quite difficult to achieve an optimal solution with traditional optimization methods due to the high computational complexity. A new hybrid approximation algorithm is developed in this work to solve the problem. In the hybrid algorithm, discrete particle swarm optimization (DPSO) combines global search and local search to search for the optimal results and simulated annealing (SA) uses certain probability to avoid being trapped in a local optimum. The computational study showed that the proposed algorithm is a feasible and effective approach for capacitated vehicle routing problem, especially for large scale problems.
Optimization of Capacitated Vehicle Routing Problem by Nested Particle Swarm Optimization
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Karuppusamy Kanthavel
2011-01-01
Full Text Available Problem statement: Vehicle routing problem determines the optimum route for each vehicle as a sequence of visiting cities. The problem has been defined as NP-hard and exact solution is relatively difficult to achieve for real time large scale models. Though several attempts to solve the problem were made in the literature, new approaches may be tried to solve the problem to further reduce computational efforts. Approach: In this context this study focuses on maximum utilization of loading capacity and determines the optimum set of vehicle routes for Capacitated Vehicle Routing Problem (CVRP by a Nested Particle Swarm Optimization (NPSO technique. The algorithm is implemented as Master PSO and slave PSO for the identification of candidate list and route sequence in nested form to optimize the model. Results: Benchmarking data set of capacitated vehicle routing is considered for the evaluations. The total distance of set vehicle route obtained by the new approach is compared with the best known solution and other existing techniques. Conclusions/Recommendations: The NPSO produces significant results and computational performance than the existing PSO algorithms. This newly proposed NPSO algorithm develops the vehicle schedule without any local optimization technique.
The waste collection vehicle routing problem with time windows in a city logistics context
DEFF Research Database (Denmark)
Buhrkal, Katja Frederik; Larsen, Allan; Røpke, Stefan
2012-01-01
Collection of waste is an important logistic activity within any city. In this paper we study how to collect waste in an efficient way. We study the Waste Collection Vehicle Routing Problem with Time Window which is concerned with finding cost optimal routes for garbage trucks such that all garbage...
A savings based method for real-life vehicle routing problems
A. Poot; G. Kant; A.P.M. Wagelmans (Albert)
1999-01-01
textabstractThis paper describes a Savings Based algorithm for the Extended Vehicle Routing Problem. This algorithm is compared with a Sequential Insertion algorithm on real-life data. Besides the traditional quality measures such as total distance traveled and total workload, we compare the routing
The vehicle routing problem with time windows: State-of-the-art exact solution methods
DEFF Research Database (Denmark)
Desaulniers, Guy; Desrosiers, Jacques; Spoorendonk, Simon
2011-01-01
The vehicle routing problem with time windows (VRPTW) consists of finding least-cost vehicle routes to service given customers exactly once each while satisfying the vehicle capacity and customer time windows. The VRPTW has been widely studied. We present here a short survey on the successful exact...
Exact methods for time constrained routing and related scheduling problems
DEFF Research Database (Denmark)
Kohl, Niklas
1995-01-01
real difference is how the coordinating master problem - a concave non-differentiable maximization problem - is solved. We show how the constrained shortest path problem can be solved efficiently, and present a number of different strategies for solving the master problem. The lower bound obtainable...
Directory of Open Access Journals (Sweden)
V.PURUSHOTHAM REDDY
2011-02-01
Full Text Available In computer networks the routing is based on shortest path routing algorithms. Based on its advantages, an alternative method is used known as Genetic Algorithm based routing algorithm, which is highly scalable and insensitive to variations in network topology. Here we propose a coarse-grained parallel genetic algorithm to solve the shortest path routing problem with the primary goal of computation time reduction along with the use of migration scheme. This algorithm is developed and implemented on an MPI cluster. The effects of migration and its performance is studied in this paper.
Two-Phase Heuristic for the Vehicle Routing Problem with Time Windows
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Sándor Csiszár
2007-08-01
Full Text Available The subject of the paper is a complete solution for the vehicle routing problemwith time windows, an industrial realization of an NP hard combinatorial optimizationproblem. The primary objective –the minimization of the number of routes- is aimed in thefirst phase, the secondary objective –the travel distance minimization- is going to berealized in the second phase by tabu search. The initial route construction applies aprobability density function for seed selection. Guided Route Elimination procedure wasalso developed. The solution was tested on the Solomon Problem Set and seems to be verycompeitive with the best heuristics published in the latest years (2003-2005.
A Rounding by Sampling Approach to the Minimum Size k-Arc Connected Subgraph Problem
Laekhanukit, Bundit; Singh, Mohit
2012-01-01
In the k-arc connected subgraph problem, we are given a directed graph G and an integer k and the goal is the find a subgraph of minimum cost such that there are at least k-arc disjoint paths between any pair of vertices. We give a simple (1 + 1/k)-approximation to the unweighted variant of the problem, where all arcs of G have the same cost. This improves on the 1 + 2/k approximation of Gabow et al. [GGTW09]. Similar to the 2-approximation algorithm for this problem [FJ81], our algorithm simply takes the union of a k in-arborescence and a k out-arborescence. The main difference is in the selection of the two arborescences. Here, inspired by the recent applications of the rounding by sampling method (see e.g. [AGM+ 10, MOS11, OSS11, AKS12]), we select the arborescences randomly by sampling from a distribution on unions of k arborescences that is defined based on an extreme point solution of the linear programming relaxation of the problem. In the analysis, we crucially utilize the sparsity property of the ext...
A branch-and-cut algorithm for the vehicle routing problem with multiple use of vehicles
Directory of Open Access Journals (Sweden)
İsmail Karaoğlan
2015-06-01
Full Text Available This paper addresses the vehicle routing problem with multiple use of vehicles (VRPMUV, an important variant of the classic vehicle routing problem (VRP. Unlike the classical VRP, vehicles are allowed to use more than one route in the VRPMUV. We propose a branch-and-cut algorithm for solving the VRPMUV. The proposed algorithm includes several valid inequalities from the literature for the purpose of improving its lower bounds, and a heuristic algorithm based on simulated annealing and a mixed integer programming-based intensification procedure for obtaining the upper bounds. The algorithm is evaluated in terms of the test problems derived from the literature. The computational results which follow show that, if there were 120 customers on the route (in the simulation, the problem would be solved optimally in a reasonable amount of time.
Adaptive search techniques for problems in vehicle routing, part II: A numerical comparison
Directory of Open Access Journals (Sweden)
Kritzinger Stefanie
2015-01-01
Full Text Available Research in the field of vehicle routing often focused on finding new ideas and concepts in the development of fast and efficient algorithms for an improved solution process. Early studies introduce static tailor-made strategies, but trends show that algorithms with generic adaptive policies - which emerged in the past years - are more efficient to solve complex vehicle routing problems. In this first part of the survey, we present an overview of recent literature dealing with adaptive or guided search techniques for problems in vehicle routing.
Adaptive search techniques for problems in vehicle routing, part I: A survey
Directory of Open Access Journals (Sweden)
Kritzinger Stefanie
2015-01-01
Full Text Available Research in the field of vehicle routing often focused on finding new ideas and concepts in the development of fast and efficient algorithms for an improved solution process. Early studies introduce static tailor-made strategies, but trends show that algorithms with generic adaptive policies - which emerged in the past years - are more efficient to solve complex vehicle routing problems. In this first part of the survey, we present an overview of recent literature dealing with adaptive or guided search techniques for problems in vehicle routing.
A heterogeneous fleet vehicle routing model for solving the LPG distribution problem: A case study
Onut, S.; Kamber, M. R.; Altay, G.
2014-03-01
Vehicle Routing Problem (VRP) is an important management problem in the field of distribution and logistics. In VRPs, routes from a distribution point to geographically distributed points are designed with minimum cost and considering customer demands. All points should be visited only once and by one vehicle in one route. Total demand in one route should not exceed the capacity of the vehicle that assigned to that route. VRPs are varied due to real life constraints related to vehicle types, number of depots, transportation conditions and time periods, etc. Heterogeneous fleet vehicle routing problem is a kind of VRP that vehicles have different capacity and costs. There are two types of vehicles in our problem. In this study, it is used the real world data and obtained from a company that operates in LPG sector in Turkey. An optimization model is established for planning daily routes and assigned vehicles. The model is solved by GAMS and optimal solution is found in a reasonable time.
Developing a chaotic pattern of dynamic Hazmat routing problem
Directory of Open Access Journals (Sweden)
Abbas Mahmoudabadi
2014-03-01
Full Text Available The present paper proposes an iterative procedure based on chaos theory on dynamic risk definition to determine the best route for transporting hazardous materials (Hazmat. In the case of possible natural disasters, the safety of roads may be seriously affected. So the main objective of this paper is to simultaneously improve the travel time and risk to satisfy the local and national authorities in the transportation network. Based on the proposed procedure, four important risk components including accident information, population, environment, and infrastructure aspects have been presented under linguistic variables. Furthermore, the extent analysis method was utilized to convert them to crisp values. To apply the proposed procedure, a road network that consists of fifty nine nodes and eighty two-way edges with a pre-specified affected area has been considered. The results indicate that applying the dynamic risk is more appropriate than having a constant risk. The application of the proposed model indicates that, while chaotic variables depend on the initial conditions, the most frequent path will remain independent. The points that would help authorities to come to the better decision when they are dealing with Hazmat transportation route selection.
REFINEMENTS OF THE COLUMN GENERATION PROCESS FOR THE VEHICLE ROUTING PROBLEM WITH TIME WINDOWS
Institute of Scientific and Technical Information of China (English)
Jesper LARSEN
2004-01-01
The Vehicle Routing Problem with Time Windows is a generalization of the well known capacity constrained Vehicle Routing Problem. A homogeneous fleet of vehicles has to service a set of customers. The service of the customers can only start within a well-defined time interval denoted the time window. The objective is to determine routes for the vehicles that minimizes the accumulated cost (or distance). Currently the best approaches for determining optimal solutions are based on column generation and Branch-and-Bound, also known as Branch-and-Price. This paper presents two ideas for run-time improvements of the Branch-and-Price framework for the Vehicle Routing Problem with Time Windows. Both ideas reveal a significant potential for run-time refinements when speeding up an exact approach without compromising optimality.
Location-routing Problem with Fuzzy time windows and Traffic time
Directory of Open Access Journals (Sweden)
Shima Teimoori
2014-05-01
Full Text Available The location-routing problem is a relatively new branch of logistics system. Its objective is to determine a suitable location for constructing distribution warehouses and proper transportation routing from warehouse to the customer. In this study, the location-routing problem is investigated with considering fuzzy servicing time window for each customer. Another important issue in this regard is the existence of congested times during the service time and distributing goods to the customer. This caused a delay in providing service for customer and imposed additional costs to distribution system. Thus we have provided a mathematical model for designing optimal distributing system. Since the vehicle location-routing problem is Np-hard, thus a solution method using genetic meta-heuristic algorithm was developed and the optimal sequence of servicing for the vehicle and optimal location for the warehouses were determined through an example.
Applying AN Integrated Route Optimization Method as a Solution to the Problem of Waste Collection
Salleh, A. H.; Ahamad, M. S. S.; Yusoff, M. S.
2016-09-01
Solid waste management (SWM) is very subjective to budget control where the utmost expenses are devoted to the waste collection's travel route. The common understanding of the travel route in SWM is that shorter route is cheaper. However, in reality it is not necessarily true as the SWM compactor truck is affected by various aspects which leads to higher fuel consumption. Thus, this ongoing research introduces a solution to the problem using multiple criteria route optimization process integrated with AHP/GIS as its main analysis tools. With the criteria obtained from the idea that leads to higher fuel consumption based on road factors, road networks and human factors. The weightage of criteria is obtained from the combination of AHP with the distance of multiple shortest routes obtained from GIS. A solution of most optimum routes is achievable and comparative analysis with the currently used route by the SWM compactor truck can be compared. It is expected that the decision model will be able to solve the global and local travel route problem in MSW.
Route of cocaine administration: patterns of use and problems among a Brazilian sample.
Ferri, C P; Gossop, M
1999-01-01
Route of administration has important implications for the understanding of drug addiction and related-problems. This cross-sectional study investigates patterns of consumption and cocaine-related problems among snorting and crack cocaine users in São Paulo and outlines changes in route of cocaine administration in Brazil between 1980-1997. Crack cocaine users had more social and health problems and higher involvement in crime than intranasal users. These problems, compounded by the larger doses being used and their greater involvement in prostitution, place crack cocaine users at higher risk from HIV infection and other sexually transmitted diseases as well as other physical risks.
Genetic Algorithm and Tabu Search for Vehicle Routing Problems with Stochastic Demand
Ismail, Zuhaimy; Irhamah
2010-11-01
This paper presents a problem of designing solid waste collection routes, involving scheduling of vehicles where each vehicle begins at the depot, visits customers and ends at the depot. It is modeled as a Vehicle Routing Problem with Stochastic Demands (VRPSD). A data set from a real world problem (a case) is used in this research. We developed Genetic Algorithm (GA) and Tabu Search (TS) procedure and these has produced the best possible result. The problem data are inspired by real case of VRPSD in waste collection. Results from the experiment show the advantages of the proposed algorithm that are its robustness and better solution qualities.
2016-01-01
The multi Vehicle Routing Problem with Pickup and Delivery with Time Windows is a challenging version of the Vehicle Routing Problem. In this paper, by embedding many complex assignment routing constraints through constructing a multi dimensional network, we intend to reach optimality for local clusters derived from a reasonably large set of passengers on real world transportation networks. More specifically, we introduce a multi vehicle state space time network representation in which only t...
Directory of Open Access Journals (Sweden)
X. Q. Tian
2012-01-01
Full Text Available Traffic network equilibrium problems with capacity constraints of arcs are studied. A (weak vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of Lin (2010, and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a (weak vector equilibrium flow to be a parametric equilibrium flow are derived. Relationships between a parametric equilibrium flow and a solution of a scalar variational inequality problem are also discussed. Some examples are given to illustrate our results.
A Hybrid Algorithm Based on ACO and PSO for Capacitated Vehicle Routing Problems
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Yucheng Kao
2012-01-01
Full Text Available The vehicle routing problem (VRP is a well-known combinatorial optimization problem. It has been studied for several decades because finding effective vehicle routes is an important issue of logistic management. This paper proposes a new hybrid algorithm based on two main swarm intelligence (SI approaches, ant colony optimization (ACO and particle swarm optimization (PSO, for solving capacitated vehicle routing problems (CVRPs. In the proposed algorithm, each artificial ant, like a particle in PSO, is allowed to memorize the best solution ever found. After solution construction, only elite ants can update pheromone according to their own best-so-far solutions. Moreover, a pheromone disturbance method is embedded into the ACO framework to overcome the problem of pheromone stagnation. Two sets of benchmark problems were selected to test the performance of the proposed algorithm. The computational results show that the proposed algorithm performs well in comparison with existing swarm intelligence approaches.
The integrated model for solving the single-period deterministic inventory routing problem
Rahim, Mohd Kamarul Irwan Abdul; Abidin, Rahimi; Iteng, Rosman; Lamsali, Hendrik
2016-08-01
This paper discusses the problem of efficiently managing inventory and routing problems in a two-level supply chain system. Vendor Managed Inventory (VMI) policy is an integrating decisions between a supplier and his customers. We assumed that the demand at each customer is stationary and the warehouse is implementing a VMI. The objective of this paper is to minimize the inventory and the transportation costs of the customers for a two-level supply chain. The problem is to determine the delivery quantities, delivery times and routes to the customers for the single-period deterministic inventory routing problem (SP-DIRP) system. As a result, a linear mixed-integer program is developed for the solutions of the SP-DIRP problem.
Considering lost sale in inventory routing problems for perishable goods
DEFF Research Database (Denmark)
Mirzaei, Samira; Seifi, Abbas
2015-01-01
to optimality for small instances and is used to obtain lower bounds for larger instances. We have also devised an efficient meta-heuristic algorithm to find good solutions for this class of problems based on Simulated Annealing (SA) and Tabu Search (TS). Computational results indicate that, for small problems......, the average optimality gaps are less than 10.9% and 13.4% using linear and exponential lost sale functions, respectively. Furthermore, we show that the optimality gaps found by CPLEX grow exponentially with the problem size while those obtained by the proposed meta-heuristic algorithm increase linearly....
MULTI-VEHICLE COVERING TOUR PROBLEM: BUILDING ROUTES FOR URBAN PATROLLING
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Washington Alves de Oliveira
2015-12-01
Full Text Available ABSTRACT In this paper we study a particular aspect of the urban community policing: routine patrol route planning. We seek routes that guarantee visibility, as this has a sizable impact on the community perceived safety, allowing quick emergency responses and providing surveillance of selected sites (e.g., hospitals, schools. The planning is restricted to the availability of vehicles and strives to achieve balanced routes. We study an adaptation of the model for the multi-vehicle covering tour problem, in which a set of locations must be visited, whereas another subset must be close enough to the planned routes. It constitutes an NP-complete integer programming problem. Suboptimal solutions are obtained with several heuristics, some adapted from the literature and others developed by us. We solve some adapted instances from TSPLIB and an instance with real data, the former being compared with results from literature, and latter being compared with empirical data.
Optimization of min-max vehicle routing problem based on genetic algorithm
Liu, Xia
2013-10-01
In some cases, there are some special requirements for the vehicle routing problem. Personnel or goods geographically scattered, should be delivered simultaneously to an assigned place by a fleet of vehicles as soon as possible. In this case the objective is to minimize the distance of the longest route among all sub-routes. An improved genetic algorithm was adopted to solve these problems. Each customer has a unique integer identifier and the chromosome is defined as a string of integers. Initial routes are constructed randomly, and then standard proportional selection incorporating elitist is chosen to guarantee the best member survives. New crossover and 2-exchange mutation is adopted to increase the diversity of group. The algorithm was implemented and tested on some instances. The results demonstrate the effectiveness of the method.
AUTOMATED GUIDED VEHICLE (AGV SYSTEMS AND ROUTING PROBLEM IN DEPOT MAINTENANCE
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Fatih YİĞİT
2003-02-01
Full Text Available When full automation is realized in factory automation, material handing systems (MHS have a fairly important role. The most technological development among MHS's has been concentrated on Automated Guided Vehicle (AGV systems. An AGV is an unmanned vehicle capable of following an external guidance signal to deliver a unit load from destination to destination. Nowadays, there are a lot of applications lie along service sector to industrial sector because of flexibilities of AGVs. In this study, these subjects have been applied on the Army Aviation Depot Maintenance where aircraft's and aircraft parts can be maintained and overhauled is an application fields of AGV, requiring AGV numbers and AGV routing. The AGV routing problem and traveling sales person (TSP problems are identical problems; where the AGV routing problem is formulated as a zero one integer programming. Examples are presented to demonstrate the approach and LINGO has been used to solve the example.
Approximate solution of the multiple watchman routes problem with restricted visibility range.
Faigl, Jan
2010-10-01
In this paper, a new self-organizing map (SOM) based adaptation procedure is proposed to address the multiple watchman route problem with the restricted visibility range in the polygonal domain W. A watchman route is represented by a ring of connected neuron weights that evolves in W, while obstacles are considered by approximation of the shortest path. The adaptation procedure considers a coverage of W by the ring in order to attract nodes toward uncovered parts of W. The proposed procedure is experimentally verified in a set of environments and several visibility ranges. Performance of the procedure is compared with the decoupled approach based on solutions of the art gallery problem and the consecutive traveling salesman problem. The experimental results show the suitability of the proposed procedure based on relatively simple supporting geometrical structures, enabling application of the SOM principles to watchman route problems in W.
Nair, T R Gopalakrishnan; Yashoda, M B
2011-01-01
In Internet Routing, the static shortest path (SP) problem has been addressed using well known intelligent optimization techniques like artificial neural networks, genetic algorithms (GAs) and particle swarm optimization. Advancement in wireless communication lead more and more mobile wireless networks, such as mobile networks [mobile ad hoc networks (MANETs)] and wireless sensor networks. Dynamic nature of the network is the main characteristic of MANET. Therefore, the SP routing problem in MANET turns into dynamic optimization problem (DOP). Here the nodes ae made aware of the environmental condition, thereby making it intelligent, which goes as the input for GA. The implementation then uses GAs with immigrants and memory schemes to solve the dynamic SP routing problem (DSPRP) in MANETS. In our paper, once the network topology changes, the optimal solutions in the new environment can be searched using the new immigrants or the useful information stored in the memory. Results shows GA with new immigrants sho...
Vehicle Routing Problem Using Savings-Insertion and Reactive Tabu with a Variable Threshold
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Moussa Bagayoko
2016-12-01
Full Text Available This paper focuses on how the competitiveness of companies is impacted by products distribution and transportation costs, especially in the context of exports. This paper uses our two steps approach, consisting in building a good initial solution and then improving it to solve vehicle routing problem. To that end, first, our mathematical model is adapted; secondly, our Savings-insertion builds a good initial solution, and thirdly, our Reactive tabu with a variable threshold improves the initial solution. The objective is the minimization of the total distance of transport by respecting the specified time window and the demand of all customers, which are important for some transportation companies’. Finally, the experimental results obtained with our methodology for Solomon 100 customers 56 vehicle routing problems are provided and discussed. Our methodology provides the best solutions for problems types R2 and RC2. Therefore, using our methodology reduces the total distance for long-haul vehicle routing problems.
Solving Practical Vehicle Routing Problem with Time Windows Using Metaheuristic Algorithms
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Filip Taner
2012-07-01
Full Text Available This paper addresses the Vehicle Routing Problem with Time Windows (VRPTW and shows that implementing algorithms for solving various instances of VRPs can significantly reduce transportation costs that occur during the delivery process. Two metaheuristic algorithms were developed for solving VRPTW: Simulated Annealing and Iterated Local Search. Both algorithms generate initial feasible solution using constructive heuristics and use operators and various strategies for an iterative improvement. The algorithms were tested on Solomon’s benchmark problems and real world vehicle routing problems with time windows. In total, 44 real world problems were optimized in the case study using described algorithms. Obtained results showed that the same distribution task can be accomplished with savings up to 40% in the total travelled distance and that manually constructed routes are very ineffective.
A heuristic approach based on Clarke-Wright algorithm for open vehicle routing problem.
Pichpibul, Tantikorn; Kawtummachai, Ruengsak
2013-01-01
We propose a heuristic approach based on the Clarke-Wright algorithm (CW) to solve the open version of the well-known capacitated vehicle routing problem in which vehicles are not required to return to the depot after completing service. The proposed CW has been presented in four procedures composed of Clarke-Wright formula modification, open-route construction, two-phase selection, and route postimprovement. Computational results show that the proposed CW is competitive and outperforms classical CW in all directions. Moreover, the best known solution is also obtained in 97% of tested instances (60 out of 62).
A weighted min-max model for balanced freight train routing problem with fuzzy information
Yang, Lixing; Gao, Ziyou; Li, Xiang; Li, Keping
2011-12-01
A multi-objective freight train routing problem with fuzzy information is investigated in this article. To handle the fuzziness in the railway transportation system, the measure ℳλ (i.e. the convex combination of a possibility measure and a necessity measure) is first introduced. Then, a min-max chance-constrained programming model is constructed to obtain optimal train routing plans. In order to solve the model, a potential route algorithm, fuzzy simulation and tabu search algorithm are integrated as a hybrid algorithm. Finally, some numerical experiments are performed to show the applications of the model and the algorithm.
A route-based decomposition for the Multi-Commodity k-splittable Maximum Flow Problem
DEFF Research Database (Denmark)
Gamst, Mette
2012-01-01
The Multi-Commodity k-splittable Maximum Flow Problem routes flow through a capacitated graph such that each commodity uses at most k paths and such that the total amount of routedflow is maximized. This paper proposes a branch-and-price algorithm based on a route-based Dantzig-Wolfe decomposition......, where a route consists of up to k paths. Computational results show that the new algorithm has best performance on seven benchmark instances and is capable of solving two previously unsolved instances....
The vehicle routing problem with edge set costs
DEFF Research Database (Denmark)
Reinhardt, Line Blander; Jepsen, Mads Kehlet; Pisinger, David
. The certifications and contributions impose a cost for the company while they also give unlimited usage of a set of roads to all vehicles belonging to the company. Different versions for defining the edge sets are discussed and formulated. A MIP-formulation of the problem is presented, and a solution method based...
A savings based method for real-life vehicle routing problems
1999-01-01
textabstractThis paper describes a Savings Based algorithm for the Extended Vehicle Routing Problem. This algorithm is compared with a Sequential Insertion algorithm on real-life data. Besides the traditional quality measures such as total distance traveled and total workload, we compare the routing plans of both algorithms according to non-standard quality measures that help to evaluate the "visual attractiveness" of the plan. Computational results show that, in general, the Savings Based al...
A Variable Neighborhood Search-Based Heuristic for the Multi-Depot Vehicle Routing Problem
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Arif Imran
2013-01-01
Full Text Available The multi-depot vehicle routing problem (MDVRP is addressed using an adaptation of the variable neighborhood search (VNS. The proposed VNS algorithm besides using several neighborhoods and a number of local searches has a number of additional features. These include a scheme for identifying borderline customers, a diversivication procedure and a mechanism that aggregates and disaggregates routes between depots. The proposed algorithm is tested on the data instances from the literature and produces competitive results.
Determining which Orders to Outsource in the Vehicle Routing Problem with Order Outsourcing
Huijink, Sybren; Kant, Goos; Peeters, Rene
2015-01-01
In practice, many package transportation companies lower their costs by hiring outside carriers to serve orders that cannot be served efficiently by their own trucks. The problem which takes the order outsource option into account is the Vehicle Routing Problem with Private Fleet and Common Carrier.
A branch-and-cut algorithm for the symmetric two-echelon capacitated vehicle routing problem
DEFF Research Database (Denmark)
Jepsen, Mads Kehlet; Spoorendonk, Simon; Røpke, Stefan
2013-01-01
This paper presents an exact method for solving the symmetric two-echelon capacitated vehicle routing problem, a transportation problem concerned with the distribution of goods from a depot to a set of customers through a set of satellite locations. The presented method is based on an edge flow...
An Adaptable Variable Neighborhood Search for the Vehicle Routing Problem with Order Outsourcing
Huijink, S.; Kant, G.; Peeters, M.J.P.
2014-01-01
In practice, many package transportation companies lower their costs by hiring outside carriers to serve orders that cannot be served efficiently by their own trucks. The problem which takes the order outsource option into account is the Vehicle Routing Problem with Private Fleet and Common Carrier.
A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands
DEFF Research Database (Denmark)
Christiansen, Christian Holk; Lysgaard, Jens
2007-01-01
This article introduces a new exact algorithm for the Capacitated Vehicle Routing Problem with Stochastic Demands (CVRPSD). The CVRPSD can be formulated as a Set Partitioning Problem and it is shown that the associated column generation subproblem can be solved using a dynamic programming scheme...
Using Grey Wolf Algorithm to Solve the Capacitated Vehicle Routing Problem
Korayem, L.; Khorsid, M.; Kassem, S. S.
2015-05-01
The capacitated vehicle routing problem (CVRP) is a class of the vehicle routing problems (VRPs). In CVRP a set of identical vehicles having fixed capacities are required to fulfill customers' demands for a single commodity. The main objective is to minimize the total cost or distance traveled by the vehicles while satisfying a number of constraints, such as: the capacity constraint of each vehicle, logical flow constraints, etc. One of the methods employed in solving the CVRP is the cluster-first route-second method. It is a technique based on grouping of customers into a number of clusters, where each cluster is served by one vehicle. Once clusters are formed, a route determining the best sequence to visit customers is established within each cluster. The recently bio-inspired grey wolf optimizer (GWO), introduced in 2014, has proven to be efficient in solving unconstrained, as well as, constrained optimization problems. In the current research, our main contributions are: combining GWO with the traditional K-means clustering algorithm to generate the ‘K-GWO’ algorithm, deriving a capacitated version of the K-GWO algorithm by incorporating a capacity constraint into the aforementioned algorithm, and finally, developing 2 new clustering heuristics. The resulting algorithm is used in the clustering phase of the cluster-first route-second method to solve the CVR problem. The algorithm is tested on a number of benchmark problems with encouraging results.
Half a Century of Oman Ophiolite Studies: SSZ or MOR, the Arc Disposal Problem
Gregory, R. T.; Gray, D.
2014-12-01
The Samail Ophiolite, one of the largest and best exposed ophiolite complexes, is a Tethyan ophiolite obducted in the Late Cretaceous onto the formerly passive Arabian platform as Arabia began its most recent >1000 km northward migration towards a Miocene collision with Eurasia. The Oman Mountains, northeastern Arabian Peninsula have yet to collide with Eurasia; present uplift and form of the mountains also date to the Miocene. In addition to the scientific scrutiny of the ophiolite complex, the geologic constraints on the timing and emplacement of the ophiolite are abundant with no consensus on the obduction mechanism or its original tectonic setting. The crustal thickness of the ophiolite is comparable to thicknesses observed for "normal" mid-ocean ridges. Largely on the basis of structural and paleomagnetic arguments, some workers have attributed its origin to Pacific-type fast spreading ridges and complex micro plate geometries. Indeed the lower pillow lava sequences and much of the gabbroic crust have isotope and geochemical signatures consistent with a MORB source. However, because of the geochemistry of the upper pillow lavas, the ophiolite is most often characterized as a supra-subduction zone (SSZ) ophiolite, i.e. it sits in the hanging wall of some large tectonic structure for part of its history. In the absence of a preserved arc, the SSZ designation has little explanatory power only being a declaration of allochthony or about chemical properties of the mantle source. That associated continental shelf and oceanic crustal sections have suffered either clockwise or counterclockwise PT time trajectories requires some type of nascent subduction and hanging wall thrust transport of the young ridge crest. The widespread Late Cretaceous obduction of Tethyan oceanic crust and mantle over thousands of kilometers strike length is a problem for SSZ models (arc, forearc, back arc etc.) because arc initiation results in thick crust on short time scales, none of which
Green open location-routing problem considering economic and environmental costs
Directory of Open Access Journals (Sweden)
Eliana M. Toro
2016-12-01
Full Text Available This paper introduces a new bi-objective vehicle routing problem that integrates the Open Location Routing Problem (OLRP, recently presented in the literature, coupled with the growing need for fuel consumption minimization, named Green OLRP (G-OLRP. Open routing problems (ORP are known to be NP-hard problems, in which vehicles start from the set of existing depots and are not required to return to the starting depot after completing their service. The OLRP is a strategic-level problem involving the selection of one or many depots from a set of candidate locations and the planning of delivery radial routes from the selected depots to a set of customers. The concept of radial paths allows us to use a set of constraints focused on maintaining the radiality condition of the paths, which significantly simplifies the set of constraints associated with the connectivity and capacity requirements and provides a suitable alternative when compared with the elimination problem of sub-tours traditionally addressed in the literature. The emphasis in the paper will be placed on modeling rather than solution methods. The model proposed is formulated as a bi-objective problem, considering the minimization of operational costs and the minimization of environmental effects, and it is solved by using the epsilon constraint technique. The results illustrate that the proposed model is able to generate a set of trade-off solutions leading to interesting conclusions about the relationship between operational costs and environmental impact.
On the Integrated Job Scheduling and Constrained Network Routing Problem
DEFF Research Database (Denmark)
Gamst, Mette
This paper examines the NP-hard problem of scheduling a number of jobs on a finite set of machines such that the overall profit of executed jobs is maximized. Each job demands a number of resources, which must be sent to the executing machine via constrained paths. Furthermore, two resource demand...... transmissions cannot use the same edge in the same time period. An exact solution approach based on Dantzig-Wolfe decomposition is proposed along with several heuristics. The methods are computationally evaluated on test instances arising from telecommunications with up to 500 jobs and 500 machines. Results...
Research on multi-objective emergency logistics vehicle routing problem under constraint conditions
Directory of Open Access Journals (Sweden)
Miaomiao Du
2013-03-01
Full Text Available Purpose: Aim at choosing a relative good vehicle routing in emergency conditions under constraint conditions when disaster happens. Rapid response and rescue can save a lot of people. Design/methodology/approach: Modeling analysis: establishing a mathematical model of multi-objective emergency logistics vehicle routing problem. And in end of the paper, we intend to use genetic algorithms to solve the problem. Findings: Considering time requirement and cost limit both while choosing vehicle routing when the disasters happens is meaningful. We can get a relative good result and give a guidance to rescue teams. Originality/value: Consider cost and time objectives and kinds of realistic conditions (such as the road congestion in the model when solving the problem, having expanded the theory scope.
Vehicle Routing Problem with Backhaul, Multiple Trips and Time Window
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Johan Oscar Ong
2011-01-01
Full Text Available Transportation planning is one of the important components to increase efficiency and effectiveness in the supply chain system. Good planning will give a saving in total cost of the supply chain. This paper develops the new VRP variants’, VRP with backhauls, multiple trips, and time window (VRPBMTTW along with its problem solving techniques by using Ant Colony Optimization (ACO and Sequential Insertion as initial solution algorithm. ACO is modified by adding the decoding process in order to determine the number of vehicles, total duration time, and range of duration time regardless of checking capacity constraint and time window. This algorithm is tested by using set of random data and verified as well as analyzed its parameter changing’s. The computational results for hypothetical data with 50% backhaul and mix time windows are reported.
A note on "A LP-based heuristic for a time-constrained routing problem"
Muter, İbrahim; Muter, Ibrahim; Birbil, Ş. İlker; Birbil, S. Ilker; Bülbül, Kerem; Bulbul, Kerem; Şahin, Güvenç; Sahin, Guvenc
2012-01-01
Avella et al. (2006) [Avella, P., D'Auria, B., Salerno, S. (2006). A LP-based heuristic for a time-constrained routing problem. European Journal of Operational Research 173:120-124] investigate a time-constrained routing (TCR) problem. The core of the proposed solution approach is a large-scale linear program (LP) that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this LP optimally, and an optimality conditi...
The Electric Fleet Size and Mix Vehicle Routing Problem with Time Windows and Recharging Stations
DEFF Research Database (Denmark)
Hiermann, Gerhard; Puchinger, Jakob; Røpke, Stefan
2016-01-01
Due to new regulations and further technological progress in the field of electric vehicles, the research community faces the new challenge of incorporating the electric energy based restrictions into vehicle routing problems. One of these restrictions is the limited battery capacity which makes...... detours to recharging stations necessary, thus requiring efficient tour planning mechanisms in order to sustain the competitiveness of electric vehicles compared to conventional vehicles. We introduce the Electric Fleet Size and Mix Vehicle Routing Problem with Time Windows and Recharging Stations (E...
Developing a Direct Search Algorithm for Solving the Capacitated Open Vehicle Routing Problem
Simbolon, Hotman
2011-06-01
In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The strategy of releasing nonbasic variables from their bounds, combined with the "active constraint" method and the notion of superbasics, has been developed for efficiently requirements; this strategy is used to force the appropriate non-integer basic variables to move to their neighborhood integer points. A study of criteria for choosing a nonbasic variable to work with in the integerizing strategy has also been made.
Multi-depot Vehicle Routing Problem with Pickup and Delivery Requests
Sombuntham, Pandhapon; Kachitvichyanukul, Voratas
2010-10-01
This paper considers a multi-depot vehicle routing problem with pickup and delivery requests. In the problem of interest, each location may have goods for both pickup and delivery with multiple delivery locations that may not be the depots. These characteristics are quite common in industrial practice. A particle swarm optimization algorithm with multiple social learning structures is proposed for solving the practical case of multi-depot vehicle routing problem with simultaneous pickup and delivery and time window. A new decoding procedure is implemented using the PSO class provided in the ETLib object library. Computational experiments are carried out using the test instances for the pickup and delivery problem with time windows (PDPTW) as well as a newly generated instance. The preliminary results show that the proposed algorithm is able to provide good solutions to most of the test problems.
Solution to the problem of ant being stuck by ant colony routing algorithm
Institute of Scientific and Technical Information of China (English)
ZHAO Jing; TONG Wei-ming
2009-01-01
Many ant colony routing (ACR) algorithms have been presented in recent years, but few have studied the problem that ants will get stuck with probability in any terminal host when they are searching paths to route packets around a network. The problem has to be faced when designing and implementing the ACR algorithm. This article analyzes in detail the differences between the ACR and the ant colony optimization (ACO). Besides, particular restrictions on the ACR are pointed out and the three causes of ant being-stuck problem are obtained. Furthermore, this article proposes a new ant searching mechanism through dual path-checking and online routing loop removing by every intermediate node an ant visited and the destination host respectively, to solve the problem of ant being stuck and routing loop simultaneously. The result of numerical simulation is abstracted from one real network. Compared with existing two typical ACR algorithms, it shows that the proposed algorithm can settle the problem of ant being stuck and achieve more effective searching outcome for optimization path.
2013-01-01
Transportation costs constitute a significant fraction of total logistics cost in Supply Chain Management (SCM). To reduce transportation costs, improve customer service and to achieve maximum customer satisfaction, the optimal selection of the vehicle route is a frequent decision problem and this is commonly known as vehicle routing problem. Vehicle routing problem with one-sided time constraint, where the delivery of products from depots to distribution centers has to take place within the ...
An Investigation of Using Parallel Genetic Algorithm for Solving the Shortest Path Routing Problem
Directory of Open Access Journals (Sweden)
Salman Yussof
2011-01-01
Full Text Available Problem statement: Shortest path routing is the type of routing widely used in computer network nowadays. Even though shortest path routing algorithms are well established, other alternative methods may have their own advantages. One such alternative is to use a GA-based routing algorithm. According to previous researches, GA-based routing algorithm has been found to be more scalable and insensitive to variations in network topologies. However, it is also known that GA-based routing algorithm is not fast enough for real-time computation. Approach: To improve the computation time of GA-based routing algorithm, this study proposes a coarse-grained parallel GA routing algorithm for solving the shortest path routing problem. The proposed algorithm is evaluated using simulation where the proposed algorithm is executed on networks with various topologies and sizes. The parallel computation is performed using an MPI cluster. Three different experiments were conducted to identify the best value for the migration rate, the accuracy and execution time with respect to the number of computing nodes and speedup achieved as compared to the serial version of the same algorithm. Results: The result of the simulation shows that the best result is achieved for a migration rate around 0.1 and 0.2. The experiments also show that with larger number of computing nodes, accuracy decreases linearly, but computation time decreases exponentially, which justifies the use parallel implementation of GA to improve the speed of GA-based routing algorithm. Finally, the experiments also show that the proposed algorithm is able to achieve a speedup of up to 818.11% on the MPI cluster used to run the simulation. Conclusion/Recommendations: We have successfully shown that the performance of GA-based shortest path routing algorithm can be improved by using a coarse-grained parallel GA implementation. Even though in this study the proposed algorithm is executed
Kok, A.L.; Meyer, C.M.; Kopfer, H.; Schutten, J.M.J.
2010-01-01
In practice, apart from the problem of vehicle routing, schedulers also face the problem of finding feasible driver schedules complying with complex restrictions on drivers' driving and working hours. To address this complex interdependent problem of vehicle routing and break scheduling, we propose
The Green Ship Routing and Scheduling Problem (GSRSP): A conceptual approach
DEFF Research Database (Denmark)
Kontovas, Christos A.
2014-01-01
Recent reviews of the literature on ship routing and scheduling note the increased attention to environmental issues. This is an area of paramount importance for international shipping and will be even more so in the future. This short communication is motivated by the increasing attention...... to 'green' routing and scheduling and outlines some possible ways to incorporate the air emissions dimension into maritime transportation OR. The main contribution of this note vis-a-vis the state of the art is that it conceptualizes the formulation of the 'Green Ship Routing and Scheduling Problem' (GSRSP......) based on existing formulations and highlights all the important parameters of the problem. (C) 2014 Elsevier Ltd. All rights reserved....
An Artificial Bee Colony Algorithm for the Capacitated Vehicle Routing Problem
DEFF Research Database (Denmark)
Szeto, W.Y.; Wu, Yongzhong; Ho, Sin C.
This paper introduces an artificial bee colony heuristic for the capacitated vehicle routing problem. The artificial bee colony heuristic is a swarm-based heuristic, which mimics the foraging behavior of a honey bee swarm. The performance of the heuristic is evaluated on two sets of benchmark ins...
An artificial bee colony algorithm for the capacitated vehicle routing problem
DEFF Research Database (Denmark)
Szeto, W.Y.; Wu, Yongzhong; Ho, Sin C.
2011-01-01
This paper introduces an artificial bee colony heuristic for solving the capacitated vehicle routing problem. The artificial bee colony heuristic is a swarm-based heuristic, which mimics the foraging behavior of a honey bee swarm. An enhanced version of the artificial bee colony heuristic is also...
2015-03-26
Inventory and Distribution. Management Science, 47(8), 1101. 12. Kleywegt, Anton J., Nori , Vijay S., & Savelsbergh, Martin W. P. 2002. The Stochastic...Inventory Routing Problem with Direct Deliveries. Transportation Sci- ence, 36(1), 94. 13. Kleywegt, Anton J., Nori , Vijay S., & Savelsbergh, Martin W
Metaheuristics applied to vehicle routing. A case study. Parte 1: formulating the problem
Directory of Open Access Journals (Sweden)
Guillermo González Vargas
2010-04-01
Full Text Available This paper deals with VRP (vehicle routing problem mathematical formulation and presents some methodologies used by different authors to solve VRP variation. This paper is presented as the springboard for introducing future papers about a manufacturing company’s location decisions based on the total distance traveled to distribute its product.
The Edge Set Cost of the Vehicle Routing Problem with Time Windows
DEFF Research Database (Denmark)
Reinhardt, Line Blander; Jepsen, Mads Kehlet; Pisinger, David
2016-01-01
We consider an important generalization of the vehicle routing problem with time windows in which a fixed cost must be paid for accessing a set of edges. This fixed cost could reflect payment for toll roads, investment in new facilities, the need for certifications, and other costly investments...
Constraint Programming based Local Search for the Vehicle Routing Problem with Time Windows
Sala Reixach, Joan
2012-01-01
El projecte es centra en el "Vehicle Routing Problem with Time Windows". Explora i testeja un mètode basat en una formulació del problema en termes de programació de restriccions. Implementa un mètode de cerca local amb la capacitat de fer grans moviments anomenat "Large Neighbourhood Search".
Lagrangian duality applied to the vehicle routing problem with time windows
DEFF Research Database (Denmark)
Kallehauge, Brian; Larsen, Jesper; Madsen, Oli B.G.
2006-01-01
This paper considers the vehicle routing problem with time windows, where the service of each customer must start within a specified time interval. We consider the Lagrangian relaxation of the constraint set requiring that each customer must be served by exactly one vehicle yielding a constrained...
Stochastic time-dependent vehicle routing problem: Mathematical models and ant colony algorithm
Directory of Open Access Journals (Sweden)
Zhengyu Duan
2015-11-01
Full Text Available This article addresses the stochastic time-dependent vehicle routing problem. Two mathematical models named robust optimal schedule time model and minimum expected schedule time model are proposed for stochastic time-dependent vehicle routing problem, which can guarantee delivery within the time windows of customers. The robust optimal schedule time model only requires the variation range of link travel time, which can be conveniently derived from historical traffic data. In addition, the robust optimal schedule time model based on robust optimization method can be converted into a time-dependent vehicle routing problem. Moreover, an ant colony optimization algorithm is designed to solve stochastic time-dependent vehicle routing problem. As the improvements in initial solution and transition probability, ant colony optimization algorithm has a good performance in convergence. Through computational instances and Monte Carlo simulation tests, robust optimal schedule time model is proved to be better than minimum expected schedule time model in computational efficiency and coping with the travel time fluctuations. Therefore, robust optimal schedule time model is applicable in real road network.
Davendra, Donald; Zelinka, Ivan; Senkerik, Roman; Jasek, Roman; Bialic-Davendra, Magdalena
2012-11-01
One of the new emerging application strategies for optimization is the hybridization of existing metaheuristics. The research combines the unique paradigms of solution space sampling of SOMA and memory retention capabilities of Scatter Search for the task of capacitated vehicle routing problem. The new hybrid heuristic is tested on the Taillard sets and obtains good results.
THREE-DIMENSIONAL LOADING VEHICLE ROUTING PROBLEM SOLUTION WITH SET-PARTITIONING-BASED METHOD
2013-01-01
The article considers the optimization problem of vehicle routing with three-dimensional loading constraints. Several practical loading constraints encountered in freight transportation are formalized. The efficiency of using the set-partitioning approach to improve heuristic solution is shown by means of computational experiment.
Procedures for Vehicle Routing Problems with An Application to Milk Assembly in New York
1982-01-01
This paper discusses improved procedures for applying heuristic methods to well-known transportation and routing algorithms for solving a milk assembly problem. Miles traveled to assemble milk are reduced by up to 20 percent in a detailed case study in New York.
A Food Chain Algorithm for Capacitated Vehicle Routing Problem with Recycling in Reverse Logistics
Song, Qiang; Gao, Xuexia; Santos, Emmanuel T.
2015-12-01
This paper introduces the capacitated vehicle routing problem with recycling in reverse logistics, and designs a food chain algorithm for it. Some illustrative examples are selected to conduct simulation and comparison. Numerical results show that the performance of the food chain algorithm is better than the genetic algorithm, particle swarm optimization as well as quantum evolutionary algorithm.
The Effects of the Tractor and Semitrailer Routing Problem on Mitigation of Carbon Dioxide Emissions
Directory of Open Access Journals (Sweden)
Hongqi Li
2013-01-01
Full Text Available The incorporation of CO2 emissions minimization in the vehicle routing problem (VRP is of critical importance to enterprise practice. Focusing on the tractor and semitrailer routing problem with full truckloads between any two terminals of the network, this paper proposes a mathematical programming model with the objective of minimizing CO2 emissions per ton-kilometer. A simulated annealing (SA algorithm is given to solve practical-scale problems. To evaluate the performance of the proposed algorithm, a lower bound is developed. Computational experiments on various problems generated randomly and a realistic instance are conducted. The results show that the proposed methods are effective and the algorithm can provide reasonable solutions within an acceptable computational time.
A framework for the interactive resolution of multi-objective vehicle routing problems
Geiger, Martin Josef
2008-01-01
The article presents a framework for the resolution of rich vehicle routing problems which are difficult to address with standard optimization techniques. We use local search on the basis on variable neighborhood search for the construction of the solutions, but embed the techniques in a flexible framework that allows the consideration of complex side constraints of the problem such as time windows, multiple depots, heterogeneous fleets, and, in particular, multiple optimization criteria. In order to identify a compromise alternative that meets the requirements of the decision maker, an interactive procedure is integrated in the resolution of the problem, allowing the modification of the preference information articulated by the decision maker. The framework is prototypically implemented in a computer system. First results of test runs on multiple depot vehicle routing problems with time windows are reported.
Single-Commodity Vehicle Routing Problem with Pickup and Delivery Service
Directory of Open Access Journals (Sweden)
Goran Martinovic
2008-01-01
Full Text Available We present a novel variation of the vehicle routing problem (VRP. Single commodity cargo with pickup and delivery service is considered. Customers are labeled as either cargo sink or cargo source, depending on their pickup or delivery demand. This problem is called a single commodity vehicle routing problem with pickup and delivery service (1-VRPPD. 1-VRPPD deals with multiple vehicles and is the same as the single-commodity traveling salesman problem (1-PDTSP when the number of vehicles is equal to 1. Since 1-VRPPD specializes VRP, it is hard in the strong sense. Iterative modified simulated annealing (IMSA is presented along with greedy random-based initial solution algorithm. IMSA provides a good approximation to the global optimum in a large search space. Experiment is done for the instances with different number of customers and their demands. With respect to average values of IMSA execution times, proposed method is appropriate for practical applications.
Solving the Tractor and Semi-Trailer Routing Problem Based on a Heuristic Approach
Directory of Open Access Journals (Sweden)
Hongqi Li
2012-01-01
Full Text Available We study the tractor and semi-trailer routing problem (TSRP, a variant of the vehicle routing problem (VRP. In the TSRP model for this paper, vehicles are dispatched on a trailer-flow network where there is only one main depot, and all tractors originate and terminate in the main depot. Two types of decisions are involved: the number of tractors and the route of each tractor. Heuristic algorithms have seen widespread application to various extensions of the VRP. However, this approach has not been applied to the TSRP. We propose a heuristic algorithm to solve the TSRP. The proposed heuristic algorithm first constructs the initial route set by the limitation of a driver’s on-duty time. The candidate routes in the initial set are then filtered by a two-phase approach. The computational study shows that our algorithm is feasible for the TSRP. Moreover, the algorithm takes relatively little time to obtain satisfactory solutions. The results suggest that our heuristic algorithm is competitive in solving the TSRP.
Directory of Open Access Journals (Sweden)
C Hauman
2014-06-01
Full Text Available The vehicle routing problem with time windows is a widely studied problem with many real-world applications. The problem considered here entails the construction of routes that a number of identical vehicles travel to service different nodes within a certain time window. New benchmark problems with multi-objective features were recently suggested in the literature and the multi-objective optimisation cross-entropy method is applied to these problems to investigate the feasibility of the method and to determine and propose reference solutions for the benchmark problems. The application of the cross-entropy method to the multi-objective vehicle routing problem with soft time windows is investigated. The objectives that are evaluated include the minimisation of the total distance travelled, the number of vehicles and/or routes, the total waiting time and delay time of the vehicles and the makespan of a route.
Formulations and exact algorithms for the vehicle routing problem with time windows
DEFF Research Database (Denmark)
Kallehauge, Brian
2008-01-01
In this paper we review the exact algorithms proposed in the last three decades for the solution of the vehicle routing problem with time windows (VRPTW). The exact algorithms for the VRPTW are in many aspects inherited from work on the traveling salesman problem (TSP). In recognition of this fact...... with the analysis of the polyhedral structure of the VRPTW. We conclude by examining possible future lines of research in the area of the VRPTW....
The vehicle routing problem: State of the art classification and review
Braekers, Kris; Ramaekers, Katrien; Van Nieuwenhuyse, Inneke
2016-01-01
Over the past decades, the Vehicle Routing Problem (VRP) and its variants have grown ever more popular in the academic literature. Yet, the problem characteristics and assumptions vary widely and few literature reviews have made an effort to classify the existing articles accordingly. In this article, we present a taxonomic review of the VRP literature published between 2009 and June 2015. Based on an adapted version of an existing comprehensive taxonomy, we classify 277 articles and analyze ...
A hybrid differential evolution algorithm to vehicle routing problem with fuzzy demands
Erbao, Cao; Mingyong, Lai
2009-09-01
In this paper, the vehicle routing problem with fuzzy demands (VRPFD) is considered, and a fuzzy chance constrained program model is designed, based on fuzzy credibility theory. Then stochastic simulation and differential evolution algorithm are integrated to design a hybrid intelligent algorithm to solve the fuzzy chance constrained program model. Moreover, the influence of the dispatcher preference index on the final objective of the problem is discussed using stochastic simulation, and the best value of the dispatcher preference index is obtained.
Hybrid tabu search for the multi-depot vehicle routing problem
Hu, Shan-Liang
2010-07-01
A hybrid tabu search for the multi-depot vehicle routing problem is considered in this paper. The purpose of the proposed approach is to decrease the number of used vehicles and the total travel cost. An extensive numerical experiment was performed on benchmark problem instances available in literature, the computational results are presented to show the high effectiveness and performance of the proposed approaches.
An exact algorithm for the vehicle routing problem with stochastic demands
Energy Technology Data Exchange (ETDEWEB)
Louveaux, F.
1994-12-31
The classical deterministic Vehicle Routing Problem (VRP) can be defined as follows. Let G = (V, E) be an undirected graph where V = {l_brace}v{sub 1}, {center_dot}{center_dot}, v{sub n}{r_brace} is a set of vertices representing cities or customers, and E = {l_brace}(v{sub i}, V{sub j}) : i < j; v{sub i}, v{sub j} {element_of} V{r_brace} is an edge set. With each vertex v{sub i}(i {>=} 2) (v{sub i}, v{sub j}) is associated a non-negative cost (distance, travel time) c{sub ij}. Vertex v{sub 1} represents a depot at which are based m identical vehicle of capacity Q > 0. Depending on the version of the problem considered, the value of m is either fixed, or bounded above by a constant {<=} m. The VRP consists of determining vehicle routes in such a way that (i) all routes start and end at the depot; (ii) each vertex other than the depot is visited exactly once; (iii) the total demand of any given route does not exceed Q; (iv) the total distance traveled by all vehicles is minimized. In the Stochastic Vehicle Routing Problem (SVRP), the demand associated with vertex v{sub i} is a random variable {xi}{sub i}. As a result, it is no longer possible to assume that vehicle routes may be followed as planned. The SRVP is modeled in two stages. In the first stage, a priori vehicle routes satisyfing conditions (i) and (ii) are constructed, without full information on the demands. In the second stage, when this information becomes available, routes are followed as planned, until the accumulated demand attains or exceeds the vehicle capacity. In this case, failure is said to occur and a recourse action is taken: the vehicle returns to the depot to unload, and resumes its visits at the point of failure. The SVRP consists of determining an a priori set of routes so as to minimize the expected cost of the second stage solution. The corresponding model can be solved using the relaxation approach in Laporte and Louveaux.
Heuristic algorithms for solving of the tool routing problem for CNC cutting machines
Chentsov, P. A.; Petunin, A. A.; Sesekin, A. N.; Shipacheva, E. N.; Sholohov, A. E.
2015-11-01
The article is devoted to the problem of minimizing the path of the cutting tool to shape cutting machines began. This problem can be interpreted as a generalized traveling salesman problem. Earlier version of the dynamic programming method to solve this problem was developed. Unfortunately, this method allows to process an amount not exceeding thirty circuits. In this regard, the task of constructing quasi-optimal route becomes relevant. In this paper we propose options for quasi-optimal greedy algorithms. Comparison of the results of exact and approximate algorithms is given.
Solving the Vehicle Routing Problem with Stochastic Demands via Hybrid Genetic Algorithm-Tabu Search
Directory of Open Access Journals (Sweden)
Z. Ismail
2008-01-01
Full Text Available This study considers a version of the stochastic vehicle routing problem where customer demands are random variables with known probability distribution. A new scheme based on a hybrid GA and Tabu Search heuristic is proposed for this problem under a priori approach with preventive restocking. The relative performance of the proposed HGATS is compared to each GA and TS alone, on a set of randomly generated problems following some discrete probability distributions. The problem data are inspired by real case of VRPSD in waste collection. Results from the experiment show the advantages of the proposed algorithm that are its robustness and better solution qualities resulted.
Simulated annealing (SA to vehicle routing problems with soft time windows
Directory of Open Access Journals (Sweden)
Suphan Sodsoon
2014-12-01
Full Text Available The researcher has applied and develops the meta-heuristics method to solve Vehicle Routing Problems with Soft Time Windows (VRPSTW. For this case there was only one depot, multi customers which each generally sparse either or demand was different though perceived number of demand and specific period of time to receive them. The Operation Research was representative combinatorial optimization problems and is known to be NP-hard. In this research algorithm, use Simulated Annealing (SA to determine the optimum solutions which rapidly time solving. After developed the algorithms, apply them to examine the factors and the optimum extended time windows and test these factors with vehicle problem routing under specific time windows by Solomon in OR-Library in case of maximum 25 customers. Meanwhile, 6 problems are including of C101, C102, R101, R102, RC101 and RC102 respectively. The result shows the optimum extended time windows at level of 50%. At last, after comparison these answers with the case of vehicle problem routing under specific time windows and flexible time windows, found that percentage errors on number of vehicles approximately by -28.57% and percentage errors on distances approximately by -28.57% which this algorithm spent average processing time on 45.5 sec/problems.
GREEDY NON-DOMINATED SORTING IN GENETIC ALGORITHM-II FOR VEHICLE ROUTING PROBLEM IN DISTRIBUTION
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Vehicle routing problem in distribution (VRPD) is a widely used type of vehicle routing problem (VRP), which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm (GA), non-dominated sorting in genetic algorithm-Ⅱ(NSGA-Ⅱ) also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ (GNSGA-Ⅱ) is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-II is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-II, premature convergence is better avoided and search efficiency has been improved sharply.
Formulations and Branch-and-Cut Algorithms for the Generalized Vehicle Routing Problem
DEFF Research Database (Denmark)
Bektas, Tolga; Erdogan, Günes; Røpke, Stefan
2011-01-01
The Generalized Vehicle Routing Problem (GVRP) consists of nding a set of routes for a number of vehicles with limited capacities on a graph with the vertices partitioned into clusters with given demands such that the total cost of travel is minimized and all demands are met. This paper offers four...... new integer linear programming formulations for the GVRP, two based on multicommodity flow and the other two based on exponential sets of inequalities. Branch-and-cut algorithms are proposed for the latter two. Computational results on a large set of instances are presented....
Directory of Open Access Journals (Sweden)
Martin Macík
2015-09-01
Full Text Available High level of competition on postal market increases demands on reliability of postal services and lowering of transport costs. This can be achieved by optimizing the routing of postal vehicles. The article discusses the possibilities of such optimization by using graph theory. It describes basic methods of finding optimal routes using a graph. The approach, used in this article, assesses the possibility of applying meta-heuristic solution to the traveling salesman problem in the postal sector. Simulation of methods described has been applied on a regional postal network. Results showed that the software used proves to be sufficiently functional for the field of postal transport networks.
The electric vehicle routing problem with non-linear charging functions
2015-01-01
International audience; The use of electric vehicles (EVs) in freight and passenger transportation gives birth to a new family of vehicle routing problems (VRPs), the so-called electric VRPs (e-VRPs). As their name suggests, e-VRPs extend classical VRPs to account (mainly) for two constraining EV features: the short driving range and the long battery charging time. As a matter of fact, routes performed by EVs usually need to include time-consuming detours to charging stations. Most of the exi...
Vehicle Routing Problem for Fashion Supply Chains with Cross-Docking
Directory of Open Access Journals (Sweden)
Zhi-Hua Hu
2013-01-01
Full Text Available Cross-docking, as a strategy to reduce lead time and enhance the efficiency of the fashion supply chain, has attracted substantial attention from both the academy and the industry. Cross-docking is a critical part of many fashion and textiles supply chains in practice because it can help to achieve many supply chain strategies such as postponement. We consider a model where there are multiple suppliers and customers in a single cross-docking center. With such a model setting, the issue concerning the coordinated routing between the inbound and outbound routes is much more complex than many traditional vehicle routing problems (VRPs. We formulate the optimal route selection problems from the suppliers to the cross-docking center and from the cross-docking center to the customers as the respective VRPs. Based on the relationships between the suppliers and the customers, we integrate the two VRP models to optimize the overall traveling time, distance, and waiting time at the cross-docking center. In addition, we propose a novel mixed 0/1 integer linear programming model by which the complexity of the problem can be reduced significantly. As demonstrated by the simulation analysis, our proposed model can be solved very efficiently by a commonly used optimization software package.
A Mathematical Model for the Industrial Hazardous Waste Location-Routing Problem
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Omid Boyer
2013-01-01
Full Text Available Technology progress is a cause of industrial hazardous wastes increasing in the whole world . Management of hazardous waste is a significant issue due to the imposed risk on environment and human life. This risk can be a result of location of undesirable facilities and also routing hazardous waste. In this paper a biobjective mixed integer programing model for location-routing industrial hazardous waste with two objectives is developed. First objective is total cost minimization including transportation cost, operation cost, initial investment cost, and cost saving from selling recycled waste. Second objective is minimization of transportation risk. Risk of population exposure within bandwidth along route is used to measure transportation risk. This model can help decision makers to locate treatment, recycling, and disposal centers simultaneously and also to route waste between these facilities considering risk and cost criteria. The results of the solved problem prove conflict between two objectives. Hence, it is possible to decrease the cost value by marginally increasing the transportation risk value and vice versa. A weighted sum method is utilized to combine two objectives function into one objective function. To solve the problem GAMS software with CPLEX solver is used. The problem is applied in Markazi province in Iran.
Relative Performance of Certain Meta Heuristics on Vehicle Routing Problem with Time Windows
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Sandhya
2015-11-01
Full Text Available —Solving Vehicle Routing Problem (VRP and its variants arise in many real life distribution systems. Classical VRP can be described as the problem of finding minimum cost routes with identical vehicles having fixed capacity which starts from a depot and reaches a number of customers with known demands with the proviso that each route starts and ends at the depot and the demand of each customer does not exceed the vehicle capacity is met. One of the generalizations of standard VRP is Vehicle Routing Problem with Time Windows (VRPTW with added complexity of serving every customer within a specified time window. Since VRPTW is a NP hard meta heuristics have often been designed for solving it. In this paper we compare the performance of Simulated Annealing (SA, genetic Algorithm (GA and Ant Colony Optimization (ACO for solving VRPTW based on their performance using different parameters taking total travel distance as the objective to be minimized. The results indicate that ACO is in general slightly more efficient then SA and GA.
Optimized Crossover Genetic Algorithm for Vehicle Routing Problem with Time Windows
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H. Nazif
2010-01-01
Full Text Available Problem statement: In this study, we considered the application of a genetic algorithm to vehicle routing problem with time windows where a set of vehicles with limits on capacity and travel time are available to service a set of customers with demands and earliest and latest time for serving. The objective is to find routes for the vehicles to service all the customers at a minimal cost without violating the capacity and travel time constraints of the vehicles and the time window constraints set by the customers. Approach: We proposed a genetic algorithm using an optimized crossover operator designed by a complete undirected bipartite graph that finds an optimal set of delivery routes satisfying the requirements and giving minimal total cost. Various techniques have also been introduced into the proposed algorithm to further enhance the solutions quality. Results: We tested our algorithm with benchmark instances and compared it with some other heuristics in the literature. The results showed that the proposed algorithm is competitive in terms of the quality of the solutions found. Conclusion/Recommendations: This study presented a genetic algorithm for solving vehicle routing problem with time windows using an optimized crossover operator. From the results, it can be concluded that the proposed algorithm is competitive when compared with other heuristics in the literature.
A new memetic algorithm for solving split delivery vehicle routing problem
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Ali Bozorgi-Amiri
2015-11-01
Full Text Available Split delivery vehicle routing problem is one of the traditional types of routing problems in which the demand of different points can be divided among vehicles and the objective is to minimize the path length, which vehicles travel. In this paper, fuel cost of vehicles which is assumed to be dependent on their traveled path and load is considered as the objective functions. Namely, the cost of the consumed fuel is proportionate to the unit of load carried per unit of distance. In order to solve the proposed model a new memetic algorithm is developed which has two rows. The performance of the proposed algorithm for 21 standard problems is compared with the optimum solutions obtained from mathematical programming standard solver and the solutions of the same algorithm with single row solution representation. The results express the efficiency of developed algorithm.
Solving the vehicle routing problem by a hybrid meta-heuristic algorithm
Yousefikhoshbakht, Majid; Khorram, Esmaile
2012-08-01
The vehicle routing problem (VRP) is one of the most important combinational optimization problems that has nowadays received much attention because of its real application in industrial and service problems. The VRP involves routing a fleet of vehicles, each of them visiting a set of nodes such that every node is visited by exactly one vehicle only once. So, the objective is to minimize the total distance traveled by all the vehicles. This paper presents a hybrid two-phase algorithm called sweep algorithm (SW) + ant colony system (ACS) for the classical VRP. At the first stage, the VRP is solved by the SW, and at the second stage, the ACS and 3-opt local search are used for improving the solutions. Extensive computational tests on standard instances from the literature confirm the effectiveness of the presented approach.
Cost Optimisation in Freight Distribution with Cross-Docking: N-Echelon Location Routing Problem
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Jesus Gonzalez-Feliu
2012-03-01
Full Text Available Freight transportation constitutes one of the main activities that influence the economy and society, as it assures a vital link between suppliers and customers and represents a major source of employment. Multi-echelon distribution is one of the most common strategies adopted by the transportation companies in an aim of cost reduction. Although vehicle routing problems are very common in operational research, they are essentially related to single-echelon cases. This paper presents the main concepts of multi-echelon distribution with cross-docks and a unified notation for the N-echelon location routing problem. A literature review is also presented, in order to list the main problems and methods that can be helpful for scientists and transportation practitioners.
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Kui-Ting CHEN
2015-12-01
Full Text Available Capacitated vehicle routing problem with pickups and deliveries (CVRPPD is one of the most challenging combinatorial optimization problems which include goods delivery/pickup optimization, vehicle number optimization, routing path optimization and transportation cost minimization. The conventional particle swarm optimization (PSO is difficult to find an optimal solution of the CVRPPD due to its simple search strategy. A PSO with adaptive multi-swarm strategy (AMSPSO is proposed to solve the CVRPPD in this paper. The proposed AMSPSO employs multiple PSO algorithms and an adaptive algorithm with punishment mechanism to search the optimal solution, which can deal with large-scale optimization problems. The simulation results prove that the proposed AMSPSO can solve the CVRPPD with the least number of vehicles and less transportation cost, simultaneously.
A generalized multi-depot vehicle routing problem with replenishment based on LocalSolver
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Ying Zhang
2015-01-01
Full Text Available In this paper, we consider the multi depot heterogeneous vehicle routing problem with time windows in which vehicles may be replenished along their trips. Using the modeling technique in a new-generation solver, we construct a novel formulation considering a rich series of constraint conditions and objective functions. Computation results are tested on an example comes from the real-world application and some cases obtained from the benchmark problems. The results show the good performance of local search method in the efficiency of replenishment system and generalization ability. The variants can be used to almost all kinds of vehicle routing problems, without much modification, demonstrating its possibility of practical use.
Multiple Charging Station Location-Routing Problem with Time Window of Electric Vehicle
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Wang Li-ying
2015-11-01
Full Text Available This paper presents the electric vehicle (EV multiple charging station location-routing problem with time window to optimize the routing plan of capacitated EVs and the strategy of charging stations. In particular, the strategy of charging stations includes both infrastructure-type selection and station location decisions. The problem accounts for two critical constraints in logistic practice: the vehicle loading capacity and the customer time windows. A hybrid heuristic that incorporates an adaptive variable neighborhood search (AVNS with the tabu search algorithm for intensification was developed to address the problem. The specialized neighborhood structures and the selection methods of charging station used in the shaking step of AVNS were proposed. In contrast to the commercial solver CPLEX, experimental results on small-scale test instances demonstrate that the algorithm can find nearly optimal solutions on small-scale instances. The results on large-scale instances also show the effectiveness of the algorithm.
About a Routing Problem of the Tool Motion on Sheet Cutting
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A. A. Petunin
2015-01-01
Full Text Available For the routing problem of tool permutations under the thermal cutting of parts from sheet material realized on CNC machines, questions connected with constructing precise (optimal and heuristic algorithms used on the stage of mathematical simulation of route elements under sequential megalopolises circuit are investigated. Cutting points and points of tool cut-off are items (cities of the above-mentioned megalopolises. In each megalopolis, interior works are provided. These works are connected with motion to the equidistant curve of the cut contour of a part from the cutting point and (with cutting completed with motion from the equidistant curve to the tool cut-off (we keep in mind a working run. The problem about the time-optimal process of cutting which is a special variant of the generalized courier problem is investigated (the problem of the routing on the megalopolises with precedence conditions. An optimal procedure based on the dynamic programming and an effective heuristic algorithm realized on a multicore computer are proposed. A dynamic programming based procedure uses a special extension of the main problem. This extension provides the replacement of admissibility by precedence with the admissibility by deletion (from the list of tasks. Precedence conditions are used for decreasing computational complexity: it excludes the building of the whole array of the Bellman function values (this function is replaced by the layers system.
STRATEGY OF SOLUTION FOR THE INVENTORY ROUTING PROBLEM BASED ON SEPARABLE CROSS DECOMPOSITION
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M. Elizondo-Cortés
2005-08-01
Full Text Available The Inventory-Routing Problem (IRP involves a central warehouse, a fleet of trucks wlth finlte capacity, a set of customers, and a known storage capacity. The objective is to determine when to serve each customer, as well as what route each truck should take, with the lowest expense. IRP is a NP-hard problem, this means that searching for solutions can take a very long time. A three-phase strategy is used to solve the problem. This strategy is constructedn by answering the key questions: Which customers should be attended in a planned period? What volume of n products should be delivered to each customer? And, which route should be followed by each truck? The second phase uses Cross Separable Decomposition to solve an Allocation Problem, in order to answer questions two and three, solving a location problem. The result is a very efficient ranking algorithm O(n3 for large cases of the lRP.
Electric Vehicle Routing Problem with Charging Time and Variable Travel Time
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Sai Shao
2017-01-01
Full Text Available An electric vehicle routing problem with charging time and variable travel time is developed to address some operational issues such as range limitation and charging demand. The model is solved by using genetic algorithm to obtain the routes, the vehicle departure time at the depot, and the charging plan. Meanwhile, a dynamic Dijkstra algorithm is applied to find the shortest path between any two adjacent nodes along the routes. To prevent the depletion of all battery power and ensure safe operation in transit, electric vehicles with insufficient battery power can be repeatedly recharged at charging stations. The fluctuations in travel time are implemented to reflect a dynamic traffic environment. In conclusion, a large and realistic case study with a road network in the Beijing urban area is conducted to evaluate the model performance and the solution technology and analyze the results.
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Cihan Ercan
2013-02-01
Full Text Available Outwith the technological developments made with Unmanned Aerial Vehicles (UAV; other important issues for the users like effective planning and re-planning; providing the clear, concise and timely information to the decision makers is part of the Network Enabled Capability. Significant improvements to the Communication and Information systems have made it possible to find dynamic solutions for Vehicle Routing Problems. In this context, "Vehicle Routing" applications for UAVs in reconnaissance missions are increasing exponentially. This study investigates the literature in "dynamic route planning", defining the scope and identifying shortcomings for future studies in Unmanned Aerial Systems. Using this approach not only reduces stagnant travel time to target time but increases the usable times spent on targets.
A multi-objective location routing problem using imperialist competitive algorithm
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Amir Mohammad Golmohammadi
2016-06-01
Full Text Available Nowadays, most manufacturing units try to locate their requirements and the depot vehicle routing in order to transport the goods at optimum cost. Needless to mention that the locations of the required warehouses influence on the performance of vehicle routing. In this paper, a mathematical programming model to optimize the storage location and vehicle routing are presented. The first objective function of the model minimizes the total cost associated with the transportation and storage, and the second objective function minimizes the difference distance traveled by vehicles. The study uses Imperialist Competitive Algorithm (ICA to solve the resulted problems in different sizes. The preliminary results have indicated that the proposed study has performed better than NSGA-II and PAES methods in terms of Quality metric and Spacing metric.
A set-covering based heuristic algorithm for the periodic vehicle routing problem.
Cacchiani, V; Hemmelmayr, V C; Tricoire, F
2014-01-30
We present a hybrid optimization algorithm for mixed-integer linear programming, embedding both heuristic and exact components. In order to validate it we use the periodic vehicle routing problem (PVRP) as a case study. This problem consists of determining a set of minimum cost routes for each day of a given planning horizon, with the constraints that each customer must be visited a required number of times (chosen among a set of valid day combinations), must receive every time the required quantity of product, and that the number of routes per day (each respecting the capacity of the vehicle) does not exceed the total number of available vehicles. This is a generalization of the well-known vehicle routing problem (VRP). Our algorithm is based on the linear programming (LP) relaxation of a set-covering-like integer linear programming formulation of the problem, with additional constraints. The LP-relaxation is solved by column generation, where columns are generated heuristically by an iterated local search algorithm. The whole solution method takes advantage of the LP-solution and applies techniques of fixing and releasing of the columns as a local search, making use of a tabu list to avoid cycling. We show the results of the proposed algorithm on benchmark instances from the literature and compare them to the state-of-the-art algorithms, showing the effectiveness of our approach in producing good quality solutions. In addition, we report the results on realistic instances of the PVRP introduced in Pacheco et al. (2011) [24] and on benchmark instances of the periodic traveling salesman problem (PTSP), showing the efficacy of the proposed algorithm on these as well. Finally, we report the new best known solutions found for all the tested problems.
Institute of Scientific and Technical Information of China (English)
Bin Jiang; Chao Yang; Takao Terano
2015-01-01
This paper proposes an adaptive agent model with a hybrid routing selection strategy for studying the road⁃network congestion problem. We focus on improving those severely congested links. Firstly, a multi⁃agent system is built, where each agent stands for a vehicle, and it makes its routing selection by considering the shortest path and the minimum congested degree of the target link simultaneously. The agent⁃based model captures the nonlinear feedback between vehicle routing behaviors and road⁃network congestion status. Secondly, a hybrid routing selection strategy is provided, which guides the vehicle routes adapting to the real⁃time road⁃network congestion status. On this basis, we execute simulation experiments and compare the simulation results of network congestion distribution, by Floyd agent with shortest path strategy and our proposed adaptive agent with hybrid strategy. The simulation results show that our proposed model has reduced the congestion degree of those seriously congested links of road⁃network. Finally, we execute our model on a real road map. The results finds that those seriously congested roads have some common features such as located at the road junction or near the unique road connecting two areas. And, the results also show an effectiveness of our model on reduction of those seriously congested links in this actual road network. Such a bottom⁃up congestion control approach with a hybrid congestion optimization perspective will have its significance for actual traffic congestion control.
A HYBRID GENETIC ALGORITHM IMPLEMENTATION FOR VEHICLE ROUTING PROBLEM WITH TIME WINDOWS
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Muhammad Faisal Ibrahim
2016-01-01
Full Text Available This article is related to approach development in order to determine the most appropriate route for bottled water delivery from warehouse to retail from particular boundaries such as a limit on number of vehicle, vehicle capacity, and time windows to each retail. A mathematical model of VRPTW is adopted to solve the problem. Malang is one of the drinking water production centers in Indonesia, definitely it will be difficult for the company to determine the optimal delivery route with the existing restrictions. In this research hybrid genetic algorithm is use to determine the route shipping companies with the Java programming language. After analyzing the results obtained show that the results of the implementation of hybrid genetic algorithm is better than the company actual route. Moreover, authors also analyze the effect the number of iterations for the computation time, and the influence the number of iterations for the fitness value or violation. This algorithm can be applied for the routing and the result obtained is an optimal solution
Anders, Andre
2003-01-01
Cathodic arc plasma deposition has become the technology of choice for hard, wear and corrosion resistant coatings for a variety of applications. The history, basic physics of cathodic arc operation, the infamous macroparticle problem and common filter solutions, and emerging high-tech applications are briefly reviewed. Cathodic arc plasmas stand out due to their high degree of ionization, with important consequences for film nucleation, growth, and efficient utilization of substrate bia...
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T.A. Yakovleva
2011-05-01
Full Text Available This paper is dealing with the vehicle routing problem, where different types of vehicles are managing to deliver different types of products. Three step heuristic with genetic algorithm is proposed for solving the problem.
DEFF Research Database (Denmark)
Gamst, M.
2014-01-01
This paper examines the problem of scheduling a number of jobs on a finite set of machines such that the overall profit of executed jobs is maximized. Each job has a certain demand, which must be sent to the executing machine via constrained paths. A job cannot start before all its demands have...... arrived at the machine. Furthermore, two resource demand transmissions cannot use the same edge in the same time period. The problem has application in grid computing, where a number of geographically distributed machines work together for solving large problems. The machines are connected through...... an optical network. The problem is formulated as an IP problem and is shown to be NP-hard. An exact solution approach based on Dantzig-Wolfe decomposition is proposed. Also, several heuristic methods are developed by combining heuristics for the job scheduling problem and for the constrained network routing...
Determination of optimal self-drive tourism route using the orienteering problem method
Hashim, Zakiah; Ismail, Wan Rosmanira; Ahmad, Norfaieqah
2013-04-01
This paper was conducted to determine the optimal travel routes for self-drive tourism based on the allocation of time and expense by maximizing the amount of attraction scores assigned to each city involved. Self-drive tourism represents a type of tourism where tourists hire or travel by their own vehicle. It only involves a tourist destination which can be linked with a network of roads. Normally, the traveling salesman problem (TSP) and multiple traveling salesman problems (MTSP) method were used in the minimization problem such as determination the shortest time or distance traveled. This paper involved an alternative approach for maximization method which is maximize the attraction scores and tested on tourism data for ten cities in Kedah. A set of priority scores are used to set the attraction score at each city. The classical approach of the orienteering problem was used to determine the optimal travel route. This approach is extended to the team orienteering problem and the two methods were compared. These two models have been solved by using LINGO12.0 software. The results indicate that the model involving the team orienteering problem provides a more appropriate solution compared to the orienteering problem model.
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Ika Ayu Fajarwati
2012-09-01
Full Text Available Vehicle Routing Problem (VRP merupakan permasalahan optimasi kombinatorial kompleks yang memiliki peranan penting dalam manajemen sistem distribusi dengan tujuan meminimalkan biaya yang diperlukan, dimana penentuan biaya berkaitan dengan jarak dari rute yang ditempuh oleh armada distribusi. Ciri dari VRP yaitu penggunaan armada dengan kapasitas tertentu dan kegiatannya berpusat pada satu titik depot untuk melayani pelanggan pada titik-titik tertentu dengan jumlah permintaan yang diketahui. Kasus distribusi yang menggabungkan aktifitas pengiriman dan pengambilan produk termasuk dalam salah satu jenis VRP yaitu Vehicle Routing Problem Delivery and Pick-Up (VRP-DP. Banyak metode yang dapat digunakan untuk menyelesaikan permasalahan VRP-DP, salah satunya adalah metode optimasi metaheuristik yaitu Algoritma Differential Evolution yang akan diperkenalkan dalam penelitian ini. Hasil yang diharapkan nantinya adalah rute distribusi optimal untuk armada perusahaan sehingga menghasilkan jarak tempuh dan tentunya total biaya yang minimal dalam memenuhi semua permintaan pelanggan
The Problems in QoS Routing%QoS中的路由问题
Institute of Scientific and Technical Information of China (English)
彭孜; 曾家智; 周明天
2000-01-01
The next-greneration high-speed networks are expected to suppot a wide range of delay-sensitive multimedia applications. They need a different routing algorithm from the conventional one. The goal of the new algorithm is twofold: (1)satisfying the QoS requirements for every admitted connections,and(2)achieving global efficiency in resource utilization. Thus,most of problems in QoS routing area have multiple constraints which make them NP-Hard. Until now,the generally effcient algorithm has not been found. In this paper,we pose two algorithms for PCPO problems common in QoS communication,and analyze respective characteristics and uses.
The life and times of the Savings Method for Vehicle Routing Problems
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GK Rand
2009-12-01
Full Text Available Forty five years ago, an academic and practitioner from the north of England published a method of tackling the vehicle routing problem (VRP in an American journal. Little could they have realised how the method they devised would still be a significant part of the research agenda nearly half a century later. Adaptations of their method are significant components in the analysis of the many different extensions to the problem that have been investigated. This paper provides the historical background to the development of the savings method and subsequent proposed variations to the basic savings formula and other improvements, and then charts the role the savings method has played in the investigation of VRPs with additional constraints. Some interesting examples of practical applications of the savings method are reported. Finally, comments are made on the use of the savings method in commercial routing packages.
Solving the Capacitated Vehicle Routing Problem Based on Improved Ant-clustering Algorithm
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Zhang Jiashan
2015-01-01
Full Text Available The capacitated vehicle routing problems (CVRP are NP-hard. Most approaches can solve small-scale case studies to optimality. Furthermore, they are time-consuming. To overcome the limitation, this paper presents a novel three-phase heuristic approach for the capacitated vehicle routing problem. The first phase aims to identify sets of cost-effective feasible clusters through an improved ant-clustering algorithm, in which the adaptive strategy is adopted. The second phase assigns clusters to vehicles and sequences them on each tour. The third phase orders nodes within clusters for every tour and genetic algorithm is used to order nodes within clusters. The simulation indicates the algorithm attains high quality results in a short time.
Xu, Sheng-Hua; Liu, Ji-Ping; Zhang, Fu-Hao; Wang, Liang; Sun, Li-Jian
2015-08-27
A combination of genetic algorithm and particle swarm optimization (PSO) for vehicle routing problems with time windows (VRPTW) is proposed in this paper. The improvements of the proposed algorithm include: using the particle real number encoding method to decode the route to alleviate the computation burden, applying a linear decreasing function based on the number of the iterations to provide balance between global and local exploration abilities, and integrating with the crossover operator of genetic algorithm to avoid the premature convergence and the local minimum. The experimental results show that the proposed algorithm is not only more efficient and competitive with other published results but can also obtain more optimal solutions for solving the VRPTW issue. One new well-known solution for this benchmark problem is also outlined in the following.
A variable neighborhood descent based heuristic to solve the capacitated location-routing problem
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M. S. Jabal-Ameli
2011-01-01
Full Text Available Location-routing problem (LRP is established as a new research area in the context of location analysis. The primary concern of LRP is on locating facilities and routing of vehicles among established facilities and existing demand points. In this work, we address the capacitated LRP which arises in many practical applications within logistics and supply chain management. The objective is to minimize the overall system costs which include the fixed costs of opening depots and using vehicles at each depot site, and the variable costs associated with delivery activities. A novel heuristic is proposed which is based on variable neighborhood descent (VND algorithm to solve the resulted problem. The computational study indicates that the proposed VND based heuristic is highly competitive with the existing solution algorithms in terms of solution quality.
A Hybrid Genetic Algorithm for Vehicle Routing Problem with Complex Constraints
Institute of Scientific and Technical Information of China (English)
CHEN Yan; LU Jun; LI Zeng-zhi
2006-01-01
Most research on the Vehicle Routing Problem (VRP) is focused on standard conditions, which is not suitable for specific cases. A Hybrid Genetic Algorithm is proposed to solve a Vehicle Routing Problem (VRP) with complex side constraints. A novel coding method is designed especially for side constraints. A greedy algorithm combined with a random algorithm is introduced to enable the diversity of the initial population, as well as a local optimization algorithm employed to improve the searching efficiency. In order to evaluate the performance, this mechanism has been implemented in an oil distribution center, the experimental and executing results show that the near global optimal solution can be easily and quickly obtained by this method, and the solution is definitely satisfactory in the VRP application.
The Edge Set Cost of the Vehicle Routing Problem with Time Windows
DEFF Research Database (Denmark)
Reinhardt, Line Blander; Jepsen, Mads Kehlet; Pisinger, David
2016-01-01
We consider an important generalization of the vehicle routing problem with time windows in which a fixed cost must be paid for accessing a set of edges. This fixed cost could reflect payment for toll roads, investment in new facilities, the need for certifications, and other costly investments...... results show that instances with up to 40 customers can be solved in a reasonable time, and that the branch-cut-and-price algorithm generally outperforms CPLEX....
A Column Generation Approach to the Capacitated Vehicle Routing Problem with Stochastic Demands
DEFF Research Database (Denmark)
Christiansen, Christian Holk; Lysgaard, Jens
In this article we introduce a new exact solution approach to the Capacitated Vehicle Routing Problem with Stochastic Demands (CVRPSD). In particular, we consider the case where all customer demands are distributed independently and where each customer's demand follows a Poisson distribution...... approach we have embedded this column generation scheme in a branch-and-price algorithm. Computational experiments on a large set of test instances show promising results....
A Comparison of Homogeneous and Heterogeneous Vehicle Fleet Size in Green Vehicle Routing Problem
Moutaoukil, Abdelhamid; Neubert, Gilles; Derrouiche, Ridha
2014-01-01
Part 1: Knowledge-Based Sustainability; International audience; To balance a fragmented logistics organization, Small and Medium Enterprises have to find collective solutions to decrease their environmental impact. Especially when the demand at each producer takes the form of small packages and low quantities this paper examines the effect of the introduction of a consolidation center on the environmental issue. Therefore, the Fleet Size and Mix Vehicle Routing Problem (FSMVRP) was adapted in...
A Novel Heuristic Algorithm Based on Clark and Wright Algorithm for Green Vehicle Routing Problem
Mehdi Alinaghian; Zahra Kaviani; Siyavash Khaledan
2015-01-01
A significant portion of Gross Domestic Production (GDP) in any country belongs to the transportation system. Transportation equipment, in the other hand, is supposed to be great consumer of oil products. Many attempts have been assigned to the vehicles to cut down Greenhouse Gas (GHG). In this paper a novel heuristic algorithm based on Clark and Wright Algorithm called Green Clark and Wright (GCW) for Vehicle Routing Problem regarding to fuel consumption is presented. The objective function ...
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Qi Hu
2013-04-01
Full Text Available State-of-the-art heuristic algorithms to solve the vehicle routing problem with time windows (VRPTW usually present slow speeds during the early iterations and easily fall into local optimal solutions. Focusing on solving the above problems, this paper analyzes the particle encoding and decoding strategy of the particle swarm optimization algorithm, the construction of the vehicle route and the judgment of the local optimal solution. Based on these, a hybrid chaos-particle swarm optimization algorithm (HPSO is proposed to solve VRPTW. The chaos algorithm is employed to re-initialize the particle swarm. An efficient insertion heuristic algorithm is also proposed to build the valid vehicle route in the particle decoding process. A particle swarm premature convergence judgment mechanism is formulated and combined with the chaos algorithm and Gaussian mutation into HPSO when the particle swarm falls into the local convergence. Extensive experiments are carried out to test the parameter settings in the insertion heuristic algorithm and to evaluate that they are corresponding to the data’s real-distribution in the concrete problem. It is also revealed that the HPSO achieves a better performance than the other state-of-the-art algorithms on solving VRPTW.
A Novel Joint Problem of Routing, Scheduling, and Variable-Width Channel Allocation in WMNs
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Chun-Cheng Lin
2014-01-01
Full Text Available This paper investigates a novel joint problem of routing, scheduling, and channel allocation for single-radio multichannel wireless mesh networks in which multiple channel widths can be adjusted dynamically through a new software technology so that more concurrent transmissions and suppressed overlapping channel interference can be achieved. Although the previous works have studied this joint problem, their linear programming models for the problem were not incorporated with some delicate constraints. As a result, this paper first constructs a linear programming model with more practical concerns and then proposes a simulated annealing approach with a novel encoding mechanism, in which the configurations of multiple time slots are devised to characterize the dynamic transmission process. Experimental results show that our approach can find the same or similar solutions as the optimal solutions for smaller-scale problems and can efficiently find good-quality solutions for a variety of larger-scale problems.
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Marc Reimann
2014-05-01
Full Text Available Keen competition and increasingly demanding customers have forced companies to use their resources more efficiently and to integrate production and transportation planning. In the last few years more and more researchers have also focused on this challenging problem by trying to determine the complexity of the individual problems and then developing fast and robust algorithms to solve them. This paper reviews existing literature on integrated production and distribution decisions at the tactical and operational level, where the distribution part is modelled as some variation of the well-known Vehicle Routing Problem (VRP. The focus is thereby on problems that explicitly consider deliveries to multiple clients in a less-than-truckload fashion. In terms of the production decisions we distinguish in our review between tactical and operational production problems by considering lot-sizing/capacity allocation and scheduling models, respectively.
Energy Technology Data Exchange (ETDEWEB)
Anders, Andre
2003-10-29
Cathodic arc plasma deposition has become the technology of choice for hard, wear and corrosion resistant coatings for a variety of applications. The history, basic physics of cathodic arc operation, the infamous macroparticle problem and common filter solutions, and emerging high-tech applications are briefly reviewed. Cathodic arc plasmas standout due to their high degree of ionization, with important consequences for film nucleation, growth, and efficient utilization of substrate bias. Industrial processes often use cathodic arc plasma in reactive mode. In contrast, the science of arcs has focused on the case of vacuum arcs. Future research directions include closing the knowledge gap for reactive mode, large area coating, linear sources and filters, metal plasma immersion process, with application in high-tech and biomedical fields.
A new approach on auxiliary vehicle assignment in capacitated location routing problem
Bashiri, Mahdi; Rasoulinejad, Zeinab; Fallahzade, Ehsan
2016-03-01
The location routing problem (LRP) considers locating depots and vehicle routing decisions simultaneously. In classic LRP the number of customers in each route depends on the capacity of the vehicle. In this paper a capacitated LRP model with auxiliary vehicle assignment is presented in which the length of each route is not restricted by main vehicle capacity. Two kinds of vehicles are considered: main vehicles with higher capacity and fixed cost and auxiliary vehicles with lower capacity and fixed cost. The auxiliary vehicles can be added to the transportation system as an alternative strategy to cover the capacity limitations and they are just used to transfer goods from depots to vehicles and cannot serve the customers by themselves. To show the applicability of the proposed model, some numerical examples derived from the well-known instances are used. Moreover the model has been solved by some meta-heuristics for large sized instances. The results show the efficiency of the proposed model and the solution approach, considering the classic model and the exact solution approach, respectively.
A new formulation for the 2-echelon capacitated vehicle routing problem
DEFF Research Database (Denmark)
Jepsen, Mads Kehlet; Røpke, Stefan; Spoorendonk, Simon
The 2-echelon capacitated vehicle routing problem (2E-CVRP) is a transportation and distribution problem where goods are transported from a depot to a set of customers possible via optional satellite facilities. The 2E-CVRP is relevant in city-logistic applications where legal restrictions make...... it infeasible to use large trucks within the center of large cities. We propose a new mathematical formulation for the 2E-CVRP with much fewer variables than the previously proposed but with several constraint sets of exponential size. The strength of the model is implied by the facts that many cutting planes...
Clique inequalities applied to the vehicle routing problem with time windows
DEFF Research Database (Denmark)
Spoorendonk, Simon; Desaulniers, Guy
2010-01-01
This work presents an exact branch-cut-and-price algorithm for the vehicle routing problem with time windows (VRPTW) where the well-known clique inequalities are used as cutting planes defined on the set partitioning master problem variables. It shows how these cutting planes affect the dominance......, to our knowledge, this is a first attempt at incorporating for the VRPTW a set of valid inequalities specialized for the set partitioning polytope. Computational results show that the use of clique inequalities improves the lower bound at the root node of the search tree and reduces the number of nodes...
Directory of Open Access Journals (Sweden)
Yan Sun
2015-09-01
Full Text Available Purpose: The purpose of study is to solve the multi-modal transportation routing planning problem that aims to select an optimal route to move a consignment of goods from its origin to its destination through the multi-modal transportation network. And the optimization is from two viewpoints including cost and time. Design/methodology/approach: In this study, a bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. Minimizing the total transportation cost and the total transportation time are set as the optimization objectives of the model. In order to balance the benefit between the two objectives, Pareto optimality is utilized to solve the model by gaining its Pareto frontier. The Pareto frontier of the model can provide the multi-modal transportation operator (MTO and customers with better decision support and it is gained by the normalized normal constraint method. Then, an experimental case study is designed to verify the feasibility of the model and Pareto optimality by using the mathematical programming software Lingo. Finally, the sensitivity analysis of the demand and supply in the multi-modal transportation organization is performed based on the designed case. Findings: The calculation results indicate that the proposed model and Pareto optimality have good performance in dealing with the bi-objective optimization. The sensitivity analysis also shows the influence of the variation of the demand and supply on the multi-modal transportation organization clearly. Therefore, this method can be further promoted to the practice. Originality/value: A bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. The Pareto frontier based sensitivity analysis of the demand and supply in the multi-modal transportation organization is performed based on the designed case.
Sebastian Henn; André Scholz; Meike Stuhlmann; Gerhard Wäscher
2015-01-01
The Single-Picker Routing Problem deals with the determination of sequences according to which items have to be picked in a distribution warehouse and the identification of the corresponding paths which have to be travelled by human operators (order pickers). The Single-Picker Routing Problem represents a special case of the classic Traveling Salesman Problem (TSP) and, therefore, can also be modeled as a TSP. However, the picking area of a warehouse typically possesses a block layout, i.e. t...
Ant colony system (ACS with hybrid local search to solve vehicle routing problems
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Suphan Sodsoon
2016-02-01
Full Text Available This research applied an Ant Colony System algorithm with a Hybrid Local Search to solve Vehicle Routing Problems (VRP from a single depot when the customers’ requirements are known. VRP is an NP-hard optimization problem and has usually been successfully solved optimum by heuristics. A fleet of vehicles of a specific capacity are used to serve a number of customers at minimum cost, without violating the constraints of vehicle capacity. There are meta-heuristic approaches to solve these problems, such as Simulated Annealing, Genetic Algorithm, Tabu Search and the Ant Colony System algorithm. In this case a hybrid local search was used (Cross-Exchange, Or-Opt and 2-Opt algorithm with an Ant Colony System algorithm. The Experimental Design was tested on 7 various problems from the data set online in the OR-Library. There are five different problems in which customers are randomly distributed with the depot in an approximately central location. The customers were grouped into clusters. The results are evaluated in terms of optimal routes using optimal distances. The experimental results are compared with those obtained from meta-heuristics and they show that the proposed method outperforms six meta-heuristics in the literature.
A modified ant colony optimization to solve multi products inventory routing problem
Wong, Lily; Moin, Noor Hasnah
2014-07-01
This study considers a one-to-many inventory routing problem (IRP) network consisting of a manufacturer that produces multi products to be transported to many geographically dispersed customers. We consider a finite horizon where a fleet of capacitated homogeneous vehicles, housed at a depot/warehouse, transport products from the warehouse to meet the demand specified by the customers in each period. The demand for each product is deterministic and time varying and each customer requests a distinct product. The inventory holding cost is product specific and is incurred at the customer sites. The objective is to determine the amount on inventory and to construct a delivery schedule that minimizes both the total transportation and inventory holding costs while ensuring each customer's demand is met over the planning horizon. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (best integer solution) for each problem considered. We propose a modified ant colony optimization (ACO) to solve the problem and the built route is improved by using local search. ACO performs better on large instances compared to the upper bound.
Approximability of the d-dimensional Euclidean capacitated vehicle routing problem
Khachay, Michael; Dubinin, Roman
2016-10-01
Capacitated Vehicle Routing Problem (CVRP) is the well known intractable combinatorial optimization problem, which remains NP-hard even in the Euclidean plane. Since the introduction of this problem in the middle of the 20th century, many researchers were involved into the study of its approximability. Most of the results obtained in this field are based on the well known Iterated Tour Partition heuristic proposed by M. Haimovich and A. Rinnoy Kan in their celebrated paper, where they construct the first Polynomial Time Approximation Scheme (PTAS) for the single depot CVRP in ℝ2. For decades, this result was extended by many authors to numerous useful modifications of the problem taking into account multiple depots, pick up and delivery options, time window restrictions, etc. But, to the best of our knowledge, almost none of these results go beyond the Euclidean plane. In this paper, we try to bridge this gap and propose a EPTAS for the Euclidean CVRP for any fixed dimension.
Intelligent Iterated Local Search Methods for Solving Vehicle Routing Problem with Different Fleets
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to appropriate vehicles. In the second phase, the iterated dynasearch algorithm is adopted to route each selected vehicle with the assigned customers. The iterated dynasearch algorithm combines dynasearch algorithm with iterated local search algorithm based on random kicks. The second methodplogy adopts the idea of cyclic transfer which is performed by using dynamic programming algorithm, and the iterated dynasearch algorithm is also embedded in it. The test results show that both methodologies generate better solutions than the traditional method, and the second methodology is superior to the first one.
Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem
DEFF Research Database (Denmark)
Fukasawa, R.; Longo, H.; Lysgaard, Jens
2006-01-01
The best exact algorithms for the Capacitated Vehicle Routing Problem (CVRP) have been based on either branch-and-cut or Lagrangean relaxation/column generation. This paper presents an algorithm that combines both approaches: it works over the intersection of two polytopes, one associated...... with a traditional Lagrangean relaxation over q-routes, the other defined by bound, degree and capacity constraints. This is equivalent to a linear program with exponentially many variables and constraints that can lead to lower bounds that are superior to those given by previous methods. The resulting branch......-and-cut-and-price algorithm can solve to optimality all instances from the literature with up to 135 vertices. This more than doubles the size of the instances that can be consistently solved....
DEFF Research Database (Denmark)
Christensen, Jonas Mark; Røpke, Stefan
The Vehicle Routing Problem with Time Windows (VRPTW) consist of determining a set of feasible vehicle routes to deliver goods to a set of customers using a hierarchical objective; first minimising the number of vehicles used and, second, the total driving distance. A three-stage method is proposed...
An Inverse Robust Optimisation Approach for a Class of Vehicle Routing Problems under Uncertainty
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Liang Sun
2016-01-01
Full Text Available There is a trade-off between the total penalty paid to customers (TPC and the total transportation cost (TTC in depot for vehicle routing problems under uncertainty (VRPU. The trade-off refers to the fact that the TTC in depot inevitably increases when the TPC decreases and vice versa. With respect to this issue, the vehicle routing problem (VRP with uncertain customer demand and travel time was studied to optimise the TPC and the TTC in depot. In addition, an inverse robust optimisation approach was proposed to solve this kind of VRPU by combining the ideas of inverse optimisation and robust optimisation so as to improve both the TPC and the TTC in depot. The method aimed to improve the corresponding TTC of the robust optimisation solution under the minimum TPC through minimising the adjustment of benchmark road transportation cost. According to the characteristics of the inverse robust optimisation model, a genetic algorithm (GA and column generation algorithm are combined to solve the problem. Moreover, 39 test problems are solved by using an inverse robust optimisation approach: the results show that both the TPC and TTC obtained by using the inverse robust optimisation approach are less than those calculated using a robust optimisation approach.
A two-stage heuristic method for vehicle routing problem with split deliveries and pickups
Institute of Scientific and Technical Information of China (English)
Yong WANG; Xiao-lei MA; Yun-teng LAO; Hai-yan YU; Yong LIU
2014-01-01
The vehicle routing problem (VRP) is a well-known combinatorial optimization issue in transportation and logistics network systems. There exist several limitations associated with the traditional VRP. Releasing the restricted conditions of traditional VRP has become a research focus in the past few decades. The vehicle routing problem with split deliveries and pickups (VRPSPDP) is particularly proposed to release the constraints on the visiting times per customer and vehicle capacity, that is, to allow the deliveries and pickups for each customer to be simultaneously split more than once. Few studies have focused on the VRPSPDP problem. In this paper we propose a two-stage heuristic method integrating the initial heuristic algorithm and hybrid heuristic algorithm to study the VRPSPDP problem. To validate the proposed algorithm, Solomon benchmark datasets and extended Solomon benchmark datasets were modified to compare with three other popular algorithms. A total of 18 datasets were used to evaluate the effectiveness of the proposed method. The computational results indicated that the proposed algorithm is superior to these three algorithms for VRPSPDP in terms of total travel cost and average loading rate.
A sequential insertion heuristic for the initial solution to a constrained vehicle routing problem
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JW Joubert
2006-06-01
Full Text Available The Vehicle Routing Problem (VRP is a well-researched problem in the Operations Research literature. It is the view of the authors of this paper that the various VRP variants have been researched in isolation. This paper embodies an attempt to integrate three specific variants of the VRP, namely the VRP with multiple time windows, the VRP with a heterogeneous fleet, and the VRP with double scheduling, into an initial solution algorithm. The proposed initial solution algorithm proves feasible for the integration, while the newly introduced concept of time window compatibility decreases the computational burden when using benchmark data sets from literature as a basis for efficiency testing. The algorithm also improves the quality of the initial solution for a number of problem classes.
A heuristic algorithm for a multi-product four-layer capacitated location-routing problem
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Mohsen Hamidi
2014-01-01
Full Text Available The purpose of this study is to solve a complex multi-product four-layer capacitated location-routing problem (LRP in which two specific constraints are taken into account: 1 plants have limited production capacity, and 2 central depots have limited capacity for storing and transshipping products. The LRP represents a multi-product four-layer distribution network that consists of plants, central depots, regional depots, and customers. A heuristic algorithm is developed to solve the four-layer LRP. The heuristic uses GRASP (Greedy Randomized Adaptive Search Procedure and two probabilistic tabu search strategies of intensification and diversification to tackle the problem. Results show that the heuristic solves the problem effectively.
Bhanja, Urmila; Roy, Rajarshi; 10.5121/ijcnc.2010.2209
2010-01-01
We present an evolutionary programming algorithm for solving the dynamic routing and wavelength assignment (DRWA) problem in optical wavelength-division multiplexing (WDM) networks under wavelength continuity constraint. We assume an ideal physical channel and therefore neglect the blocking of connection requests due to the physical impairments. The problem formulation includes suitable constraints that enable the algorithm to balance the load among the individuals and thus results in a lower blocking probability and lower mean execution time than the existing bio-inspired algorithms available in the literature for the DRWA problems. Three types of wavelength assignment techniques, such as First fit, Random, and Round Robin wavelength assignment techniques have been investigated here. The ability to guarantee both low blocking probability without any wavelength converters and small delay makes the improved algorithm very attractive for current optical switching networks.
Multi-trip vehicle routing and scheduling problem with time window in real life
Sze, San-Nah; Chiew, Kang-Leng; Sze, Jeeu-Fong
2012-09-01
This paper studies a manpower scheduling problem with multiple maintenance operations and vehicle routing considerations. Service teams located at a common service centre are required to travel to different customer sites. All customers must be served within given time window, which are known in advance. The scheduling process must take into consideration complex constraints such as a meal break during the team's shift, multiple travelling trips, synchronisation of service teams and working shifts. The main objective of this study is to develop a heuristic that can generate high quality solution in short time for large problem instances. A Two-stage Scheduling Heuristic is developed for different variants of the problem. Empirical results show that the proposed solution performs effectively and efficiently. In addition, our proposed approximation algorithm is very flexible and can be easily adapted to different scheduling environments and operational requirements.
Metaheuristics for multi products inventory routing problem with time varying demand
Moin, Noor Hasnah; Ab Halim, Huda Zuhrah; Yuliana, Titi
2014-07-01
This paper addresses the inventory routing problem (IRP) with a many-to-one distribution network, consisting of a single depot, an assembly plant, and geographically dispersed suppliers where a capacitated homogeneous vehicle delivers a distinct product from the suppliers to fulfill the demand specified by the assembly plant over the planning horizon. The inventory holding cost is assumed to be product specific and only incurred at the assembly plant. Two metaheuristics comprise of artificial bee colony (ABC) and scatter search (SS) algorithms are proposed to solve the problem. Computational testing on instances which represents small, medium, and large data sets show that the ABC algorithm performs slightly better when compared the SS overall except for fifty suppliers problems.
A Novel Heuristic Algorithm Based on Clark and Wright Algorithm for Green Vehicle Routing Problem
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Mehdi Alinaghian
2015-08-01
Full Text Available A significant portion of Gross Domestic Production (GDP in any country belongs to the transportation system. Transportation equipment, in the other hand, is supposed to be great consumer of oil products. Many attempts have been assigned to the vehicles to cut down Greenhouse Gas (GHG. In this paper a novel heuristic algorithm based on Clark and Wright Algorithm called Green Clark and Wright (GCW for Vehicle Routing Problem regarding to fuel consumption is presented. The objective function is fuel consumption, drivers, and the usage of vehicles. Being compared to exact methods solutions for small-sized problems and to Differential Evolution (DE algorithm solutions for large-scaled problems, the results show efficient performance of the proposed GCW algorithm.
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Ernst, W.; Neidhardt, J. [Christian Doppler Laboratory for Advanced Hard Coatings, Department of Physical Metallurgy and Materials Testing, Franz-Josef Strasse 18, University of Leoben, 8700 Leoben (Austria); Willmann, H. [Materials Center Leoben, Franz-Josef Strasse 13, 8700 Leoben (Austria); Sartory, B. [Institute of Mineralogy and Petrography, University of Innsbruck, Innrain 52, 6020 Innsbruck (Austria); Mayrhofer, P.H. [Department of Physical Metallurgy and Materials Testing, Franz-Josef Strasse 18, University of Leoben, 8700 Leoben (Austria)], E-mail: paul.mayrhofer@unileoben.ac.at; Mitterer, C. [Christian Doppler Laboratory for Advanced Hard Coatings, Department of Physical Metallurgy and Materials Testing, Franz-Josef Strasse 18, University of Leoben, 8700 Leoben (Austria); Department of Physical Metallurgy and Materials Testing, Franz-Josef Strasse 18, University of Leoben, 8700 Leoben (Austria)
2008-11-28
This study presents a comparison of the thermal decomposition of CrN hard coatings synthesized by reactive arc evaporation and magnetron sputtering. Structural changes in the coating material were determined by in-situ high-temperature X-ray diffraction and correlated to the results of simultaneous thermal analysis. Annealing temperatures up to 1440 deg. C in Ar and a variation in heating rates gave insights to the different decomposition kinetics for the material deposited by reactive arc evaporation and magnetron sputtering. Both single-phase CrN coatings start to decompose above 925 deg. C under release of nitrogen in two major reaction steps to pure Cr via the intermediate step of Cr{sub 2}N. While the kinetics for the first decomposition reaction from CrN to Cr{sub 2}N is different for both samples, the second step from Cr{sub 2}N into Cr is similar. This behavior can be understood considering the differences in structure, composition, and morphology of both as-deposited coatings and their evolution during thermal analysis.
Directory of Open Access Journals (Sweden)
Kenan Karagül
2014-07-01
Full Text Available In this study, Fleet Size and Mix Vehicle Routing Problem is considered in order to optimize the distribution of the tourists who have traveled between the airport and the hotels in the shortest distance by using the minimum cost. The initial solution space for the related methods are formed as a combination of Savings algorithm, Sweep algorithm and random permutation alignment. Then, two well-known solution methods named as Standard Genetic Algorithms and random search algorithms are used for changing the initial solutions. Computational power of the machine and heuristic algorithms are used instead of human experience and human intuition in order to solve the distribution problem of tourists coming to hotels in Alanya region from Antalya airport. For this case study, daily data of tourist distributions performed by an agency operating in Alanya region are considered. These distributions are then modeled as Vehicle Routing Problem to calculate the solutions for various applications. From the comparisons with the decision of a human expert, it is seen that the proposed methods produce better solutions with respect to human experience and insight. Random search method produces a solution more favorable in terms of time. As a conclusion, it is seen that, owing to the distribution plans offered by the obtained solutions, the agencies may reduce the costs by achieving savings up to 35%.
On the Miller-Tucker-Zemlin Based Formulations for the Distance Constrained Vehicle Routing Problems
Kara, Imdat
2010-11-01
Vehicle Routing Problem (VRP), is an extension of the well known Traveling Salesman Problem (TSP) and has many practical applications in the fields of distribution and logistics. When the VRP consists of distance based constraints it is called Distance Constrained Vehicle Routing Problem (DVRP). However, the literature addressing on the DVRP is scarce. In this paper, existing two-indexed integer programming formulations, having Miller-Tucker-Zemlin based subtour elimination constraints, are reviewed. Existing formulations are simplified and obtained formulation is presented as formulation F1. It is shown that, the distance bounding constraints of the formulation F1, may not generate the distance traveled up to the related node. To do this, we redefine the auxiliary variables of the formulation and propose second formulation F2 with new and easy to use distance bounding constraints. Adaptation of the second formulation to the cases where new restrictions such as minimal distance traveled by each vehicle or other objectives such as minimizing the longest distance traveled is discussed.
A memory structure adapted simulated annealing algorithm for a green vehicle routing problem.
Küçükoğlu, İlker; Ene, Seval; Aksoy, Aslı; Öztürk, Nursel
2015-03-01
Currently, reduction of carbon dioxide (CO2) emissions and fuel consumption has become a critical environmental problem and has attracted the attention of both academia and the industrial sector. Government regulations and customer demands are making environmental responsibility an increasingly important factor in overall supply chain operations. Within these operations, transportation has the most hazardous effects on the environment, i.e., CO2 emissions, fuel consumption, noise and toxic effects on the ecosystem. This study aims to construct vehicle routes with time windows that minimize the total fuel consumption and CO2 emissions. The green vehicle routing problem with time windows (G-VRPTW) is formulated using a mixed integer linear programming model. A memory structure adapted simulated annealing (MSA-SA) meta-heuristic algorithm is constructed due to the high complexity of the proposed problem and long solution times for practical applications. The proposed models are integrated with a fuel consumption and CO2 emissions calculation algorithm that considers the vehicle technical specifications, vehicle load, and transportation distance in a green supply chain environment. The proposed models are validated using well-known instances with different numbers of customers. The computational results indicate that the MSA-SA heuristic is capable of obtaining good G-VRPTW solutions within a reasonable amount of time by providing reductions in fuel consumption and CO2 emissions.
Lamdjaya, T.; Jobiliong, E.
2017-01-01
PT Anugrah Citra Boga is a food processing industry that produces meatballs as their main product. The distribution system of the products must be considered, because it needs to be more efficient in order to reduce the shipment cost. The purpose of this research is to optimize the distribution time by simulating the distribution channels with capacitated vehicle routing problem method. Firstly, the distribution route is observed in order to calculate the average speed, time capacity and shipping costs. Then build the model using AIMMS software. A few things that are required to simulate the model are customer locations, distances, and the process time. Finally, compare the total distribution cost obtained by the simulation and the historical data. It concludes that the company can reduce the shipping cost around 4.1% or Rp 529,800 per month. By using this model, the utilization rate can be more optimal. The current value for the first vehicle is 104.6% and after the simulation it becomes 88.6%. Meanwhile, the utilization rate of the second vehicle is increase from 59.8% to 74.1%. The simulation model is able to produce the optimal shipping route with time restriction, vehicle capacity, and amount of vehicle.
A Framing Link Based Tabu Search Algorithm for Large-Scale Multidepot Vehicle Routing Problems
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Xuhao Zhang
2014-01-01
Full Text Available A framing link (FL based tabu search algorithm is proposed in this paper for a large-scale multidepot vehicle routing problem (LSMDVRP. Framing links are generated during continuous great optimization of current solutions and then taken as skeletons so as to improve optimal seeking ability, speed up the process of optimization, and obtain better results. Based on the comparison between pre- and postmutation routes in the current solution, different parts are extracted. In the current optimization period, links involved in the optimal solution are regarded as candidates to the FL base. Multiple optimization periods exist in the whole algorithm, and there are several potential FLs in each period. If the update condition is satisfied, the FL base is updated, new FLs are added into the current route, and the next period starts. Through adjusting the borderline of multidepot sharing area with dynamic parameters, the authors define candidate selection principles for three kinds of customer connections, respectively. Link split and the roulette approach are employed to choose FLs. 18 LSMDVRP instances in three groups are studied and new optimal solution values for nine of them are obtained, with higher computation speed and reliability.
Topology aggregation with multiple QoS parameters for scalable routing problem
Institute of Scientific and Technical Information of China (English)
LUO Yong-jun; SHI Ming-hong; BAI Ying-cai
2005-01-01
In this paper, we investigate the problem of topology aggregation in QoS-based routing. We propose a new algorithm to perform full-mesh and modified-star aggregation, which is simple and effective in a network with additive and concave parameters constrained. The time complexity is O( b2 ) , where b is the number of border nodes. We extend the algorithm to topology aggregation with multi-parameters constrained. The simulation results show that our algorithm has very good performance in terms of success ratio.
Vehicle Routing Problem Solving Method for a Cooperative Logistics Network by Using Multi-Stage GA
Onoyama, Takashi; Maekawa, Takuya; Kubota, Sen; Tsuruta, Setsuo; Komoda, Norihisa
A GA applied VRP (Vehicle Routing Problem) solving-method which realizes optimization of a cooperative logistics network is proposed. For this optimization a VRP solving-method that can obtain human expert-level solution, which realizes steady logistics operation, in interactive response time is required. The multi-stage GA enables to obtain the accurate solution under both hard and weak time constraints in interactive response time. Moreover, to realize the stable logistics operation, the daily fluctuation of shipping volume is taken into the fitness value of each individual in GA. The experimental result reveals the proposed method obtains the accurate solution that realizes the stable operation in interactive response time.
Improved Fractal Space Filling Curves Hybrid Optimization Algorithm for Vehicle Routing Problem
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Yi-xiang Yue
2015-01-01
Full Text Available Vehicle Routing Problem (VRP is one of the key issues in optimization of modern logistics system. In this paper, a modified VRP model with hard time window is established and a Hybrid Optimization Algorithm (HOA based on Fractal Space Filling Curves (SFC method and Genetic Algorithm (GA is introduced. By incorporating the proposed algorithm, SFC method can find an initial and feasible solution very fast; GA is used to improve the initial solution. Thereafter, experimental software was developed and a large number of experimental computations from Solomon’s benchmark have been studied. The experimental results demonstrate the feasibility and effectiveness of the HOA.
Improved Fractal Space Filling Curves Hybrid Optimization Algorithm for Vehicle Routing Problem
Yue, Yi-xiang; Zhang, Tong; Yue, Qun-xing
2015-01-01
Vehicle Routing Problem (VRP) is one of the key issues in optimization of modern logistics system. In this paper, a modified VRP model with hard time window is established and a Hybrid Optimization Algorithm (HOA) based on Fractal Space Filling Curves (SFC) method and Genetic Algorithm (GA) is introduced. By incorporating the proposed algorithm, SFC method can find an initial and feasible solution very fast; GA is used to improve the initial solution. Thereafter, experimental software was developed and a large number of experimental computations from Solomon's benchmark have been studied. The experimental results demonstrate the feasibility and effectiveness of the HOA. PMID:26167171
The problem of the availability of nautical charts and publications on the Northern Sea Route
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Pastusiak Tadeusz
2015-03-01
Full Text Available Statistical studies of marine accidents and unfortunate events in ice-covered areas in 1995–2004 and 2004–2011 showed a general lack of information from the area under the jurisdiction of the Russian Federation. The author’s research for the period 2004–2011 showed a large number of unfortunate events caused by lack of adequate provision of nautical charts, shortage of accurate position systems on board vessels as well as weak technical condition of these vessels. The author examined the problem of navigation safety on the Northern Sea Route in terms of availability of the official nautical charts and publications.
Improved Fractal Space Filling Curves Hybrid Optimization Algorithm for Vehicle Routing Problem.
Yue, Yi-xiang; Zhang, Tong; Yue, Qun-xing
2015-01-01
Vehicle Routing Problem (VRP) is one of the key issues in optimization of modern logistics system. In this paper, a modified VRP model with hard time window is established and a Hybrid Optimization Algorithm (HOA) based on Fractal Space Filling Curves (SFC) method and Genetic Algorithm (GA) is introduced. By incorporating the proposed algorithm, SFC method can find an initial and feasible solution very fast; GA is used to improve the initial solution. Thereafter, experimental software was developed and a large number of experimental computations from Solomon's benchmark have been studied. The experimental results demonstrate the feasibility and effectiveness of the HOA.
A multiple ship routing and speed optimization problem under time, cost and environmental objectives
DEFF Research Database (Denmark)
Wen, M.; Pacino, Dario; Kontovas, C.A.
2017-01-01
The purpose of this paper is to investigate a multiple ship routing and speed optimization problem under time, cost and environmental objectives. A branch and price algorithm as well as a constraint programming model are developed that consider (a) fuel consumption as a function of payload, (b......) fuel price as an explicit input, (c) freight rate as an input, and (d) in-transit cargo inventory costs. The alternative objective functions are minimum total trip duration, minimum total cost and minimum emissions. Computational experience with the algorithm is reported on a variety of scenarios....
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Hossein Asefi
2015-09-01
Full Text Available Municipal solid waste management is one of the challenging issues in mega cities due to various interrelated factors such as operational costs and environmental concerns. Cost as one of the most significant constraints of municipal solid waste management can be effectively economized by efficient planning approaches. Considering diverse waste types in an integrated municipal solid waste system, a mathematical model of the location-routing problem is formulated and solved in this study in order to minimize the total cost of transportation and facility establishment.
Simanullang, Herlin
2013-01-01
Vehicle Routing Problem (VRP) is a problem of combinatorial optimization complexeses that has essential role in management distribution system which is aimed to minimize the needed cost, the cost is determined in relationship with the distance of route which is taken by the distribution vehicle. The characteristic from VRP is the use of vehicle in certain capacity and its activity is centralized in one depot to serve the customer on certain locations with certain known demand. ...
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Gendreau, M.; Seguin, R.; Laporte, G.
1995-10-01
This paper considers a version of the stochastic vehicle routing problem where customers are present with some probability and have random demands. A tabu search heuristic is developed for this problem. Comparisons with known optimal solutions indicate that the heuristic solves the problem to optimality in the vast majority of cases and deviations from optimality are almost always small.
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Subbaraj Potti
2011-01-01
Full Text Available Problem statement: A new multi-objective approach, Strength Pareto Evolutionary Algorithm (SPEA, is presented in this paper to solve the shortest path routing problem. The routing problem is formulated as a multi-objective mathematical programming problem which attempts to minimize both cost and delay objectives simultaneously. Approach: SPEA handles the shortest path routing problem as a true multi-objective optimization problem with competing and noncommensurable objectives. Results: SPEA combines several features of previous multi-objective evolutionary algorithms in a unique manner. SPEA stores nondominated solutions externally in another continuously-updated population and uses a hierarchical clustering algorithm to provide the decision maker with a manageable pareto-optimal set. SPEA is applied to a 20 node network as well as to large size networks ranging from 50-200 nodes. Conclusion: The results demonstrate the capabilities of the proposed approach to generate true and well distributed pareto-optimal nondominated solutions.
A new algorithm for solving the inventory routing problem with direct shipment
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Ali Hossein Mirzaei
2012-02-01
Full Text Available In this paper a multi-commodity multi-period inventory routing problem in a two-echelon supply chain consisting of a manufacturer and a set of retailers has been studied. In addition to inventory management and distribution planning, production planning has also been considered in the above problem. The objective is to minimize total system cost that consists of production setup, inventory holding and distribution costs. The commodities are delivered to the retailers by an identical fleet of limited capacity vehicles through direct shipment strategy. Also it is assumed that production and storage capacity is limited and stockout is not allowed. Since similar problems without distribution planning are known as NP-hard, this is also an NP-hard problem. Therefore, in this paper, a new improved particle swarm optimization algorithm has been developed consisting of two distinguished phases for problem solving. First, the values of binary variables are determined using the proposed algorithm and then, the continuous variables are calculated by solving a linear programming model. Performance of the proposed algorithm has been compared with genetic and original particle swarm optimization algorithms using various samples of random problems. The findings imply significant performance of the proposed algorithm.
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Ligang Cui
2013-01-01
Full Text Available The capacitated vehicle routing problem (CVRP is the most classical vehicle routing problem (VRP; many solution techniques are proposed to find its better answer. In this paper, a new improved quantum evolution algorithm (IQEA with a mixed local search procedure is proposed for solving CVRPs. First, an IQEA with a double chain quantum chromosome, new quantum rotation schemes, and self-adaptive quantum Not gate is constructed to initialize and generate feasible solutions. Then, to further strengthen IQEA's searching ability, three local search procedures 1-1 exchange, 1-0 exchange, and 2-OPT, are adopted. Experiments on a small case have been conducted to analyze the sensitivity of main parameters and compare the performances of the IQEA with different local search strategies. Together with results from the testing of CVRP benchmarks, the superiorities of the proposed algorithm over the PSO, SR-1, and SR-2 have been demonstrated. At last, a profound analysis of the experimental results is presented and some suggestions on future researches are given.
Jawarneh, Sana; Abdullah, Salwani
2015-01-01
This paper presents a bee colony optimisation (BCO) algorithm to tackle the vehicle routing problem with time window (VRPTW). The VRPTW involves recovering an ideal set of routes for a fleet of vehicles serving a defined number of customers. The BCO algorithm is a population-based algorithm that mimics the social communication patterns of honeybees in solving problems. The performance of the BCO algorithm is dependent on its parameters, so the online (self-adaptive) parameter tuning strategy is used to improve its effectiveness and robustness. Compared with the basic BCO, the adaptive BCO performs better. Diversification is crucial to the performance of the population-based algorithm, but the initial population in the BCO algorithm is generated using a greedy heuristic, which has insufficient diversification. Therefore the ways in which the sequential insertion heuristic (SIH) for the initial population drives the population toward improved solutions are examined. Experimental comparisons indicate that the proposed adaptive BCO-SIH algorithm works well across all instances and is able to obtain 11 best results in comparison with the best-known results in the literature when tested on Solomon's 56 VRPTW 100 customer instances. Also, a statistical test shows that there is a significant difference between the results.
Modified artificial bee colony for the vehicle routing problems with time windows.
Alzaqebah, Malek; Abdullah, Salwani; Jawarneh, Sana
2016-01-01
The natural behaviour of the honeybee has attracted the attention of researchers in recent years and several algorithms have been developed that mimic swarm behaviour to solve optimisation problems. This paper introduces an artificial bee colony (ABC) algorithm for the vehicle routing problem with time windows (VRPTW). A Modified ABC algorithm is proposed to improve the solution quality of the original ABC. The high exploration ability of the ABC slows-down its convergence speed, which may due to the mechanism used by scout bees in replacing abandoned (unimproved) solutions with new ones. In the Modified ABC a list of abandoned solutions is used by the scout bees to memorise the abandoned solutions, then the scout bees select a solution from the list based on roulette wheel selection and replace by a new solution with random routs selected from the best solution. The performance of the Modified ABC is evaluated on Solomon benchmark datasets and compared with the original ABC. The computational results demonstrate that the Modified ABC outperforms the original ABC also produce good solutions when compared with the best-known results in the literature. Computational investigations show that the proposed algorithm is a good and promising approach for the VRPTW.
Chen, Xianshun; Feng, Liang; Ong, Yew Soon
2012-07-01
In this article, we proposed a self-adaptive memeplex robust search (SAMRS) for finding robust and reliable solutions that are less sensitive to stochastic behaviours of customer demands and have low probability of route failures, respectively, in vehicle routing problem with stochastic demands (VRPSD). In particular, the contribution of this article is three-fold. First, the proposed SAMRS employs the robust solution search scheme (RS 3) as an approximation of the computationally intensive Monte Carlo simulation, thus reducing the computation cost of fitness evaluation in VRPSD, while directing the search towards robust and reliable solutions. Furthermore, a self-adaptive individual learning based on the conceptual modelling of memeplex is introduced in the SAMRS. Finally, SAMRS incorporates a gene-meme co-evolution model with genetic and memetic representation to effectively manage the search for solutions in VRPSD. Extensive experimental results are then presented for benchmark problems to demonstrate that the proposed SAMRS serves as an efficable means of generating high-quality robust and reliable solutions in VRPSD.
Geiger, Martin Josef
2008-01-01
The article describes an investigation of the effectiveness of genetic algorithms for multi-objective combinatorial optimization (MOCO) by presenting an application for the vehicle routing problem with soft time windows. The work is motivated by the question, if and how the problem structure influences the effectiveness of different configurations of the genetic algorithm. Computational results are presented for different classes of vehicle routing problems, varying in their coverage with time windows, time window size, distribution and number of customers. The results are compared with a simple, but effective local search approach for multi-objective combinatorial optimization problems.
A Library of Local Search Heuristics for the Vehicle Routing Problem
Energy Technology Data Exchange (ETDEWEB)
Groer, Christopher S [ORNL; Golden, Bruce [University of Maryland; Edward, Wasil [American University
2010-01-01
The vehicle routing problem (VRP) is a difficult and well-studied combinatorial optimization problem. Real-world instances of the VRP can contain hundreds and even thousands of customer locations and can involve many complicating constraints, necessitating the use of heuristic methods. We present a software library of local search heuristics that allow one to quickly generate good solutions to VRP instances. The code has a logical, object-oriented design and uses efficient data structures to store and modify solutions. The core of the library is the implementation of seven local search operators that share a similar interface and are designed to be extended to handle additional options with minimal code change. The code is well-documented, is straightforward to compile, and is freely available for download at http://sites.google.com/site/vrphlibrary/ . The distribution of the code contains several applications that can be used to generate solutions to instances of the capacitated VRP.
Wang, Jiahai; Zhou, Ying; Wang, Yong; Zhang, Jun; Chen, C L Philip; Zheng, Zibin
2016-03-01
This paper investigates a practical variant of the vehicle routing problem (VRP), called VRP with simultaneous delivery and pickup and time windows (VRPSDPTW), in the logistics industry. VRPSDPTW is an important logistics problem in closed-loop supply chain network optimization. VRPSDPTW exhibits multiobjective properties in real-world applications. In this paper, a general multiobjective VRPSDPTW (MO-VRPSDPTW) with five objectives is first defined, and then a set of MO-VRPSDPTW instances based on data from the real-world are introduced. These instances represent more realistic multiobjective nature and more challenging MO-VRPSDPTW cases. Finally, two algorithms, multiobjective local search (MOLS) and multiobjective memetic algorithm (MOMA), are designed, implemented and compared for solving MO-VRPSDPTW. The simulation results on the proposed real-world instances and traditional instances show that MOLS outperforms MOMA in most of instances. However, the superiority of MOLS over MOMA in real-world instances is not so obvious as in traditional instances.
Application of Modified Ant Colony Optimization (MACO for Multicast Routing Problem
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Sudip Kumar Sahana
2016-04-01
Full Text Available It is well known that multicast routing is combinatorial problem finds the optimal path between source destination pairs. Traditional approaches solve this problem by establishment of the spanning tree for the network which is mapped as an undirected weighted graph. This paper proposes a Modified Ant Colony Optimization (MACO algorithm which is based on Ant Colony System (ACS with some modification in the configuration of starting movement and in local updation technique to overcome the basic limitations of ACS such as poor initialization and slow convergence rate. It is shown that the proposed Modified Ant Colony Optimization (MACO shows better convergence speed and consumes less time than the conventional ACS to achieve the desired solution.
Research on cultural algorithm for solving routing problem of mobile agent
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The key idea behind cultural algorithm is to explicitly acquire problem-solving knowledge from the evolving population and in return apply that knowledge to guide the search. In this article, cultural algorithm-simulated annealing is proposed to solve the routing problem of mobile agent. The optimal individual is accepted to improve the belief space's evolution of cultural algorithms by simulated annealing. The step size in search is used as situational knowledge to guide the search of optimal solution in the population space. Because of this feature, the search time is reduced. Experimental results show that the algorithm proposed in this article can ensure the quality of optimal solutions, and also has better convergence speed. The operation efficiency of the system is considerably improved.
Computational results with a branch and cut code for the capacitated vehicle routing problem
Energy Technology Data Exchange (ETDEWEB)
Augerat, P.; Naddef, D. [Institut National Polytechnique, 38 - Grenoble (France); Belenguer, J.M.; Benavent, E.; Corberan, A. [Valencia Univ. (Spain); Rinaldi, G. [Consiglio Nazionale delle Ricerche, Rome (Italy)
1995-09-01
The Capacitated Vehicle Routing Problem (CVRP) we consider in this paper consists in the optimization of the distribution of goods from a single depot to a given set of customers with known demand using a given number of vehicles of fixed capacity. There are many practical routing applications in the public sector such as school bus routing, pick up and mail delivery, and in the private sector such as the dispatching of delivery trucks. We present a Branch and Cut algorithm to solve the CVRP which is based in the partial polyhedral description of the corresponding polytope. The valid inequalities used in our method can ne found in Cornuejols and Harche (1993), Harche and Rinaldi (1991) and in Augerat and Pochet (1995). We concentrated mainly on the design of separation procedures for several classes of valid inequalities. The capacity constraints (generalized sub-tour eliminations inequalities) happen to play a crucial role in the development of a cutting plane algorithm for the CVRP. A large number of separation heuristics have been implemented and compared for these inequalities. There has been also implemented heuristic separation algorithms for other classes of valid inequalities that also lead to significant improvements: comb and extended comb inequalities, generalized capacity inequalities and hypo-tour inequalities. The resulting cutting plane algorithm has been applied to a set of instances taken from the literature and the lower bounds obtained are better than the ones previously known. Some branching strategies have been implemented to develop a Branch an Cut algorithm that has been able to solve large CVRP instances, some of them which had never been solved before. (authors). 32 refs., 3 figs., 10 tabs.
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Omprakash Kaiwartya
2015-01-01
Full Text Available A multiobjective dynamic vehicle routing problem (M-DVRP has been identified and a time seed based solution using particle swarm optimization (TS-PSO for M-DVRP has been proposed. M-DVRP considers five objectives, namely, geographical ranking of the request, customer ranking, service time, expected reachability time, and satisfaction level of the customers. The multiobjective function of M-DVRP has four components, namely, number of vehicles, expected reachability time, and profit and satisfaction level. Three constraints of the objective function are vehicle, capacity, and reachability. In TS-PSO, first of all, the problem is partitioned into smaller size DVRPs. Secondly, the time horizon of each smaller size DVRP is divided into time seeds and the problem is solved in each time seed using particle swarm optimization. The proposed solution has been simulated in ns-2 considering real road network of New Delhi, India, and results are compared with those obtained from genetic algorithm (GA simulations. The comparison confirms that TS-PSO optimizes the multiobjective function of the identified problem better than what is offered by GA solution.
Baron, Danielle M; Ramirez, Alejandro J; Bulitko, Vadim; Madan, Christopher R; Greiner, Ariel; Hurd, Peter L; Spetch, Marcia L
2015-01-01
Visiting multiple locations and returning to the start via the shortest route, referred to as the traveling salesman (or salesperson) problem (TSP), is a valuable skill for both humans and non-humans. In the current study, pigeons were trained with increasing set sizes of up to six goals, with each set size presented in three distinct configurations, until consistency in route selection emerged. After training at each set size, the pigeons were tested with two novel configurations. All pigeons acquired routes that were significantly more efficient (i.e., shorter in length) than expected by chance selection of the goals. On average, the pigeons also selected routes that were more efficient than expected based on a local nearest-neighbor strategy and were as efficient as the average route generated by a crossing-avoidance strategy. Analysis of the routes taken indicated that they conformed to both a nearest-neighbor and a crossing-avoidance strategy significantly more often than expected by chance. Both the time taken to visit all goals and the actual distance traveled decreased from the first to the last trials of training in each set size. On the first trial with novel configurations, average efficiency was higher than chance, but was not higher than expected from a nearest-neighbor or crossing-avoidance strategy. These results indicate that pigeons can learn to select efficient routes on a TSP problem.
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Satria Nur Alam
2012-09-01
Full Text Available Seiring dengan bertambahnya jumlah kendaraan setiap tahun, akan mempengaruhi konsumsi bahan bakar yang dibutuhkan. Tingginya kebutuhan bahan bakar di Indonesia didominasi oleh jenis bahan bakar premium. Persentase konsumsi bahan bakar premium di daerah Jawa-Bali mencapai 59% dari kuota premium nasional. Besarnya persentase kebutuhan akan bahan bakar premium, menyebabkan manajemen distribusi menjadi hal krusial yang perlu ditingkatkan secara berkala. Depo yang berperan sebagai supplier terhadap retailer -yang dalam studi kasus ini adalah SPBU- diusulkan menerapkan model Vendor Managed Inventory (VMI, yaitu proses pengadaan barang dimana supplier mengelola inventori dari retailernya. VMI memiliki salah satu perencanaan yaitu Inventory Routing Problem (IRP, IRP merupakan suatu bentuk perencanaan berbasis vendor hasil perpaduan antara Inventory Management dengan Inventory Routing yang mengatur kuantitas pengiriman dan retailer mana yang harus dikunjungi dalam suatu waktu perencanaan dalam jangka waktu tertentu yang bersifat terbatas (finite planning horizon. Dengan hasil akhir berupa penjadwalan, perencanaan model IRP mempertimbangkan jarak supplier-retailer dan biaya stockout yang mungkin terjadi pada retailer, sehingga diharapkan pengiriman optimal dan tidak terjadi stockout pada pos-pos penjualan bahan bakar.
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P. L. N. U. Cooray
2017-01-01
Full Text Available During the last decade, tremendous focus has been given to sustainable logistics practices to overcome environmental concerns of business practices. Since transportation is a prominent area of logistics, a new area of literature known as Green Transportation and Green Vehicle Routing has emerged. Vehicle Routing Problem (VRP has been a very active area of the literature with contribution from many researchers over the last three decades. With the computational constraints of solving VRP which is NP-hard, metaheuristics have been applied successfully to solve VRPs in the recent past. This is a threefold study. First, it critically reviews the current literature on EMVRP and the use of metaheuristics as a solution approach. Second, the study implements a genetic algorithm (GA to solve the EMVRP formulation using the benchmark instances listed on the repository of CVRPLib. Finally, the GA developed in Phase 2 was enhanced through machine learning techniques to tune its parameters. The study reveals that, by identifying the underlying characteristics of data, a particular GA can be tuned significantly to outperform any generic GA with competitive computational times. The scrutiny identifies several knowledge gaps where new methodologies can be developed to solve the EMVRPs and develops propositions for future research.
Tavakkoli-Moghaddam, Reza; Alinaghian, Mehdi; Salamat-Bakhsh, Alireza; Norouzi, Narges
2012-05-01
A vehicle routing problem is a significant problem that has attracted great attention from researchers in recent years. The main objectives of the vehicle routing problem are to minimize the traveled distance, total traveling time, number of vehicles and cost function of transportation. Reducing these variables leads to decreasing the total cost and increasing the driver's satisfaction level. On the other hand, this satisfaction, which will decrease by increasing the service time, is considered as an important logistic problem for a company. The stochastic time dominated by a probability variable leads to variation of the service time, while it is ignored in classical routing problems. This paper investigates the problem of the increasing service time by using the stochastic time for each tour such that the total traveling time of the vehicles is limited to a specific limit based on a defined probability. Since exact solutions of the vehicle routing problem that belong to the category of NP-hard problems are not practical in a large scale, a hybrid algorithm based on simulated annealing with genetic operators was proposed to obtain an efficient solution with reasonable computational cost and time. Finally, for some small cases, the related results of the proposed algorithm were compared with results obtained by the Lingo 8 software. The obtained results indicate the efficiency of the proposed hybrid simulated annealing algorithm.
Lower and upper bounds for the two-echelon capacitated location-routing problem
Contardo, Claudio; Hemmelmayr, Vera; Crainic, Teodor Gabriel
2012-01-01
In this paper, we introduce two algorithms to address the two-echelon capacitated location-routing problem (2E-CLRP). We introduce a branch-and-cut algorithm based on the solution of a new two-index vehicle-flow formulation, which is strengthened with several families of valid inequalities. We also propose an adaptive large-neighbourhood search (ALNS) meta-heuristic with the objective of finding good-quality solutions quickly. The computational results on a large set of instances from the literature show that the ALNS outperforms existing heuristics. Furthermore, the branch-and-cut method provides tight lower bounds and is able to solve small- and medium-size instances to optimality within reasonable computing times. PMID:24511176
A hybrid genetic algorithm for route optimization in the bale collecting problem
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C. Gracia
2013-06-01
Full Text Available The bale collecting problem (BCP appears after harvest operations in grain and other crops. Its solution defines the sequence of collecting bales which lie scattered over the field. Current technology on navigation-aid systems or auto-steering for agricultural vehicles and machines, is able to provide accurate data to make a reliable bale collecting planning. This paper presents a hybrid genetic algorithm (HGA approach to address the BCP pursuing resource optimization such as minimizing non-productive time, fuel consumption, or distance travelled. The algorithmic route generation provides the basis for a navigation tool dedicated to loaders and bale wagons. The approach is experimentally tested on a set of instances similar to those found in real situations. In particular, comparative results show an average improving of a 16% from those obtained by previous heuristics.
Lower and upper bounds for the two-echelon capacitated location-routing problem.
Contardo, Claudio; Hemmelmayr, Vera; Crainic, Teodor Gabriel
2012-12-01
In this paper, we introduce two algorithms to address the two-echelon capacitated location-routing problem (2E-CLRP). We introduce a branch-and-cut algorithm based on the solution of a new two-index vehicle-flow formulation, which is strengthened with several families of valid inequalities. We also propose an adaptive large-neighbourhood search (ALNS) meta-heuristic with the objective of finding good-quality solutions quickly. The computational results on a large set of instances from the literature show that the ALNS outperforms existing heuristics. Furthermore, the branch-and-cut method provides tight lower bounds and is able to solve small- and medium-size instances to optimality within reasonable computing times.
Improved Multi-Agent System for the Vehicle Routing Problem with Time Windows
Institute of Scientific and Technical Information of China (English)
DAN Zhenggang; CAI Linning; ZHENG Li
2009-01-01
The vehicle routing problem with time windows (VRPTW) involves assigning a fleet of limited ca-pacity vehicles to serve a set of customers without violating the capacity and time constraints. This paper presents a multi-agent model system for the VRPTW based on the internal behavior of agents and coordina-tion among the agents. The system presents a formal view of coordination using the traditional contract-net protocol (CNP) that relies on the basic loop of agent behavior for order receiving, order announcement, bid calculation, and order scheduling followed by order execution. An improved CNP method based on a vehicle selection strategy is used to reduce the number of negotiations and the negotiation time. The model is vali-dated using Solomon's benchmarks, with the results showing that the improved CNP uses only 30% as many negotiations and only 70% of the negotiation time of the traditional CNP.
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Jingling Zhang
2012-01-01
Full Text Available The multiobjective vehicle routing problem considering customer satisfaction (MVRPCS involves the distribution of orders from several depots to a set of customers over a time window. This paper presents a self-adaptive grid multi-objective quantum evolutionary algorithm (MOQEA for the MVRPCS, which takes into account customer satisfaction as well as travel costs. The degree of customer satisfaction is represented by proposing an improved fuzzy due-time window, and the optimization problem is modeled as a mixed integer linear program. In the MOQEA, nondominated solution set is constructed by the Challenge Cup rules. Moreover, an adaptive grid is designed to achieve the diversity of solution sets; that is, the number of grids in each generation is not fixed but is automatically adjusted based on the distribution of the current generation of nondominated solution set. In the study, the MOQEA is evaluated by applying it to classical benchmark problems. Results of numerical simulation and comparison show that the established model is valid and the MOQEA is effective for MVRPCS.
Selçuk K. İşleyen; Ö. Faruk Baykoç
2008-01-01
We define a special case for the vehicle routing problem with stochastic demands (SC-VRPSD) where customer demands are normally distributed. We propose a new linear model for computing the expected length of a tour in SC-VRPSD. The proposed model is based on the integration of the “Traveling Salesman Problem” (TSP) and the Assignment Problem. For large-scale problems, we also use an Iterated Local Search (ILS) algorithm in order to reach an effective solution.
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Vanessa de Oliveira Ferreira
2012-08-01
Full Text Available In this work we consider a variant of the vehicle routing problem that allows the assignment of multiple deliverymen to one or more routes. A practical motivation for this variant arises, for example, in the distribution of beverages in highly dense urban areas, characterized by the difficulty in serving daily requests within regular working day hours with a single deliveryman per vehicle. We present a mathematical model and a savings algorithm in order to generate low cost routes that maximize the number of requests served in compliance with the maximum route time. The impact of the extra deliverymen on the solutions provided by the proposed heuristic is assessed by means of sets of generated examples based on classical instances of literature. It is also presented the results obtained by an adaptation of a tabu search approach from the literature.
A Memetic Algorithm for the Vehicle Routing Problem with Cross Docking
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Sanae Larioui
2015-11-01
Full Text Available In this paper we address the VRPCD, in which a set of homogeneous vehicles are used to transport products from the suppliers to customers via a cross-dock. The products can be consolidated at the cross-dock but cannot be stored for very long as the cross-dock does not have long-term inventory-holding capabilities. The objective of the VRPCD is to minimize the total traveled distance while respecting time window constraints of suppliers and customers and a time horizon for the whole transportation operation. Rummaging through all the work of literature on vehicle routing problems with cross-docking, there is no work that considers that customer will receive its requests from several suppliers; this will be the point of innovation of this work. A heuristic and a memetic algorithm are used to solve the problem. The proposed algorithms are implemented and tested on data sets involving up to 200 nodes (customers and suppliers. The first results show that the memetic algorithm can produce high quality solutions.
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Wan-Yu Liu
2014-07-01
Full Text Available Torespondto the reduction of greenhouse gas emissions and global warming, this paper investigates the minimal-carbon-footprint time-dependent heterogeneous-fleet vehicle routing problem with alternative paths (MTHVRPP. This finds a route with the smallestcarbon footprint, instead of the shortestroute distance, which is the conventional approach, to serve a number of customers with a heterogeneous fleet of vehicles in cases wherethere may not be only one path between each pair of customers, and the vehicle speed differs at different times of the day. Inheriting from the NP-hardness of the vehicle routing problem, the MTHVRPP is also NP-hard. This paper further proposes a genetic algorithm (GA to solve this problem. The solution representedbyour GA determines the customer serving ordering of each vehicle type. Then, the capacity check is used to classify multiple routes of each vehicle type, and the path selection determines the detailed paths of each route. Additionally, this paper improves the energy consumption model used for calculating the carbon footprint amount more precisely. Compared with the results without alternative paths, our experimental results show that the alternative path in this experimenthas a significant impact on the experimental results in terms of carbon footprint.
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Michel Povlovitsch Seixas
2013-01-01
Full Text Available This study addresses a vehicle routing problem with time windows, accessibility restrictions on customers, and a fleet that is heterogeneous with regard to capacity and average speed. A vehicle can perform multiple routes per day, all starting and ending at a single depot, and it is assigned to a single driver whose total work hours are limited. A column generation algorithm is proposed. The column generation pricing subproblem requires a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performing multiple routes per day and to address the need to set the workday’s start time within the planning horizon. A constructive heuristic and a metaheuristic based on tabu search are also developed to find good solutions.
MULTI-VEHICLE COVERING TOUR PROBLEM: BUILDING ROUTES FOR URBAN PATROLLING
Washington Alves Oliveira; Antonio Carlos Moretti; Ednei Felix Reis
2015-01-01
ABSTRACT In this paper we study a particular aspect of the urban community policing: routine patrol route planning. We seek routes that guarantee visibility, as this has a sizable impact on the community perceived safety, allowing quick emergency responses and providing surveillance of selected sites (e.g., hospitals, schools). The planning is restricted to the availability of vehicles and strives to achieve balanced routes. We study an adaptation of the model for the multi-vehicle covering t...
van Anholt, Roel G.; Coelho, Leandro C.; Laporte, Gilbert; Vis, Iris F. A.
2016-01-01
The purpose of this paper is to introduce, model, and solve a rich multiperiod inventory-routing problem with pickups and deliveries motivated by the replenishment of automated teller machines in the Netherlands. Commodities can be brought to and from the depot, as well as being exchanged among cust
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Jianhua Ma
2013-01-01
Full Text Available The objective of vehicle routing problem is usually to minimize the total traveling distance or cost. But in practice, there are a lot of problems needed to minimize the fastest completion time. The milk-run vehicle routing problem (MRVRP is widely used in milk-run distribution. The mutation ACO is given to solve MRVRP with fastest completion time in this paper. The milk-run VRP with fastest completion time is introduced first, and then the customer division method based on dynamic optimization and split algorithm is given to transform this problem into finding the optimal customer order. At last the mutation ACO is given and the numerical examples verify the effectiveness of the algorithm.
Ma, Yanfang; Xu, Jiuping
2015-06-01
This article puts forward a cloud theory-based particle swarm optimization (CTPSO) algorithm for solving a variant of the vehicle routing problem, namely a multiple decision maker vehicle routing problem with fuzzy random time windows (MDVRPFRTW). A new mathematical model is developed for the proposed problem in which fuzzy random theory is used to describe the time windows and bi-level programming is applied to describe the relationship between the multiple decision makers. To solve the problem, a cloud theory-based particle swarm optimization (CTPSO) is proposed. More specifically, this approach makes improvements in initialization, inertia weight and particle updates to overcome the shortcomings of the basic particle swarm optimization (PSO). Parameter tests and results analysis are presented to highlight the performance of the optimization method, and comparison of the algorithm with the basic PSO and the genetic algorithm demonstrates its efficiency.
An optimization algorithm for a capacitated vehicle routing problem with time windows
Indian Academy of Sciences (India)
PINAR KIRCI
2016-05-01
In this paper, vehicle routing problem (VRP) with time windows and real world constraints are considered as a real-world application on google maps. Also, tabu search is used and Hopfield neural networks is utilized. Basic constraints consist of customer demands, time windows, vehicle speed, vehicle capacity andworking hours. Recently, cost and on-time delivery are the most important actors in logistics. Thus, the logistic applications attract attention of companies. In logistic management, determining the locations of delivery points and deciding the path are the vital components that should be considered. Deciding the paths of vehicles provides companies to use their vehicles efficiently. And with utilizing optimized paths, big amounts of cost and time savings will be gained. The main aim of the work is providing the best path according to the needs of the customers, minimizing the costs with utilizing the VRP and presenting an application for companies that need logistic management. To compare the results, simulated annealing is used on special scenarios. And t-test is performed in the study for the visited path in km with p-value of 0.05.
Approximation Algorithms and Hardness of the k-Route Cut Problem
Chuzhoy, Julia; Zhou, Yuan; Vijayaraghavan, Aravindan
2011-01-01
We study the k-route cut problem: given an undirected edge-weighted graph G=(V,E), a collection {(s_1,t_1),(s_2,t_2),...,(s_r,t_r)} of source-sink pairs, and an integer connectivity requirement k, the goal is to find a minimum-weight subset E' of edges to remove, such that the connectivity of every pair (s_i, t_i) falls below k. Specifically, in the edge-connectivity version, EC-kRC, the requirement is that there are at most (k-1) edge-disjoint paths connecting s_i to t_i in G \\ E', while in the vertex-connectivity version, NC-kRC, the same requirement is for vertex-disjoint paths. Prior to our work, poly-logarithmic approximation algorithms have been known for the special case where k >= 3, but no non-trivial approximation algorithms were known for any value k>3, except in the single-source setting. We show an O(k log^{3/2}r)-approximation algorithm for EC-kRC with uniform edge weights, and several polylogarithmic bi-criteria approximation algorithms for EC-kRC and NC-kRC, where the connectivity requirement ...
MILP for the Inventory and Routing for Replenishment Problem in the Car Assembly Line.
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Raul Pulido
2014-01-01
Full Text Available The inbound logistic for feeding the workstation inside the factory represents a critical issue in the car manufacturing industry. Nowadays, this issue is even more critical than in the past since more types of car are being produced in the assembly lines. Consequently, as workstations have to install many types of components, they also need to have an inventory of different types of the component in a compact space.The replenishment is a critical issue since a lack of inventory could cause line stoppage or reworking. On the other hand, an excess of inventory could increase the holding cost or even block the replenishment paths. The decision of the replenishment routes cannot be made without taking into consideration the inventory needed by each station during the production time which will depend on the production sequence. This problem deals with medium-sized instances and it is solved using online solvers. The contribution of this paper is a MILP for the replenishment and inventory of the components in a car assembly line.
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Alberto Ochoa-Ortíz
2015-01-01
Full Text Available El problema de ruteo de vehículos bajo las limitaciones de capacidad y basado en computación ubicua desde una perspectiva relacionada con PSS (Producto-Servicio de Sistemas para desarrollar configuraciones para el transporte urbano de mercancías es abordado. Éste trabajo considera las especificidades de la logística urbana bajo un contexto de mercados emergentes. En este caso, involucra: i bajas competencias logísticas de los tomadores de decisiones; ii la limitada disponibilidad de datos; y iii restringido acceso a tecnología de alto desempeño para calcular rutas de transporte óptimas. Por lo tanto, se propone el uso de un software libre que proporciona soluciones de bajo costo (en tiempo y recursos. El artículo muestra la aplicación de los resultados de una herramienta de software basado en la Teoría de Grafos utilizado para analizar y resolver un CVRP (Capacitated Vehicle Routing Problem. Se utilizó el caso de una empresa local de distribución de alimentos situada en una gran ciudad de México. Sobre la base de una flora de vehículos pequeños, todos con las mismas especificaciones técnicas y una capacidad de carga comparable.
A hybrid metaheuristic for the time-dependent vehicle routing problem with hard time windows
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N. Rincon-Garcia
2017-01-01
Full Text Available This article paper presents a hybrid metaheuristic algorithm to solve the time-dependent vehicle routing problem with hard time windows. Time-dependent travel times are influenced by different congestion levels experienced throughout the day. Vehicle scheduling without consideration of congestion might lead to underestimation of travel times and consequently missed deliveries. The algorithm presented in this paper makes use of Large Neighbourhood Search approaches and Variable Neighbourhood Search techniques to guide the search. A first stage is specifically designed to reduce the number of vehicles required in a search space by the reduction of penalties generated by time-window violations with Large Neighbourhood Search procedures. A second stage minimises the travel distance and travel time in an ‘always feasible’ search space. Comparison of results with available test instances shows that the proposed algorithm is capable of obtaining a reduction in the number of vehicles (4.15%, travel distance (10.88% and travel time (12.00% compared to previous implementations in reasonable time.
Directory of Open Access Journals (Sweden)
Behrouz Afshar-Nadjafi
2017-01-01
Full Text Available In this paper, we consider the time-dependent multi-depot vehicle routing problem. The objective is to minimize the total heterogeneous fleet cost assuming that the travel time between locations depends on the departure time. Also, hard time window constraints for the customers and limitation on maximum number of the vehicles in depots must be satisfied. The problem is formulated as a mixed integer programming model. A constructive heuristic procedure is proposed for the problem. Also, the efficiency of the proposed algorithm is evaluated on 180 test problems. The obtained computational results indicate that the procedure is capable to obtain a satisfying solution.
Directory of Open Access Journals (Sweden)
Peiqing Li
2015-01-01
Full Text Available Fresh fruits and vegetables, perishable by nature, are subject to additional deterioration and bruising in the distribution process due to vibration and shock caused by road irregularities. A nonlinear mathematical model was developed that considered not only the vehicle routing problem with time windows but also the effect of road irregularities on the bruising of fresh fruits and vegetables. The main objective of this work was to obtain the optimal distribution routes for fresh fruits and vegetables considering different road classes with the least amount of logistics costs. An improved genetic algorithm was used to solve the problem. A fruit delivery route among the 13 cities in Jiangsu Province was used as a real analysis case. The simulation results showed that the vehicle routing problem with time windows, considering road irregularities and different classes of toll roads, can significantly influence total delivery costs compared with traditional VRP models. The comparison between four models to predict the total cost and actual total cost in distribution showed that the improved genetic algorithm is superior to the Group-based pattern, CW pattern, and O-X type cross pattern.
Meneghetti, M; Dahle, H; Limousin, M
2013-01-01
The existence of an arc statistics problem was at the center of a strong debate in the last fifteen years. With the aim to clarify if the optical depth for giant gravitational arcs by galaxy clusters in the so called concordance model is compatible with observations, several studies were carried out which helped to significantly improve our knowledge of strong lensing clusters, unveiling their extremely complex internal structure. In particular, the abundance and the frequency of strong lensing events like gravitational arcs turned out to be a potentially very powerful tool to trace the structure formation. However, given the limited size of observational and theoretical data-sets, the power of arc statistics as a cosmological tool has been only minimally exploited so far. On the other hand, the last years were characterized by significant advancements in the field, and several cluster surveys that are ongoing or planned for the near future seem to have the potential to make arc statistics a competitive cosmo...
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available We define a special case for the vehicle routing problem with stochastic demands (SC-VRPSD where customer demands are normally distributed. We propose a new linear model for computing the expected length of a tour in SC-VRPSD. The proposed model is based on the integration of the “Traveling Salesman Problem” (TSP and the Assignment Problem. For large-scale problems, we also use an Iterated Local Search (ILS algorithm in order to reach an effective solution.
Directory of Open Access Journals (Sweden)
Xiaobing Gan
2012-01-01
Full Text Available This paper considers two additional factors of the widely researched vehicle routing problem with time windows (VRPTW. The two factors, which are very common characteristics in realworld, are uncertain number of vehicles and simultaneous delivery and pick-up service. Using minimization of the total transport costs as the objective of the extension VRPTW, a mathematic model is constructed. To solve the problem, an efficient multiswarm cooperative particle swarm optimization (MCPSO algorithm is applied. And a new encoding method is proposed for the extension VRPTW. Finally, comparing with genetic algorithm (GA and particle swarm optimization (PSO algorithm, the MCPSO algorithm performs best for solving this problem.
Hemmelmayr, Vera C; Cordeau, Jean-François; Crainic, Teodor Gabriel
2012-12-01
In this paper, we propose an adaptive large neighborhood search heuristic for the Two-Echelon Vehicle Routing Problem (2E-VRP) and the Location Routing Problem (LRP). The 2E-VRP arises in two-level transportation systems such as those encountered in the context of city logistics. In such systems, freight arrives at a major terminal and is shipped through intermediate satellite facilities to the final customers. The LRP can be seen as a special case of the 2E-VRP in which vehicle routing is performed only at the second level. We have developed new neighborhood search operators by exploiting the structure of the two problem classes considered and have also adapted existing operators from the literature. The operators are used in a hierarchical scheme reflecting the multi-level nature of the problem. Computational experiments conducted on several sets of instances from the literature show that our algorithm outperforms existing solution methods for the 2E-VRP and achieves excellent results on the LRP.
Hemmelmayr, Vera C.; Cordeau, Jean-François; Crainic, Teodor Gabriel
2012-01-01
In this paper, we propose an adaptive large neighborhood search heuristic for the Two-Echelon Vehicle Routing Problem (2E-VRP) and the Location Routing Problem (LRP). The 2E-VRP arises in two-level transportation systems such as those encountered in the context of city logistics. In such systems, freight arrives at a major terminal and is shipped through intermediate satellite facilities to the final customers. The LRP can be seen as a special case of the 2E-VRP in which vehicle routing is performed only at the second level. We have developed new neighborhood search operators by exploiting the structure of the two problem classes considered and have also adapted existing operators from the literature. The operators are used in a hierarchical scheme reflecting the multi-level nature of the problem. Computational experiments conducted on several sets of instances from the literature show that our algorithm outperforms existing solution methods for the 2E-VRP and achieves excellent results on the LRP. PMID:23483764
动态车辆路径问题研究综述%Overview on Dynamic Vehicle Routing Problems
Institute of Scientific and Technical Information of China (English)
韩娟娟; 李永先
2015-01-01
The paper reviewed dynamic vehicle routing problem .DVRP was classified into SVRP and FVRP . The paper introduced research in recent years on models ,algorithms and simulationg of dynamic vehicle rou‐ting problems ,and summarizes characteristics of dynamic vehicle routing problem .Finally ,the paper pros‐pected future research orientations of dynamic vehicle routing problem .%指出了动态车辆路径问题是运筹学和组合优化领域的前沿研究方向，研究动态车辆路径问题具有重要的理论和现实意义。阐述了动态车辆问题（DVRP），根据动态信息的特征将动态车辆路径问题分为随机车辆路径问题（SVRP）和模糊车辆路径问题（FVRP）。从动态车辆路径问题的建模、算法和仿真优化三个方面分析了其研究成果，对现有研究的不足进行了探讨，提出了动态车辆路径问题的进一步研究方向。
Inverse problem of elastica of a variable-arc-length beam subjected to a concentrated load
Institute of Scientific and Technical Information of China (English)
Xiaowei Zhang; Jialing Yang; Keren Wang
2005-01-01
An inverse problem of elastica of a variable-arclength beam subjected to a concentrated load is investigated.The beam is fixed at one end, and can slide freely over a hinge support at the other end. The inverse problem is to determine the value of the load when the deflection of the action point of the load is given. Based on the elasitca equations and the elliptic integrals, a set of nonlinear equations for the inverse problem are derived, and an analytical solution by means of iterations and Quasi-Newton method is presented. From the results, the relationship between the loads and deflections of the loading point is obtained.
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Duygu Yilmaz Eroglu
2014-01-01
Full Text Available In this paper, we analyze a real-world OVRP problem for a production company. Considering real-world constrains, we classify our problem as multicapacitated/heterogeneous fleet/open vehicle routing problem with split deliveries and multiproduct (MCHF/OVRP/SDMP which is a novel classification of an OVRP. We have developed a mixed integer programming (MIP model for the problem and generated test problems in different size (10–90 customers considering real-world parameters. Although MIP is able to find optimal solutions of small size (10 customers problems, when the number of customers increases, the problem gets harder to solve, and thus MIP could not find optimal solutions for problems that contain more than 10 customers. Moreover, MIP fails to find any feasible solution of large-scale problems (50–90 customers within time limits (7200 seconds. Therefore, we have developed a genetic algorithm (GA based solution approach for large-scale problems. The experimental results show that the GA based approach reaches successful solutions with 9.66% gap in 392.8 s on average instead of 7200 s for the problems that contain 10–50 customers. For large-scale problems (50–90 customers, GA reaches feasible solutions of problems within time limits. In conclusion, for the real-world applications, GA is preferable rather than MIP to reach feasible solutions in short time periods.
Eroglu, Duygu Yilmaz; Gencosman, Burcu Caglar; Cavdur, Fatih; Ozmutlu, H Cenk
2014-01-01
In this paper, we analyze a real-world OVRP problem for a production company. Considering real-world constrains, we classify our problem as multicapacitated/heterogeneous fleet/open vehicle routing problem with split deliveries and multiproduct (MCHF/OVRP/SDMP) which is a novel classification of an OVRP. We have developed a mixed integer programming (MIP) model for the problem and generated test problems in different size (10-90 customers) considering real-world parameters. Although MIP is able to find optimal solutions of small size (10 customers) problems, when the number of customers increases, the problem gets harder to solve, and thus MIP could not find optimal solutions for problems that contain more than 10 customers. Moreover, MIP fails to find any feasible solution of large-scale problems (50-90 customers) within time limits (7200 seconds). Therefore, we have developed a genetic algorithm (GA) based solution approach for large-scale problems. The experimental results show that the GA based approach reaches successful solutions with 9.66% gap in 392.8 s on average instead of 7200 s for the problems that contain 10-50 customers. For large-scale problems (50-90 customers), GA reaches feasible solutions of problems within time limits. In conclusion, for the real-world applications, GA is preferable rather than MIP to reach feasible solutions in short time periods.
Rabbani, Masoud; Farrokhi-Asl, Hamed; Asgarian, Bahare
2016-10-01
It is observed that the separated design of location for depots and routing for servicing customers often reach a suboptimal solution. So, solving location and routing problem simultaneously could achieve better results. In this paper, waste collection problem is considered with regard to economic and societal objective functions. A non-dominated sorting genetic algorithm (NSGA-II) is used to locate depots and treatment facilities and design the routes starting from depots to serve customers. A new mathematical model is proposed and two objective functions including economic objective (opening cost of depots and treatment facility and transportation cost) and societal objective; that is, negative impact of treatment facilities which are close to towns are addressed in this study. A straightforward order based solution representation is applied for coding solutions of the problem and clustering approach is used to generate appropriate initial solutions. Moreover, three multi-objective decomposition methods including weighted sum, goal programming, and goal attainment are applied to validate the performance of the proposed algorithm. Number of test problems are conducted and the results obtained by algorithms are compared with respect to some comparison metrics. Finally, the experimental results show that the proposed hybrid NSGA-II outperforms all decomposition methods, but the computational times for decomposition methods are less than NSGA-II.
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Hany Seidgar
2016-01-01
Full Text Available This paper investigates a scheduling combined manpower-vehicle routing problem with a central depot in and a set of multi-skilled manpower for serving to customers. Teams are in different range of competencies that it will affect the service time duration. Vehicles are in different moving speeds and costs and not all the vehicles are capable to move toward all the customers’ sites. The objective is to minimize the total cost of servicing, routing, and lateness penalties. This paper presents a mixed integer programming model and two meta-heuristic approaches of genetic algorithm (GA and artificial bee colony algorithm (ABC are developed to solve the generated problems. Furthermore, Taguchi experimental design method is applied to set the proper values of parameters. The available results show the higher performance of proposed GA compared with ABC, in quality of solutions.
Energy Technology Data Exchange (ETDEWEB)
Martins, P.; Gouveia, L.
1994-12-31
In this talk we discuss several linear integer programming formulations for a particular case of the Vehicle Routing Problem, where several classes of vehicles are considered and a fixed number of vehicles is imposed in each class. We also present a set of valid inequalities which lead to significant improvements on the lower bounds. Some heuristics are also discussed. We present computational results taken from a set of tests with the number of clients ranging from 13 to 75.
Alternative Route Techniques and their Applications to the Stochastics on-time Arrival Problem
2015-01-01
This thesis takes a close look at a wide range of different techniques for the computation of alternative routes on the two most popular speed-up techniques currently in use. From the standpoint of an algorithm engineer, we explore how to exploit the different techniques for their full potential.
Flow Merging and Hub Route Optimization in Collaborative Transportation
Directory of Open Access Journals (Sweden)
Kerui Weng
2014-01-01
Full Text Available This paper studies the optimal hub routing problem of merged tasks in collaborative transportation. This problem allows all carriers’ transportation tasks to reach the destinations optionally passing through 0, 1, or 2 hubs within limited distance, while a cost discount on arcs in the hub route could be acquired after paying fixed charges. The problem arises in the application of logistics, postal services, airline transportation, and so forth. We formulate the problem as a mixed-integer programming model, and provide two heuristic approaches, respectively, based on Lagrangian relaxation and Benders decomposition. Computational experiments show that the algorithms work well.
Directory of Open Access Journals (Sweden)
Hossein Yousefi
2017-06-01
Full Text Available A vehicle routing problem with time windows (VRPTW is an important problem with many real applications in a transportation problem. The optimum set of routes with the minimum distance and vehicles used is determined to deliver goods from a central depot, using a vehicle with capacity constraint. In the real cases, there are other objective functions that should be considered. This paper considers not only the minimum distance and the number of vehicles used as the objective function, the customer’s satisfaction with the priority of customers is also considered. Additionally, it presents a new model for a bi-objective VRPTW solved by a revised multi-choice goal programming approach, in which the decision maker determines optimistic aspiration levels for each objective function. Two meta-heuristic methods, namely simulated annealing (SA and genetic algorithm (GA, are proposed to solve large-sized problems. Moreover, the experimental design is used to tune the parameters of the proposed algorithms. The presented model is verified by a real-world case study and a number of test problems. The computational results verify the efficiency of the proposed SA and GA.
Tavakkoli-Moghaddam, Reza; Forouzanfar, Fateme; Ebrahimnejad, Sadoullah
2013-07-01
This paper considers a single-sourcing network design problem for a three-level supply chain. For the first time, a novel mathematical model is presented considering risk-pooling, the inventory existence at distribution centers (DCs) under demand uncertainty, the existence of several alternatives to transport the product between facilities, and routing of vehicles from distribution centers to customer in a stochastic supply chain system, simultaneously. This problem is formulated as a bi-objective stochastic mixed-integer nonlinear programming model. The aim of this model is to determine the number of located distribution centers, their locations, and capacity levels, and allocating customers to distribution centers and distribution centers to suppliers. It also determines the inventory control decisions on the amount of ordered products and the amount of safety stocks at each opened DC, selecting a type of vehicle for transportation. Moreover, it determines routing decisions, such as determination of vehicles' routes starting from an opened distribution center to serve its allocated customers and returning to that distribution center. All are done in a way that the total system cost and the total transportation time are minimized. The Lingo software is used to solve the presented model. The computational results are illustrated in this paper.
A Novel Discrete Differential Evolution Algorithm for the Vehicle Routing Problem in B2C E-Commerce
Xia, Chao; Sheng, Ying; Jiang, Zhong-Zhong; Tan, Chunqiao; Huang, Min; He, Yuanjian
2015-12-01
In this paper, a novel discrete differential evolution (DDE) algorithm is proposed to solve the vehicle routing problems (VRP) in B2C e-commerce, in which VRP is modeled by the incomplete graph based on the actual urban road system. First, a variant of classical VRP is described and a mathematical programming model for the variant is given. Second, the DDE is presented, where individuals are represented as the sequential encoding scheme, and a novel reparation operator is employed to repair the infeasible solutions. Furthermore, a FLOYD operator for dealing with the shortest route is embedded in the proposed DDE. Finally, an extensive computational study is carried out in comparison with the predatory search algorithm and genetic algorithm, and the results show that the proposed DDE is an effective algorithm for VRP in B2C e-commerce.
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Zheng Wang
2016-01-01
Full Text Available This paper presents a saving-based heuristic for the vehicle routing problem with time windows and stochastic travel times (VRPTWSTT. One of the basic ideas of the heuristic is to advance the latest service start time of each customer by a certain period of time. In this way, the reserved time can be used to cope with unexpected travel time delay when necessary. Another important idea is to transform the VRPTWSTT to a set of vehicle routing problems with time windows (VRPTW, each of which is defined by a given percentage used to calculate the reserved time for customers. Based on the above two key ideas, a three-stage heuristic that includes the “problem transformation” stage, the “solution construction” stage, and the “solution improvement” stage is developed. After the problem transformation in the first stage, the work of the next two stages is to first construct an initial solution for each transformed VRPTW by improving the idea of the classical Clarke-Wright heuristic and then further improve the solution. Finally, a number of numerical experiments are conducted to evaluate the efficiency of the described methodology under different uncertainty levels.
2002-06-01
Assignment Heurisitic for Vehicle Routing,” Networks: 11, 109-124 (1981). Fraleigh , John B. A First Course in Abstract Algebra, Addison-Wesley...Infantry Officer, and attended the Infantry Officer Basic Course and Ranger School. His first tour was with the 25th Infantry Division, Schofield...James Moore, for his guidance and support throughout the course of this research effort. I would also like to thank my committee members Dr. Barnes
Directory of Open Access Journals (Sweden)
Julia Rieck
2013-05-01
Full Text Available In reverse logistics networks, products (e.g., bottles or containers have to be transported from a depot to customer locations and, after use, from customer locations back to the depot. In order to operate economically beneficial, companies prefer a simultaneous delivery and pick-up service. The resulting Vehicle Routing Problem with Simultaneous Delivery and Pick-up (VRPSDP is an operational problem, which has to be solved daily by many companies. We present two mixed-integer linear model formulations for the VRPSDP, namely a vehicle-flow and a commodity-flow model. In order to strengthen the models, domain-reducing preprocessing techniques, and effective cutting planes are outlined. Symmetric benchmark instances known from the literature as well as new asymmetric instances derived from real-world problems are solved to optimality using CPLEX 12.1.
Meysam Mousavi, S.; Tavakkoli-Moghaddam, Reza; Jolai, Fariborz
2013-10-01
This article considers the design of cross-docking systems under uncertainty in a model that consists of two phases: (1) a strategic-based decision-making process for selecting the location of cross-docks to operate, and (2) an operational-based decision-making process for vehicle routing scheduling with multiple cross-docks. This logistic system contains three echelons, namely suppliers, cross-docks and retailers, in an uncertain environment. In the first phase, a new multi-period cross-dock location model is introduced to determine the minimum number of cross-docks among a set of location sites so that each retailer demand should be met. Then, in the second phase, a new vehicle routing scheduling model with multiple cross-docks is formulated in which each vehicle is able to pickup from or deliver to more than one supplier or retailer, and the pickup and delivery routes start and end at the corresponding cross-dock. This article is the first attempt to introduce an integrated model for cross-docking systems design under a fuzzy environment. To solve the presented two-phase mixed-integer programming (MIP) model, a new fuzzy mathematical programming-based possibilistic approach is used. Furthermore, experimental tests are carried out to demonstrate the effectiveness of the presented model. The computational results reveal the applicability and suitability of the developed fuzzy possibilistic two-phase model in a variety of problems in the domain of cross-docking systems.
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Jhon Jairo Santa Chávez
2016-01-01
Full Text Available This paper presents a multiobjective ant colony algorithm for the Multi-Depot Vehicle Routing Problem with Backhauls (MDVRPB where three objectives of traveled distance, traveling times and total consumption of energy are minimized. An ant colony algorithm is proposed to solve the MDVRPB. The solution scheme allows one to find a set of ordered solutions in Pareto fronts by considering the concept of dominance. The effectiveness of the proposed approach is examined by considering a set of instances adapted from the literature. The computational results show high quality results within short computing times.
Exactly solving the Split Pickup and Split Delivery Vehicle Routing Problem on a bike-sharing system
Casazza, Marco
2016-01-01
We propose an exact methodology to solve the Split Pickup and Split Delivery Vehicle Routing Problem arising in bike-sharing systems: a bike-sharing system is a public service in which bicycles are stored in rack stations and made available for shared use to individuals on a short term basis. However, during peak hours, flows along particular direction are registered, leading to high risk of empty racks in departure stations, and full racks at destination. One of the solutions chosen by many ...
Solution Representations and Local Search for the bi-objective Inventory Routing Problem
Barthélemy, Thibaut; Sevaux, Marc
2012-01-01
The solution of the biobjective IRP is rather challenging, even for metaheuristics. We are still lacking a profound understanding of appropriate solution representations and effective neighborhood structures. Clearly, both the delivery volumes and the routing aspects of the alternatives need to be reflected in an encoding, and must be modified when searching by means of local search. Our work contributes to the better understanding of such solution representations. On the basis of an experimental investigation, the advantages and drawbacks of two encodings are studied and compared.
DEFF Research Database (Denmark)
Wen, Min; Krapper, Emil; Larsen, Jesper;
2011-01-01
. The objective is to minimize the total delivery cost that is a weighted sum of two kinds of delivery costs. A multilevel variable neighborhood search heuristic is proposed for the problem. In a preprocessing step, the problem size is reduced through an aggregation procedure. Thereafter, the aggregated weekly...... planning problem is decomposed into daily planning problems, each of which is solved by a variable neighborhood search. Finally, the solution of the aggregated problem is expanded to that of the original problem. The method is implemented and tested on real‐life data consisting of up to 2,000 orders per...... week. Computational results show that the aggregation procedure and the decomposition strategy are very effective in solving this large scale problem, and our solutions are superior to the industrial solutions given the constraints considered in this work....
Directory of Open Access Journals (Sweden)
Anan Mungwattana
2016-06-01
Full Text Available This paper deals with the vehicle routing problem with time windows (VRPTW. The VRPTW routes a set of vehicles to service customers having two-sided time windows, i.e. earliest and latest start of service times. The demand requests are served by capacitated vehicles with limited travel times to return to the depot. The purpose of this paper is to develop a hybrid algorithm that uses the modified push forward insertion heuristic (MPFIH, a λ-interchange local search descent method (λ-LSD and a genetic algorithm to solve the VRPTW with two objectives. The first objective aims to determine the minimum number of vehicles required and the second is to find the solution that minimizes the total travel time. A set of well-known benchmark problems are used to compare the quality of solutions. The results show that the proposed algorithm provides effective solutions compared with best found solutions and better than another heuristic used for comparison.
Yu, Hao; Solvang, Wei Deng
2016-05-31
Hazardous waste location-routing problems are of importance due to the potential risk for nearby residents and the environment. In this paper, an improved mathematical formulation is developed based upon a multi-objective mixed integer programming approach. The model aims at assisting decision makers in selecting locations for different facilities including treatment plants, recycling plants and disposal sites, providing appropriate technologies for hazardous waste treatment, and routing transportation. In the model, two critical factors are taken into account: system operating costs and risk imposed on local residents, and a compensation factor is introduced to the risk objective function in order to account for the fact that the risk level imposed by one type of hazardous waste or treatment technology may significantly vary from that of other types. Besides, the policy instruments for promoting waste recycling are considered, and their influence on the costs and risk of hazardous waste management is also discussed. The model is coded and calculated in Lingo optimization solver, and the augmented ε-constraint method is employed to generate the Pareto optimal curve of the multi-objective optimization problem. The trade-off between different objectives is illustrated in the numerical experiment.
Yu, Hao; Solvang, Wei Deng
2016-01-01
Hazardous waste location-routing problems are of importance due to the potential risk for nearby residents and the environment. In this paper, an improved mathematical formulation is developed based upon a multi-objective mixed integer programming approach. The model aims at assisting decision makers in selecting locations for different facilities including treatment plants, recycling plants and disposal sites, providing appropriate technologies for hazardous waste treatment, and routing transportation. In the model, two critical factors are taken into account: system operating costs and risk imposed on local residents, and a compensation factor is introduced to the risk objective function in order to account for the fact that the risk level imposed by one type of hazardous waste or treatment technology may significantly vary from that of other types. Besides, the policy instruments for promoting waste recycling are considered, and their influence on the costs and risk of hazardous waste management is also discussed. The model is coded and calculated in Lingo optimization solver, and the augmented ε-constraint method is employed to generate the Pareto optimal curve of the multi-objective optimization problem. The trade-off between different objectives is illustrated in the numerical experiment. PMID:27258293
Directory of Open Access Journals (Sweden)
Hao Yu
2016-05-01
Full Text Available Hazardous waste location-routing problems are of importance due to the potential risk for nearby residents and the environment. In this paper, an improved mathematical formulation is developed based upon a multi-objective mixed integer programming approach. The model aims at assisting decision makers in selecting locations for different facilities including treatment plants, recycling plants and disposal sites, providing appropriate technologies for hazardous waste treatment, and routing transportation. In the model, two critical factors are taken into account: system operating costs and risk imposed on local residents, and a compensation factor is introduced to the risk objective function in order to account for the fact that the risk level imposed by one type of hazardous waste or treatment technology may significantly vary from that of other types. Besides, the policy instruments for promoting waste recycling are considered, and their influence on the costs and risk of hazardous waste management is also discussed. The model is coded and calculated in Lingo optimization solver, and the augmented ε-constraint method is employed to generate the Pareto optimal curve of the multi-objective optimization problem. The trade-off between different objectives is illustrated in the numerical experiment.
Modelling Problem-Solving Situations into Number Theory Tasks: The Route towards Generalisation
Papadopoulos, Ioannis; Iatridou, Maria
2010-01-01
This paper examines the way two 10th graders cope with a non-standard generalisation problem that involves elementary concepts of number theory (more specifically linear Diophantine equations) in the geometrical context of a rectangle's area. Emphasis is given on how the students' past experience of problem solving (expressed through interplay…
Does Calculation or Word-Problem Instruction Provide a Stronger Route to Prealgebraic Knowledge?
Fuchs, Lynn S.; Powell, Sarah R.; Cirino, Paul T.; Schumacher, Robin F.; Marrin, Sarah; Hamlett, Carol L.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.
2014-01-01
The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and prealgebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other…
A Hybrid Column Generation approach for an Industrial Waste Collection Routing Problem
DEFF Research Database (Denmark)
Hauge, Kristian; Larsen, Jesper; Lusby, Richard Martin;
2014-01-01
, real-world problem instances. Results indicate that the hybrid column generation outperforms a purely heuristic approach in terms of both running time and solution quality. High quality solutions to problems containing up to 100 orders can be solved in approximately 15 minutes....
移动机会网络路由问题研究%Research on Mobile Network Opportunity Routing Problem
Institute of Scientific and Technical Information of China (English)
黎智成
2016-01-01
传统的多跳无线网络只适用于一般的用户，对于那些在比较困难的环境下进行作业的无线网络而言，一旦出现无线网络连接中断的情况，不仅会出现网络性能大幅度下降导致网络不能正常运行，更没有相应的处理方案来解决这种问题。这种网络显然不能满足当下人们的需求，因此移动机会网络应运而生。但这种网络的路由问题一直是人们关心的问题。在这里，文章主要就移动机会网络的实际应用以及机会路由问题进行简单的分析与研究。%Traditional jump more wireless network is only applicable to the general user, for those who are in a dififcult environment for operation of the wireless network, once appear, the wireless network connection interruption, can appear not only network performance led to a big drop in the network can not run normally, there is no corresponding treatment scheme to solve this problem. This network obviously can't meet the needs of the present people, so the mobile network opportunity accordingly. But this kind of network routing problem has always been a problem concerned by people. Here, we mainly is the practical application of mobile opportunities to network and the opportunity to study on simple analysis and routing problem.
Directory of Open Access Journals (Sweden)
Suphan Sodsoon
2014-06-01
Full Text Available This study aims to solve a Vehicle Routing Problem with Time Windows and Speed Limits (VRPTWSL, which has received considerable attention in recent years. The vehicle routing problem with time windows is an extension of the well-known Vehicle Routing Problem (VRP and involves a fleet of vehicles set of from a depot to serve a number of customers at different geographic locations with various demands within specific time and speed limits before returning to the depot eventually. To solve the problem, an efficient Saving Method-Max Min Ant System (Saving-MMAS with Local Search algorithm is applied. Using minimization of the total transportation costs as the objective of the extension VRPTWSL, a mathematic model is constructed. Finally, the Saving-MMAS algorithms indicated the good quality of the method in this problem.
Unified heuristics to solve routing problem of reverse logistics in sustainable supply chain
Anbuudayasankar, S. P.; Ganesh, K.; Lenny Koh, S. C.; Mohandas, K.
2010-03-01
A reverse logistics problem, motivated by many real-life applications, is examined where bottles/cans in which products are delivered from a processing depot to customers in one period are available for return to the depot in the following period. The picked-up bottles/cans need to be adjusted in the place of delivery load. This problem is termed as simultaneous delivery and pick-up problem with constrained capacity (SDPC). We develop three unified heuristics based on extended branch and bound heuristic, genetic algorithm and simulated annealing to solve SDPC. These heuristics are also designed to solve standard travelling salesman problem (TSP) and TSP with simultaneous delivery and pick-up (TSDP). We tested the heuristics on standard, derived and randomly generated datasets of TSP, TSDP and SDPC and obtained satisfying results with high convergence in reasonable time.
Considering Competition to Solve a Flight Schedule and Aircraft Routing Problem for Small Airlines
Directory of Open Access Journals (Sweden)
J. Díaz-Ramírez
2012-08-01
Full Text Available For the case of low-cost airlines, which are characterized by having a single fleet with a small number of airplanes, ina previous work, a heuristic algorithm (AFS-MRA was developed to simultaneously find the flight schedule and theaircraft routes subject to maintenance constraints. This work advances this algorithm by incorporating competition inthe planning process (MAFS-MRA.Within a time frame with a given demand data, competition is seen as a game with two players (one airline and all itscompetitors, where the strategies are all the potential origin-destinations that could be included in the flight schedule,and the payment matrix contains the objective function coefficients that depend on the market share and the routespreviously selected.Numerical experimentation was undertaken using real data for the case of two airlines that operate at TolucaInternational Airport in Mexico. It was found that, by considering competition, the occupation improves to 3% and thatthe number of flights required to satisfy the demand was reduced to 21%. Besides, the updating process reduces theprofit computation error in almost 80%, as compared to the real market behavior for the period under study.
Combining Single (Mixed) Metric Approach and Genetic Algorithm for QoS Routing Problem
Institute of Scientific and Technical Information of China (English)
胡世余; 谢剑英
2004-01-01
A hybrid algorithm for the delay constrained least cost path problem is proposed through combination of single (mixed) metric approach and genetic algorithm. Compared with the known genetic algorithm for the same problem, the new algorithm adopts integral coding scheme and new genetic operator, which reduces the search space and improves the efficiency of genetic operation. Meanwhile, the single (mixed) approach accelerates the convergence speed. Simulation results indicate that the proposed algorithm can find near-optimal even optimal solutions within moderate numbers of generations.
Directory of Open Access Journals (Sweden)
Tao Jia
2014-01-01
Full Text Available We investigate an integrated inventory routing problem (IRP in which one supplier with limited production capacity distributes a single item to a set of retailers using homogeneous vehicles. In the objective function we consider a loading cost which is often neglected in previous research. Considering the deterioration in the products, we set a soft time window during the transportation stage and a hard time window during the sales stage, and to prevent jams and waiting cost, the time interval of two successive vehicles returning to the supplier’s facilities is required not to be overly short. Combining all of these factors, a two-echelon supply chain mixed integer programming model under discrete time is proposed, and a two-phase algorithm is developed. The first phase uses tabu search to obtain the retailers’ ordering matrix. The second phase is to generate production scheduling and distribution routing, adopting a saving algorithm and a neighbourhood search, respectively. Computational experiments are conducted to illustrate the effectiveness of the proposed model and algorithm.
The Complex Route to Success: Complex Problem-Solving Skills in the Prediction of University Success
Stadler, Matthias J.; Becker, Nicolas; Greiff, Samuel; Spinath, Frank M.
2016-01-01
Successful completion of a university degree is a complex matter. Based on considerations regarding the demands of acquiring a university degree, the aim of this paper was to investigate the utility of complex problem-solving (CPS) skills in the prediction of objective and subjective university success (SUS). The key finding of this study was that…
Disjunctive cuts in a branch-and-price algorithm for the capacitated vehicle routing problem
DEFF Research Database (Denmark)
Røpke, Stefan
This talk presents computational results that show the usefulness of the general-purpose valid inequalities disjunctive cuts when applied to the CVRP. Results indicate that the disjunctive cuts are able to reduce the gap between lower bound and upper bound more than state-of-the-art problem speci...
2015-01-01
Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). This paper first proposes a new time-discretized multi-commodity network flow model for the VRPPDTW based on the integration of vehicles carrying states within space-time transportation networks, so as to allow a joint optimization of passenger-to-vehicle assignment and turn-by-turn routing in congested tr...
Cain, Bruce L.
1990-01-01
The problems of weld quality control and weld process dependability continue to be relevant issues in modern metal welding technology. These become especially important for NASA missions which may require the assembly or repair of larger orbiting platforms using automatic welding techniques. To extend present welding technologies for such applications, NASA/MSFC's Materials and Processes Lab is developing physical models of the arc welding process with the goal of providing both a basis for improved design of weld control systems, and a better understanding of how arc welding variables influence final weld properties. The physics of the plasma arc discharge is reasonably well established in terms of transport processes occurring in the arc column itself, although recourse to sophisticated numerical treatments is normally required to obtain quantitative results. Unfortunately the rigor of these numerical computations often obscures the physics of the underlying model due to its inherent complexity. In contrast, this work has focused on a relatively simple physical model of the arc discharge to describe the gross features observed in welding arcs. Emphasis was placed of deriving analytic expressions for the voltage along the arc axis as a function of known or measurable arc parameters. The model retains the essential physics for a straight polarity, diffusion dominated free burning arc in argon, with major simplifications of collisionless sheaths and simple energy balances at the electrodes.
Directory of Open Access Journals (Sweden)
Weizhen Rao
2016-01-01
Full Text Available The classical model of vehicle routing problem (VRP generally minimizes either the total vehicle travelling distance or the total number of dispatched vehicles. Due to the increased importance of environmental sustainability, one variant of VRPs that minimizes the total vehicle fuel consumption has gained much attention. The resulting fuel consumption VRP (FCVRP becomes increasingly important yet difficult. We present a mixed integer programming model for the FCVRP, and fuel consumption is measured through the degree of road gradient. Complexity analysis of FCVRP is presented through analogy with the capacitated VRP. To tackle the FCVRP’s computational intractability, we propose an efficient two-objective hybrid local search algorithm (TOHLS. TOHLS is based on a hybrid local search algorithm (HLS that is also used to solve FCVRP. Based on the Golden CVRP benchmarks, 60 FCVRP instances are generated and tested. Finally, the computational results show that the proposed TOHLS significantly outperforms the HLS.
Directory of Open Access Journals (Sweden)
Ary Arvianto
2014-01-01
Full Text Available In this paper we developed a VRP model for multiple routes, multiple time windows for multiple products and heterogeneous vehicles. The solution were constructed using a heuristic approach, i.e, a sequential insertion algorithm. Additionally, this model is applied to solve fuel distributions for eight customers in East Nusa Tenggara. It needs two tankers with capacity of 4700 kilo liters, so that those distributions can be accomplished with a minimum number of vehicles, total completion time, and range of completion time. The result of this study shows that for a heterogeneous vehicles problem, a vehicle with the largest capacity may not necessarily be the vehicle that provides an optimal solution. Moreover, advance trials should be conducted by providing a limited number of tankers for each tanker capacity, so the description of heterogeneous vehicles becomes more visible. In the future research, the solution will be improved by utilizing relocation techniques.
Directory of Open Access Journals (Sweden)
Michael Polacek
2008-12-01
Full Text Available In this paper we propose two cooperation schemes to compose new parallel variants of the Variable Neighborhood Search (VNS. On the one hand, a coarse-grained cooperation scheme is introduced which is well suited for being enhanced with a solution warehouse to store and manage the so far best found solutions and a self-adapting mechanism for the most important search parameters. This makes an a priori parameter tuning obsolete. On the other hand, a fine-grained scheme was designed to reproduce the successful properties of the sequential VNS. In combination with the use of parallel exploration threads all of the best solutions and 11 out of 20 new best solutions for the Multi Depot Vehicle Routing Problem with Time Windows were found.
Directory of Open Access Journals (Sweden)
Babak Farhang Moghadam
2010-07-01
Full Text Available During the past few years, there have tremendous efforts on improving the cost of logistics using varieties of Vehicle Routing Problem (VRP models. In fact, the recent rise on fuel prices has motivated many to reduce the cost of transportation associated with their business through an improved implementation of VRP systems. We study a specific form of VRP where demand is supposed to be uncertain with unknown distribution. A Particle Swarm Optimization (PSO is proposed to solve the VRP and the results are compared with other existing methods. The proposed approach is also used for real world case study of drug distribution and the preliminary results indicate that the method could reduce the unmet demand significantly.
Directory of Open Access Journals (Sweden)
Reshani P. Liyanage
2016-08-01
Full Text Available This paper is focused on the growing need of integrating environmentally sound choices into supply-chain management. The concept of green economic practices driven by the environmental sustainability challenges posed the concept of green logistics, to evolve in the last few decades.To establish the field further, the purpose of this paper is twofold. First, it offers anextensive systematic review of literature on GL with a critical review of the studies that have been considered in the paper.Second, it offers a conceptual analytical model where the canonical capacitated vehicle routing problem is extended to add the measures of Carbon Dioxide (CO2 emissions. The proposed, multi objective optimization model tackles the conflicting objectives of CO2 emission reduction and cost minimization. The developed generic model integrates the traffic information in providing the user with opportunity to have more realistic solution. The model also enables strategic decision making to improve the GL operations while allowing greatercompetitive advantage
A Branch-and-Cut Algorithm for the Capacitated Open Vehicle Routing Problem
DEFF Research Database (Denmark)
Letchford, Adam N.; Lysgaard, Jens; Eglese, Richard W.
-and-cut. We show that, even though the open CVRP initially looks like a minor variation of the standard CVRP, the integer programming formulation and cutting planes need to be modified in subtle ways. Computational results are given for several standard test instances, which enables us for the first time...... to assess the quality of existing heuristic methods, and to compare the relative difficulty of open and closed versions of the same problem....
Directory of Open Access Journals (Sweden)
Majid Yousefikhoshbakht
2016-07-01
Full Text Available The TSP is considered one of the most well-known combinatorial optimization tasks and researchers have paid so much attention to the TSP for many years. In this problem, a salesman starts to move from an arbitrary place called depot and after visits all of the nodes, finally comes back to the depot. The objective is to minimize the total distance traveled by the salesman. Because this problem is a non-deterministic polynomial (NP-hard problem in nature, a hybrid meta-heuristic algorithm called REACSGA is used for solving the TSP. In REACSGA, a reactive bone route algorithm that uses the ant colony system (ACS for generating initial diversified solutions and the genetic algorithm (GA as an improved procedure are applied. Since the performance of the Metaheuristic algorithms is significantly influenced by their parameters, Taguchi Method is used to set the parameters of the proposed algorithm. The proposed algorithm is tested on several standard instances involving 24 to 318 nodes from the literature. The computational result shows that the results of the proposed algorithm are competitive with other metaheuristic algorithms for solving the TSP in terms of better quality of solution and computational time respectively. In addition, the proposed REACSGA is significantly efficient and finds closely the best known solutions for most of the instances in which thirteen best known solutions are also found.
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Lin Zhou
2016-08-01
Full Text Available With the increasing interest in online shopping, the Last Mile delivery is regarded as one of the most expensive and pollutive—and yet the least efficient—stages of the e-commerce supply chain. To address this challenge, a novel location-routing problem with simultaneous home delivery and customer’s pickup is proposed. This problem aims to build a more effective Last Mile distribution system by providing two kinds of service options when delivering packages to customers. To solve this specific problem, a hybrid evolution search algorithm by combining genetic algorithm (GA and local search (LS is presented. In this approach, a diverse population generation algorithm along with a two-phase solution initialization heuristic is first proposed to give high quality initial population. Then, advantaged solution representation, individual evaluation, crossover and mutation operations are designed to enhance the evolution and search efficiency. Computational experiments based on a large family of instances are conducted, and the results obtained indicate the validity of the proposed model and method.
Visualizing Internet routing changes.
Lad, Mohit; Massey, Dan; Zhang, Lixia
2006-01-01
Today's Internet provides a global data delivery service to millions of end users and routing protocols play a critical role in this service. It is important to be able to identify and diagnose any problems occurring in Internet routing. However, the Internet's sheer size makes this task difficult. One cannot easily extract out the most important or relevant routing information from the large amounts of data collected from multiple routers. To tackle this problem, we have developed Link-Rank, a tool to visualize Internet routing changes at the global scale. Link-Rank weighs links in a topological graph by the number of routes carried over each link and visually captures changes in link weights in the form of a topological graph with adjustable size. Using Link-Rank, network operators can easily observe important routing changes from massive amounts of routing data, discover otherwise unnoticed routing problems, understand the impact of topological events, and infer root causes of observed routing changes.
Institute of Scientific and Technical Information of China (English)
Hua-hui CAI; Guo-jin WANG
2009-01-01
We constructed a single C-Bezier curve with a shape parameter for G2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples.This method has the following three advantages: (1) the pattern is unified; (2) the parameter able to adjust the shape of the transition curve is available; (3) the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.
物流配送车辆路径优化问题的仿真研究%Vehicle Routing Optimization Problem of Logistics Distribution
Institute of Scientific and Technical Information of China (English)
吴洁明
2011-01-01
Logistics distribution vehicle routing optimization problem is studied to reduce logistics transportation cost. Logistics distribution vehicle routing problem is a typical NP problem, traditional optimization methods have the defects of long searching time, difficult to find the optimal path, and high logistics costs. In order to reduce logistics distribution cost and improve vehicle routing optimization efficiency, a logistics distribution vehicle routing optimization algorithm on ant colony algorithm is put forward. Firstly, the logistics distribution vehicle routing problems are analyzed, a corresponding mathematical model established, and then the ant colony algorithm is used to sovle the mathematical model for the vehicle routing problem. The algorithm is verified by experiment with instances, and the experimental results show that the ant colony algorithm can improve optimal effect, the optimal solution of vehicel route is shorter than other algorithms, and the logistics cost is reduced. It is an effective algorithm to sovle the logistics distribution vehicle routing problem.%研究物流配送车辆路径优化问题,由于物流行业要求货物及时配送,又要降低物流运输成本.物流配送车辆路径选择是重点解决的问题,传统优化方法搜索时间长,难以找到最优路径,造成物流配送成本高.为了降低物流配送成本,提高车辆路径优化效率,提出一种蚁群算法的物流配送车辆路径优化算法.首先对物流配送车辆路径问题进行分析,然后建立相应的数学模型,最后采用蚁群算法对车辆路径问题的数学模型进行求解.通过具体实例对算法进行实验,实验结果表明,蚁群算法提高寻优效果,找到的物流配送车辆路径的最优解短于其它算法,降低物流配送成本,并为物流配送车辆路径选择提供了一种有效算法.
Road and Street Centerlines - MO 2010 June MoDOT Roads - Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2012 March MoDOT Roads - Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2012 January MoDOT Roads - Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2016 March MoDOT Roads Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2015 July MoDOT Roads - Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2015 December MoDOT Roads Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2015 September MoDOT Roads - Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2014 December MoDOT Roads - Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2015 March MoDOT Roads - Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2014 February MoDOT Roads - Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2014 September MoDOT Roads - Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Road and Street Centerlines - MO 2014 July MoDOT Roads - Routes (GDB)
NSGIC GIS Inventory (aka Ramona) — Routes represent a single linear feature, such as a city street or highway. Routes are linear features composed of one or more arcs or parts of an arc; for example,...
Development and Application of Vehicle Routing Problem%车辆路径问题的发展及其应用
Institute of Scientific and Technical Information of China (English)
卞晨; 赵建东
2016-01-01
As a hotspot in the field of operational research and combinatorial optimization, vehicle routing problem is closely re-lated to real life.As long as the deepening study of vehicle routing problem, various kinds of new types of heuristic algorithm is applied to solve such problems.The vehicle routing problem with various constraint were investigated, analysis and summary in this paper, and the related domestic and foreign research results were reviewed and refined, on this basis, this paper summarizes the research of vehicle routing problem. Based on the current various standard of classification, this paper discusses and analyz-es the classical vehicle routing problem firstly, and summarized the basic methods and modern heuristic algorithm on this basis.%车辆路径问题作为运筹学和组合优化领域的热点问题，与现实生活息息相关。随着对车辆路径问题的不断深入研究，各类新型的启发式算法被运用到解决这类问题之中。文对具有各类约束条件的车辆路径问题进行了调查、分析和总结，并对国内外相关研究成果进行了提炼，在该基础之上，阐述了车辆路径问题的研究综述。基于当前多样的分类标准，讨论并分析了经典车辆路径问题，并在此基础之上综述了求解各类型车辆路径问题的基本方法和现代启发式算法。
Directory of Open Access Journals (Sweden)
Yanhui Li
2013-01-01
Full Text Available Facility location, inventory control, and vehicle routes scheduling are critical and highly related problems in the design of logistics system for e-business. Meanwhile, the return ratio in Internet sales was significantly higher than in the traditional business. Many of returned merchandise have no quality defects, which can reenter sales channels just after a simple repackaging process. Focusing on the existing problem in e-commerce logistics system, we formulate a location-inventory-routing problem model with no quality defects returns. To solve this NP-hard problem, an effective hybrid genetic simulated annealing algorithm (HGSAA is proposed. Results of numerical examples show that HGSAA outperforms GA on computing time, optimal solution, and computing stability. The proposed model is very useful to help managers make the right decisions under e-supply chain environment.
Li, Yanhui; Guo, Hao; Wang, Lin; Fu, Jing
2013-01-01
Facility location, inventory control, and vehicle routes scheduling are critical and highly related problems in the design of logistics system for e-business. Meanwhile, the return ratio in Internet sales was significantly higher than in the traditional business. Many of returned merchandise have no quality defects, which can reenter sales channels just after a simple repackaging process. Focusing on the existing problem in e-commerce logistics system, we formulate a location-inventory-routing problem model with no quality defects returns. To solve this NP-hard problem, an effective hybrid genetic simulated annealing algorithm (HGSAA) is proposed. Results of numerical examples show that HGSAA outperforms GA on computing time, optimal solution, and computing stability. The proposed model is very useful to help managers make the right decisions under e-supply chain environment.
Hazardous materials transportation: a risk-analysis-based routing methodology.
Leonelli, P; Bonvicini, S; Spadoni, G
2000-01-07
This paper introduces a new methodology based on risk analysis for the selection of the best route for the transport of a hazardous substance. In order to perform this optimisation, the network is considered as a graph composed by nodes and arcs; each arc is assigned a cost per unit vehicle travelling on it and a vehicle capacity. After short discussion about risk measures suitable for linear risk sources, the arc capacities are introduced by comparison between the societal and individual risk measures of each arc with hazardous materials transportation risk criteria; then arc costs are defined in order to take into account both transportation out-of-pocket expenses and risk-related costs. The optimisation problem can thus be formulated as a 'minimum cost flow problem', which consists of determining for a specific hazardous substance the cheapest flow distribution, honouring the arc capacities, from the origin nodes to the destination nodes. The main features of the optimisation procedure, implemented on the computer code OPTIPATH, are presented. Test results about shipments of ammonia are discussed and finally further research developments are proposed.
Kämper, Jan-Hinrich; Nöllenburg, Martin
2011-01-01
We present a new circular-arc cartogram model in which countries are drawn with circular arcs instead of straight-line segments. Given a geographic map and values associated with each country in the map, the cartogram is a new map in which the areas of the countries represent the corresponding values. In the circular-arc cartogram model straight-line segments can be replaced with circular arcs in order to achieve the desired areas, while the corners of the polygons defining each country remain fixed. The countries in circular-arc cartograms have the aesthetically pleasing appearance of clouds or snowflakes, depending on whether their edges are bent outwards or inwards. This makes is easy to determine whether a country has grown or shrunk, just by its overall shape. We show that determining whether a given map and area-values can be realized with a circular-arc cartogram is an NP-hard problem. Next we describe a heuristic method for constructing circular-arc cartograms, which uses a max-flow computation on the...
Arc-preserving subsequences of arc-annotated sequences
Popov, Vladimir Yu
2011-01-01
Arc-annotated sequences are useful in representing the structural information of RNA and protein sequences. The longest arc-preserving common subsequence problem has been introduced as a framework for studying the similarity of arc-annotated sequences. In this paper, we consider arc-annotated sequences with various arc structures. We consider the longest arc preserving common subsequence problem. In particular, we show that the decision version of the 1-{\\sc fragment LAPCS(crossing,chain)} and the decision version of the 0-{\\sc diagonal LAPCS(crossing,chain)} are {\\bf NP}-complete for some fixed alphabet $\\Sigma$ such that $|\\Sigma| = 2$. Also we show that if $|\\Sigma| = 1$, then the decision version of the 1-{\\sc fragment LAPCS(unlimited, plain)} and the decision version of the 0-{\\sc diagonal LAPCS(unlimited, plain)} are {\\bf NP}-complete.
Sun, Yan; Lang, Maoxiang; Wang, Danzhu
2016-01-01
The transportation of hazardous materials is always accompanied by considerable risk that will impact public and environment security. As an efficient and reliable transportation organization, a multimodal service should participate in the transportation of hazardous materials. In this study, we focus on transporting hazardous materials through the multimodal service network and explore the hazardous materials multimodal routing problem from the operational level of network planning. To formulate this problem more practicably, minimizing the total generalized costs of transporting the hazardous materials and the social risk along the planned routes are set as the optimization objectives. Meanwhile, the following formulation characteristics will be comprehensively modelled: (1) specific customer demands; (2) multiple hazardous material flows; (3) capacitated schedule-based rail service and uncapacitated time-flexible road service; and (4) environmental risk constraint. A bi-objective mixed integer nonlinear programming model is first built to formulate the routing problem that combines the formulation characteristics above. Then linear reformations are developed to linearize and improve the initial model so that it can be effectively solved by exact solution algorithms on standard mathematical programming software. By utilizing the normalized weighted sum method, we can generate the Pareto solutions to the bi-objective optimization problem for a specific case. Finally, a large-scale empirical case study from the Beijing–Tianjin–Hebei Region in China is presented to demonstrate the feasibility of the proposed methods in dealing with the practical problem. Various scenarios are also discussed in the case study. PMID:27483294
Sun, Yan; Lang, Maoxiang; Wang, Danzhu
2016-07-28
The transportation of hazardous materials is always accompanied by considerable risk that will impact public and environment security. As an efficient and reliable transportation organization, a multimodal service should participate in the transportation of hazardous materials. In this study, we focus on transporting hazardous materials through the multimodal service network and explore the hazardous materials multimodal routing problem from the operational level of network planning. To formulate this problem more practicably, minimizing the total generalized costs of transporting the hazardous materials and the social risk along the planned routes are set as the optimization objectives. Meanwhile, the following formulation characteristics will be comprehensively modelled: (1) specific customer demands; (2) multiple hazardous material flows; (3) capacitated schedule-based rail service and uncapacitated time-flexible road service; and (4) environmental risk constraint. A bi-objective mixed integer nonlinear programming model is first built to formulate the routing problem that combines the formulation characteristics above. Then linear reformations are developed to linearize and improve the initial model so that it can be effectively solved by exact solution algorithms on standard mathematical programming software. By utilizing the normalized weighted sum method, we can generate the Pareto solutions to the bi-objective optimization problem for a specific case. Finally, a large-scale empirical case study from the Beijing-Tianjin-Hebei Region in China is presented to demonstrate the feasibility of the proposed methods in dealing with the practical problem. Various scenarios are also discussed in the case study.
时相关车辆路径规划问题的改进A*算法%Improved A* Algorithm for Time - Dependent Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
张翼; 唐国金; 陈磊
2012-01-01
Time -dependent vehicle routing problem (TDVRP) is concerned with vehicle routing optimization in road networks with fluctuant link travel time. Firstly, Time - dependent functions about routing time cost and routing threat cost are introduced. Secondly, a time - dependent heuristic function including routing distance cost, routing time cost and routing threat cost is constructed, and an improved A * algorithm is promoted for TDVRP, where the farther information is included in the algorithm to improve search efficiency. Finally, a road network of vehicle support in troop transportation involving 100 nodes and 190 roads is constructed, and the algorithm is validated by using simulations.%时相关车辆路径问题是研究时变路网环境下的车辆路径优化问题.首先,分别采用阶跃函数和分段连续函数描述不同路径上的跨时段行驶速度和威胁度,将路径时间指标和路径威胁指标表示成时相关函数；其次,为提高搜索效率,对传统A*算法进行改进,在启发函数中增加了最短路径中当前结点的父结点信息,构造了包含里程指标、时间指标和威胁指标的时相关启发函数；最后,构造了包含100个结点、190条路径的车辆机动保障路网模型,通过仿真验证了该算法的有效性.
The hardness of routing two pairs on one face
Naves, Guyslain
2009-01-01
We prove the NP-completeness of the integer multiflow problem in planar graphs, with the following restrictions: there are only two demand edges, both lying on the infinite face of the routing graph. This was one of the open challenges concerning disjoint paths, explicitly asked by M\\"uller. It also strengthens Schw\\"arzler's recent proof of one of the open problems of Schrijver's book, about the complexity of the edge-disjoint paths problem with terminals on the outer boundary of a planar graph. We also give a directed acyclic reduction. This proves that the arc-disjoint paths problem is NP-complete in directed acyclic graphs, even with only two demand arcs.
Special Kind of Vehicle Routing Problem%一类特殊车辆路径问题(VRP)
Institute of Scientific and Technical Information of China (English)
李嘉; 王梦光; 唐立新; 宋建海
2001-01-01
A special kind of vehicle routing problem was described and its characteristics were analyzed. By defining the “fleet pattern”, a solving framework was presented, and a hybrid GA composed of GA and TS was presented. For solving the heterogeneous fleet VRP, the hybrid algorithm integrates the advantage of GA (good at global searching) and TS (good at mountain climbing). The fleet-task separately coding and decoding rules fully consider the characters of heterogeneous fleet VRP. The validity of the framework, model and algorithm were proved by some instances.%描述了一类特殊的车辆路径问题(VRP)－混合车队车辆路径问题．在分析问题特性的基础上,通过引入“车队模式”定义,提出了求解框架,设计了基于遗传算法和禁忌搜索启发式的混合算法．针对其中的混合车队车辆路径问题,所设计混合算法,利用了GA搜索全局性好,TS局部爬山能力强的特点．提出的车队、任务分段组合编码和解码规则充分考虑了混合车队车辆路径问题的特点．实例计算结果表明了框架、模型和算法的有效性．
Tabu Search Technique for Solving the Routing Problem%禁忌搜索算法用于解决网络路由问题
Institute of Scientific and Technical Information of China (English)
王东平; 李绍荣
2003-01-01
Routing problem is a very import problem in the network design. However, with the increasing of the number of vertices, the convergence speed of the conventional method (such as the Dijkstra algorithm) becomes slow. In some services, the accurate shortest path isn't requested. This paper presents a new algorithm for solving this problem based on the tabu search technique. The tabu search algorithm can get the satisfied path with the changing of the iteration times, the tabu period and neighborhood size. Simulation results demonstrate that the proposed method is very efficient for computing the shorted path, especially when the scale of the network is large.
Research on Chaos Particle Swarm Optimization Algorithm for Vehicle Routing Problem%车辆路径问题的混沌粒子群算法研究
Institute of Scientific and Technical Information of China (English)
李毅; 陆百川; 刘春旭
2012-01-01
According to characters of the vehicle routing problem, a novel chaos particle swarm optimization ( CPSO) algorithm was proposed to solve the basic type of single depot and non-full load. After the chaos was introduced to the particle swarm optimization(PSO) , the random, regularity and ergodicity were used to initialize particles in order to cover the solution space of the vehicle routing problem in large range, enhance the ability for optimal route searching, and prevent the su-boptimal solution of the PSO in the way of exerting chaos disturbance at the place of suboptimal solution to help algorithm to abandon the current searching route. Illustration results showed the CPSO had the strong ability to search the global optimal in the vehicle routing problem.%针对车辆路径问题中单仓库非满载这一基本类型的具体特性,设计了一种混沌粒子群算法；利用混沌系统的随机性、规律性和遍历性初始化粒子,大范围覆盖车辆路径问题的解空间,加强算法最优路径的搜索能力；通过在求解过程中的次优路径处施加混沌扰动,使算法放弃当前求解的路径,避免结果为次优解.并通过试验验证了该算法在车辆路径问题中具有很强的寻优能力.
Ghezavati, V. R.; Beigi, M.
2016-06-01
During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics (RL) network. The success of a logistics system may depend on the decisions of the facilities locations and vehicle routings. The location-routing problem (LRP) simultaneously locates the facilities and designs the travel routes for vehicles among established facilities and existing demand points. In this paper, the location-routing problem with time window (LRPTW) and homogeneous fleet type and designing a multi-echelon, and capacitated reverse logistics network, are considered which may arise in many real-life situations in logistics management. Our proposed RL network consists of hybrid collection/inspection centers, recovery centers and disposal centers. Here, we present a new bi-objective mathematical programming (BOMP) for LRPTW in reverse logistic. Since this type of problem is NP-hard, the non-dominated sorting genetic algorithm II (NSGA-II) is proposed to obtain the Pareto frontier for the given problem. Several numerical examples are presented to illustrate the effectiveness of the proposed model and algorithm. Also, the present work is an effort to effectively implement the ɛ-constraint method in GAMS software for producing the Pareto-optimal solutions in a BOMP. The results of the proposed algorithm have been compared with the ɛ-constraint method. The computational results show that the ɛ-constraint method is able to solve small-size instances to optimality within reasonable computing times, and for medium-to-large-sized problems, the proposed NSGA-II works better than the ɛ-constraint.
Multiobjective Route Planning Model and Algorithm for Emergency Management
Directory of Open Access Journals (Sweden)
Wen-mei Gai
2015-01-01
Full Text Available In order to model route planning problem for emergency logistics management taking both route timeliness and safety into account, a multiobjective mathematical model is proposed based on the theories of bounded rationality. The route safety is modeled as the product of safety through arcs included in the path. For solving this model, we convert the multiobjective optimization problem into its equivalent deterministic form. We take uncertainty of the weight coefficient for each objective function in actual multiobjective optimization into account. Finally, we develop an easy-to-implement heuristic in order to gain an efficient and feasible solution and its corresponding appropriate vector of weight coefficients quickly. Simulation results show the effectiveness and feasibility of the models and algorithms presented in this paper.
Directory of Open Access Journals (Sweden)
Bailing Liu
2015-01-01
Full Text Available Facility location, inventory control, and vehicle routes scheduling are three key issues to be settled in the design of logistics system for e-commerce. Due to the online shopping features of e-commerce, customer returns are becoming much more than traditional commerce. This paper studies a three-phase supply chain distribution system consisting of one supplier, a set of retailers, and a single type of product with continuous review (Q, r inventory policy. We formulate a stochastic location-inventory-routing problem (LIRP model with no quality defects returns. To solve the NP-hand problem, a pseudo-parallel genetic algorithm integrating simulated annealing (PPGASA is proposed. The computational results show that PPGASA outperforms GA on optimal solution, computing time, and computing stability.
新型遗传算法求解车辆路径问题研究%New genetic algorithm for vehicle routing problem
Institute of Scientific and Technical Information of China (English)
张瑞锋; 汪同三
2012-01-01
We stated a universal mathematical model of vehicle routing problem with time windows. On the basis of analyzing the weakness of genetic algorithm in local search, a new stochastic approach called the genetic simulated annealing algorithm was proposed to solve vehicle routing problem with time windows.and made some experimental computations. The computational results demonstrated that the genetic simulated annealing a80lgorithm could overcome the weakness of genetic algorithm and local search algorithm, and the high quality solutions of the vehicle routing problem with time windows was obtained.%建立有时间窗车辆路径问题的数学模型,针对遗传算法在局部搜索能力方面的不足,提出将模拟退火算法与遗传算法相结合,从而构造有时问窗车辆路径问题的混合遗传算法,并进行实验计算.结果表明,用混合遗传算法求解该优化问题,可以在一定程度上克服遗传算法在局部搜索能力方面的不足和模拟退火算法在全局搜索能力方面的不足,从而得到质量较高的解.
Directory of Open Access Journals (Sweden)
Marco Antonio Cruz-Chávez
2016-01-01
Full Text Available A stochastic algorithm for obtaining feasible initial populations to the Vehicle Routing Problem with Time Windows is presented. The theoretical formulation for the Vehicle Routing Problem with Time Windows is explained. The proposed method is primarily divided into a clustering algorithm and a two-phase algorithm. The first step is the application of a modified k-means clustering algorithm which is proposed in this paper. The two-phase algorithm evaluates a partial solution to transform it into a feasible individual. The two-phase algorithm consists of a hybridization of four kinds of insertions which interact randomly to obtain feasible individuals. It has been proven that different kinds of insertions impact the diversity among individuals in initial populations, which is crucial for population-based algorithm behavior. A modification to the Hamming distance method is applied to the populations generated for the Vehicle Routing Problem with Time Windows to evaluate their diversity. Experimental tests were performed based on the Solomon benchmarking. Experimental results show that the proposed method facilitates generation of highly diverse populations, which vary according to the type and distribution of the instances.
Location and Routing of the Defense Courier Service Aerial Network
1991-03-01
The Vehicle Routing Problem ................ 8 Vehicle Routing Problem Modifications ...... .0 Multiple Depot Problems...several specific formulations are applicable to the DCS aerial network. Those addressed in this review include: 1) the Vehicle Routing Problem (VRP); 2...methodologies show great promise for adaptation to the DCS network. The Vehicle Routing Problem The Travelling Salesman Problem seeks the shortest route which
Research on Vehicle Routing Problem Based on Improved Genetic Algorithm%改进遗传算法下的车辆路径问题研究
Institute of Scientific and Technical Information of China (English)
陈果
2016-01-01
The vehicle routing problem is a typical combinatorial optimization problem.With the continuous improvement of logistics requirements, the basic genetic algorithm has been difficult to meet the needs of customers.The basic genetic algorithm in solving this kind of problem,often appear premature convergence, and delivery time of the vehicle has the defects of limited,can not to solve the optimization of this kind of problem,so this paper uses improved genetic algorithm on vehicle routing problem were studied,and explore the improved genetic algorithm in solving the vehicle routing problem is effective.%车辆路径问题是一种典型的组合优化类问题，随着客户对物流要求的不断提升，基本的遗传算法已经很难满足客户的需求。基本的遗传算法在求解这类问题的时候，经常会出现早熟收敛，以及对车辆的运送时间存在限制等方面的缺陷，不能够对这类问题进行最优化求解，所以本文采用改进的遗传算法就车辆路径问题进行研究，并探究改进下的遗传算法在求解车辆路径问题时的有效性。
Directory of Open Access Journals (Sweden)
Shuai Deng
2016-01-01
Full Text Available This paper presents a closed-loop location-inventory-routing problem model considering both quality defect returns and nondefect returns in e-commerce supply chain system. The objective is to minimize the total cost produced in both forward and reverse logistics networks. We propose a combined optimization algorithm named hybrid ant colony optimization algorithm (HACO to address this model that is an NP-hard problem. Our experimental results show that the proposed HACO is considerably efficient and effective in solving this model.
Study on vehicle routing problem based on heuristic ant colony optimization%基于启发式蚁群算法的VRP问题研究
Institute of Scientific and Technical Information of China (English)
刘晓勇; 付辉
2011-01-01
When Ant Colony Optimization algorithm (ACO) is applied to vehicle routing problem, it always spends much time and has worse solutions.This paper uses ACO based on a heuristic method for vehicle routing problem.This heuristic method combines distance matrix with saving route matrix to assign initial pheromone matrix.Three benchmark datasets are chosen to verify performance of the new algorithm. Experiments show that ant colony optimization based on heuristic information has better solution and spends less time.%针对蚁群算法求解VRP问题时收敛速度慢,求解质量不高的缺点,把城市和仓库间的距离矩阵和路径节约矩阵信息融入到初始信息素矩阵中作为启发式信息引入到蚁群算法中用于求解有容量限制的车辆路径规划问题(CVRP),在三个基准数据集上的实验研究表明,基于启发式信息的蚁群算法与基本蚁群算法相比能够以较快的速度收敛到较好的解.
动态车辆路径问题的分区灵活分批TSP策略%Flexible nTSP strategy of dynamic vehicle routing problems
Institute of Scientific and Technical Information of China (English)
熊浩
2013-01-01
Dynamic vehicle routing problem(DVRP) is emerging topical issue for the vehicle routing problem, but its real-time optimization still needs to be improved. Therefore, the mod nTSP strategy is proposed based on the flexible nTSP strategy. And the competitive analysis of the new strategy shows the reason of the improvement. Finally, the simulation results show that the new strategy can reduce the average distance between the adjacent customers on the routing of vehicle while keeping the other system time constant, and the average customer system time can be reduced.%动态车辆路径问题是当前车辆路径问题的新兴热门问题，但其实时优化策略研究仍然有较大的改进空间。鉴于此，在一般分区分批旅行商问题(TSP)策略的基础上，提出了分区灵活分批TSP策略，并对策略有效性进行了分析。最后进行了实例仿真验证，结果表明，所提出策略能够减少车辆服务顾客的平均行驶距离，从而减少顾客的平均系统时间。
车辆路径规划的数学模型及算法综述%REVIEWS ON MATHEMATICAL MODELS AND ALGORITHMS FOR VEHICLE ROUTING PROBLEM
Institute of Scientific and Technical Information of China (English)
高晓菲
2015-01-01
Vehicle routing problem (VRP)is a hot spot.In the process of transportation,the reasonablevehicle route can save manpower,reduce transportation cost on the basis of the meet the requirements to a greatdegree.Models and algorithms play an important role in the research of VRP.The present models and algorithms ofVRP still have some shortcomings.In order to solve the problem,the mathematical models and algorithms of VRPare discussed in this paper.%车辆路径规划问题（Vehicle Routing Problem，VRP）是一项研究热点。在运输过程中，对车辆进行合理的路径规划可以在满足运输要求的基础上最大程度地节约人力物力，降低运输成本。在对车辆路径规划的研究过程中，模型和算法起着关键性作用。目前已有的模型和算法还存在一些不足。为此，对车辆路径规划问题的数学模型和算法进行了探讨。
Fuzzy vehicle routing problems based on credibility measure%基于可信性测度的模糊车辆路径问题
Institute of Scientific and Technical Information of China (English)
张力; 杨瑞娜; 汪钱进; 于雪梅
2012-01-01
车辆路径问题（VRP）主要用来寻找有效路径。车辆的起始点都是位于交通中心的仓库，通过车队运输来满足客户对商品的需求。文中介绍不确定条件下的车辆路径问题，即客户的服务时间窗是模糊的。设计一个基于可信性测度的模糊车辆路径模型，并通过模糊模拟和遗传算法的混合智能算法进行求解。最后，结合一个实例说明该模型的应用性和可行性。%Vehicle routing problems aim at finding efficient routes. The starting point of any vehicle lies usually in the depot of traffic centre, for which the customers can be satisfied with the needed commodity transported in vehicle. Analysis is made on the vehicle routing problem in which the travel time window are assumed to be fuzzy variables. A fuzzy optimization model is designed, and fuzzy simulation and genetic algorithm are integrated to obtain a hybrid intelligent algorithm. Finally, an example is given to show the effectiveness of the algorithm.
A Two-Stage Approach to the Orienteering Problem with Stochastic Weights
Evers, L.; Glorie, K.; Ster, S. van der; Barros, A.I.; Monsuur, H.
2014-01-01
The Orienteering Problem (OP) is a routing problem which has many interesting applications in logistics, tourism and defense. The aim of the OP is to find a maximum profit path or tour, which is feasible with respect to a capacity constraint on the total weight of the selected arcs. In this paper we
Directory of Open Access Journals (Sweden)
Wei Sun
2013-01-01
problem in Sobolev spaces is developed firstly. The solution is represented in the form of the combined angular potential and single-layer potential. The final integral equations do not contain hypersingular integrals. Uniqueness and existence of the solution to the equations are proved. The weakly singular and Cauchy singular integral arising in these equations can be computed directly by truncated series of Chebyshev polynomials with their weighting function without approximation. The numerical simulation showing the high accuracy of the scheme is presented.
混合算法在车辆路径优化问题中的应用%Application of Hybrid Algorithm in Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
陈印; 徐红梅
2012-01-01
研究车辆路径优化问题,物流配送不仅要求配送及时,而且要求运输成本低,且路径最优.车辆路径优化是解决物流配送效率的关键,传统优化方法寻优效率低,耗时长,难以得到车辆路径最优解,导致物流配送成本过高.为了提高车辆路径寻优效率,降低物流配送成本,提出一种混合算法的车辆路径优化方法.首先建立车辆路径优化数学模型,然后用遗传算法快速找到问题可行解,再将可行解转换成蚁群算法的初始信息素,最后采用蚁群算法从可行解中找到最优车辆路径.仿真结果表明,混合方法提高车辆路径寻优效率,有效地降低物流配送成本.%Research vehicle routing problem. Logistics distribution requires the timely delivery and low transporta-tion cost, and the vehicle routing is the key to solve the logistics distribution problem. The traditional optimization method has the defects of low searching efficiency, time-consuming and high cost. To improve the vehicle route opti-mization efficiency and reduce logistics cost, this paper proposed a hybrid algorithm for vehicle routing optimization method. Firstly, vehicle routing mathematical model was established, and then genetic algorithm was used to find a feasible solution quickly. Then the solution was converted into the initial pheromone of ant colony algorithm. Finally, ant colony algorithm was used to find the optimal solution from the feasible path. The simulation results show that, compared with other optimization methods, the proposed method can improve vehicle routing optimization and reduce the cost of logistics distribution effectively.
A New Vehicle Routing Problem and It's Two Stage Algorithm%一类新的车辆路径问题及其两阶段算法
Institute of Scientific and Technical Information of China (English)
王科峰; 叶春明; 唐国春
2010-01-01
本文结合汽车零部件第三方物流业的实际背景,提出了一类新的车辆路径问题,它是一种带时间窗约束的分车运输同时收发车辆路径问题(简称SVRPSPDTW).接着给出了问题的模型,并提出求解问题的启发式算法;两阶段算法.最后在改进的Solomn的算例的基础上,进行了数值试验.%In this paper,a new vehicle routing problem,split and simultaneous pickup and delivery vehicle routing problem with time windows constraints(SVRPSPDTW),was provided for the first time under the actual background in the third party logistics of auto parts.Then the mathematic model of this problem and the heuristic algorithm to solve the problem,i.e.two stage algorithm,was given.In the end,the computational experiment was done based on the modified Solomn's benchmark.
Suthikarnnarunai, N.; Olinick, E.
2009-01-01
We present a case study on the application of techniques for solving the Vehicle Routing Problem (VRP) to improve the transportation service provided by the University of The Thai Chamber of Commerce to its staff. The problem is modeled as VRP with time windows, split deliveries, and a mixed fleet. An exact algorithm and a heuristic solution procedure are developed to solve the problem and implemented in the AMPL modeling language and CPLEX Integer Programming solver. Empirical results indicate that the heuristic can find relatively good solutions in a small fraction of the time required by the exact method. We also perform sensitivity analysis and find that a savings in outsourcing cost can be achieved with a small increase in vehicle capacity.
Application of Improved Genetic Algorithm in Vehicle Routing Problem%改进遗传算法在车辆路径问题中的应用
Institute of Scientific and Technical Information of China (English)
张华庆; 张喜
2012-01-01
The mathematical model of Vehicle Routing Problem is developed in this paper. To improve the search rate of genetic algorithm and avoid the premature phenomenon of population, an improved genetic algorithm, in which the fitness function is defined with dynamic linear method and its cross-operator is improved to adopt a large variation of operation for Vehicle Routing Problem, is designed, and the detailed computation steps of the genetic algorithm are given. Finally, the genetic algorithm is applied to a numerical example. The results indicate that the genetic algorithm is better than the genetic algorithm designed in the existing reference literature over the computational performance. Furthermore, the improved strategies of the genetic algorithm are not only simple but also effective in solving the Vehicle Routing Problem.%建立了车辆路径问题的数学模型.为了提高遗传算法的搜索速率,避免种群出现“早熟”现象,对适应度函数采用动态线性标定方式,改进交叉算子,采用大变异操作,设计出了求解车辆路径问题的改进遗传算法并给出了具体的计算步骤.应用该遗传算法进行了实例计算,取得了比较满意的结果.计算结果表明,该遗传算法在计算性能上优于参考文献中设计的遗传算法.同时也表明,对遗传算法的改进策略不仅简单而且对求解VRP问题是有效的.
Optimal Design of Incident Vehicle Routing Problem for Dangerous Goods%危险品关联运输调度问题的优化设计
Institute of Scientific and Technical Information of China (English)
向周; 蔡延光; 汤雅连
2014-01-01
Aiming at IVRPHTW (Incident Vehicle Routing Problem with Hard Time Windows ) and VRP(Vehicle Routing Problem) of dangerous goods in practical application , this paper introduces and modifies the fundamental principle of CGA ( Chaos Genetic Algorithm ) adjusting adaptively crossover probability and mutation probability , bringing simulated annealing mechanism in the algorithm, and applying cluster analysis and the modified algorithm to solve IVRPHTW , as well as compared with Genetic Algo-rithm ( GA) .The results show that CGA is feasible to solve IVRP of dangerous goods , and better than GA during the optimization process.%针对带硬时间窗的关联运输调度问题（ Incident Vehicle Routing Problem with Hard Time Windows ， IVRPHTW），联系实际应用中危险品的车辆路径问题，介绍了混沌遗传算法的基本原理，并对其进行改进，自适应地调整交叉概率和变异概率，引进了模拟退火机制，并用改进的算法来对IVRPHTW求解，然后与遗传算法求解此模型的结果相比较。实例证明该算法求解危险品的关联运输调度问题是可行的，且优于传统的遗传算法。
基于真实路网的车辆路径问题研究%Solution to the Real Road Network Based Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
孙国华
2011-01-01
The paper proposea a modeling method for vehicle routing problem based on real road network which processes the shortest path problem and vehicle routing problem simultaneously.In a subsequent simulation experiment, the model proposed above is compared to the traditional one where the two yield the same optimal solution, yet the one of the paper is superior in computation time.%车辆路径问题(VRP)是广泛应用于物流配送的组合优化问题.在实际应用中,传统的处理方法是先利用路网信息求出任意两点间最短路,生成完全连通图,然后进行VRP的优化求解,这样会浪费时间和空间,降低求解效率.因此,提出了一种基于真实路网的VRP建模方法,把任意两点间最短路的求解与VRP联合起来,通过仿真实验与传统的处理方法进行了比较,两种方法得到了相同的最优解,但基于真实路网的VRP建模方法在计算时间方面占优.
Research on Vehicle Routing Problem Based on Improved Genetic Algorithm%基于改进遗传算法的车辆路径问题研究
Institute of Scientific and Technical Information of China (English)
朱志勇; 刁洪祥
2011-01-01
车辆路径问题是一个典型的组合优化类问题,而传统的算法无法满足顾客需求对物流运输提出的要求.遗传算法是求解此类问题的方法之一,针对遗传算法容易出现早熟收敛,以及车辆运送的时间限制,该文采用改进的遗传算法对有时间窗的车辆路径问题进行分析,实验验证了算法的有效性.%Vehicle routing problem is a typical combinational optimization problem, and the traditional algorithms can not meet customer needs for logistics transport. Genetic algorithm is one of the methods used to solve -VRP,because of premature convergence of genetic algorithm and the time constraints of vehicles transporting, this paper analysis vehicle routing problem with Time Window using an improved genetic algorithm. Experiment data prove the effectiveness of the algorithm.
Nowakowski, Piotr
2017-02-01
Waste electrical and electronic equipment (WEEE), also known as e-waste, is one of the most important waste streams with high recycling potential. Materials used in these products are valuable, but some of them are hazardous. The urban mining approach attempts to recycle as many materials as possible, so efficiency in collection is vital. There are two main methods used to collect WEEE: stationary and mobile, each with different variants. The responsibility of WEEE organizations and waste collection companies is to assure all resources required for these activities - bins, containers, collection vehicles and staff - are available, taking into account cost minimization. Therefore, it is necessary to correctly determine the capacity of containers and number of collection vehicles for an area where WEEE need to be collected. There are two main problems encountered in collection, storage and transportation of WEEE: container loading problems and vehicle routing problems. In this study, an adaptation of these two models for packing and collecting WEEE is proposed, along with a practical implementation plan designed to be useful for collection companies' guidelines for container loading and route optimization. The solutions are presented in the case studies of real-world conditions for WEEE collection companies in Poland.
可变线路式公交车辆调度优化模型%An Optimal Model for Flex-route Transit Scheduling Problem
Institute of Scientific and Technical Information of China (English)
林叶倩; 李文权; 邱丰; 丁钰玲
2012-01-01
Flex-route transit scheduling model is described as a mixed integer programming formulation. An optimal model for vehicle routing problem is established, with the minimization of passenger travel costs and vehicle operating costs as the objective function. In the light of the model characteristics, nearest insertion method is used to construct the initial solution and genetic algorithm is designed to solve the model. Finally, the model validation and performance comparisons between flex-route bus service and fixed-route bus service under different demand level are conducted by a simulation analysis. The results show that this scheduling model is available for flex-route transit, and that this new bus service mode has more advantages than that of fixed-route bus within residential areas with lower demand.%将可变线路式公交调度模型描述为混合整数规划问题,考虑公交公司运营成本和乘客出行费用,以系统成本最低为目标建立可变线路式公交调度模型.针对该调度模型的特点采用最近插入法构建初始解,并设计了相应的遗传算法对模型进行求解.通过数学仿真实验对该模型进行有效性验证,对比分析了可变线路式公交与常规公交在不同出行需求量下的性能指标.结果表明,该调度模型适用于可变线路式公交系统,随着出行需求的降低,可变线路式公交相比于常规公交的优势愈加明显.
基于类电磁机制算法的关联运输调度问题%Electromagnetism-like Mechanism Algorithm for Related Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
郭帅; 蔡延光; 汤雅连
2013-01-01
介绍了基本的类电磁机制算法的原理并对其进行改进,并用改进的算法来对单车场单车型的关联物流运输调度问题(Incident Vehicle Routing Problem,IVRP)求解,然后与遗传算法求解此模型的结果相比较.实例证明该算法求解关联运输调度问题是可行的,且优于传统的遗传算法.
物流配送线路优化的改进遗传算法研究%A Study of Modified Genetic Algorithm for Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
高鹏; 徐瑞华
2006-01-01
物流配送线路优化问题,即车辆路线问题(VRP,Vehicle Routing Problem)是组合优化领域中的著名NP(Nonlinear Programming)难题. 本文以VRP为基础,建立该问题的数学模型,设计了改进的遗传算法,通过大量计算机计算分析验证,此改进算法对VRP有良好的近似解和较高的收敛速度.
Modeling Routing Overhead Generated by Wireless Proactive Routing Protocols
Javaid, Nadeem; Javaid, Akmal; Malik, Shahzad A
2011-01-01
In this paper, we present a detailed framework consisting of modeling of routing overhead generated by three widely used proactive routing protocols; Destination-Sequenced Distance Vector (DSDV), Fish-eye State Routing (FSR) and Optimized Link State Routing (OLSR). The questions like, how these protocols differ from each other on the basis of implementing different routing strategies, how neighbor estimation errors affect broadcast of route requests, how reduction of broadcast overhead achieves bandwidth, how to cope with the problem of mobility and density, etc, are attempted to respond. In all of the above mentioned situations, routing overhead and delay generated by the chosen protocols can exactly be calculated from our modeled equations. Finally, we analyze the performance of selected routing protocols using our proposed framework in NS-2 by considering different performance parameters; Route REQuest (RREQ) packet generation, End-to-End Delay (E2ED) and Normalized Routing Load (NRL) with respect to varyi...
Improved Ant Colony Algorithm for Period Vehicle Routing Problem%改进蚁群算法优化周期性车辆路径问题
Institute of Scientific and Technical Information of China (English)
蔡婉君; 王晨宇; 于滨; 杨忠振; 姚宝珍
2014-01-01
周期性车辆路径问题（PVRP）是标准车辆路径问题（VRP）的扩展，PVRP将配送期由单一配送期延伸到T（ T＞1）期，因此，PVRP需要优化每个配送期的顾客组合和配送路径。由于PVRP是一个内嵌VRP的问题，其比标准VRP问题更加复杂，难于求解。本文采用蚁群算法对PVRP进行求解，并提出采用两种改进措施---多维信息素的运用和基于扫描法的局部优化方法来提高算法的性能。最后，通过9个经典PVRP算例对该算法进行了数据实验，结果表明本文提出的改进蚁群算法求解PVRP问题是可行有效的，同时也表明两种改进措施可以显著提高算法的性能。%Period Vehicle Routing Problem(PVRP)is a generalized classic vehicle routing problem (VRP), in which the planning period is extended to a t-day period .Therefore , custom group and route should be optimized every day in PVRP.Embedded in VRP, PVRP is too complicated to be solved .As many route operations are formulated in a certain period, PVRP is very popular in practice.In recent years, distribution centers have paid much attention to the problem of vehicle delivery with the growing fuel cost and fierce supply chain competition . Especially in some situations , vehicles have to serve some fixed customers in a given period , and besides , the service times of each customer are settled in advance .Optimization of the repetitive operations will significantly save cost .Many researches have shown that the heuristic method based on the simulation of biological is very suitable for solving large-scale combinatorial optimization problem .Ant colony optimization ( ACO) is founded on the behavior of ant colony foraging in nature , which has been proved to be feasibility for solving VRP problems in lots of research .Therefore , this paper presents an improved ant colony optimization ( IACO ) , in which a multi-dimension pheromone matrix and a local optimization strategy based on
基于ACS-GA算法的车辆路径问题研究%An ACS-GA Hybrid Optimization Method to Solve Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
赵婉忻; 曲仕茹
2011-01-01
Vehicle routing problem is an important research area in intelligent transportation and business logistics. Planning the vehicle routes reasonably, reducing the delivery mileage and minimizing the cost of logistic distribution are great significance to increase economic efficiency. The paper focuses on vehicle routing problem with time windows in logistic distribution and establishes an improved mathematical model in which the delivery time and delivery distance is shortest. A novel hybrid optimization method integrating ant colony system with genetic algorithm ( ACS - GA) is presented. The initial solution is obtained by ant colony system. A genetic algorithm is used to improve the performance of ACS by reproduction, crossover and mutation operations. The ACS - GA hybrid optimization method can overcome the premature phenomenon and enhance the global search ability. Based on the benchmark datasets of vehicle routing problem with time windows, the experimental results demonstrate that the proposed method has a better ability to search the global optimal solution than other optimization methods.%物流配送车辆路径问题是智能交通和商业物流领域中一个重要研究方面.合理规划车辆的行驶路线,减少配送里程,降低物流成本,对提高经济效益具有重要意义.重点分析了带时间窗的物流配送车辆路径问题,建立了兼顾配送时间与配送距离最短的改进数学模型.提出了基于蚁群系统算法和遗传算法相融合的混合算法.该算法利用蚁群系统算法得到初始解,运用遗传算法中复制、交叉、变异操作对解的种群多样性进行扩充,克服了蚁群系统算法的早熟现象,增强了算法的全局搜索能力.基于标准数据集的实验结果表明,该算法与其他优化方法相比较,具有较好的搜索车辆路径最优解的能力.
Stochastic vehicle routing with recourse
DEFF Research Database (Denmark)
Gørtz, Inge Li; Nagarajan, Viswanath; Saket, Rishi
2012-01-01
We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand...... instantiations, a recourse route is computed - but costs here become more expensive by a factor λ. We present an O(log2n ·log(nλ))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular...
突发事件下车辆路径问题的动态规划算法%Dynamic Programming Algorithm of Vehicle Routing Problems under Emergencies
Institute of Scientific and Technical Information of China (English)
欧微; 焦丽萍
2011-01-01
突发事件下的车辆运输具有紧迫性、动态性和随机不确定性等特点.本文研究了突发事件下动态车辆路径问题的数学模型,构建了一种基于混沌优化的动态规划算法,为此通过路径计算和动态规划两个模块来实现车辆路径的动态规划.为实现从混沌运动空间向问题可行解空间的有效映射,提出了相应的编码方法和操作算子.最后进行仿真,通过对静态环境、道路受损和道路拥塞三种情况的分析,验证了实时修订路经的有效性和实用性,为突发事件提供参考.%The vehicle transportation under emergencies is a kind of emergent, dynamic and random problems. The mathematics model of Dynamic Vehicle Routing Problems (DVRP) under emergencies is proposed, and an ap-proach solving DVRP based on chaos optimization is formulated, in which a route computing module and a dynamic programming module are introduced, and the corresponding coding method and operators are proposed to mapping the chaos space to feasible solution space. Finally, three cases of initial - state, road - damaged and road - congested are analyzed separately to demonstrate the necessary of real - time route adjusting and the efficiency of the proposed algorithm by computer simulations.
Vehicle Routing Problem with Integration of Resources%求解整合资源条件下的运输调度问题
Institute of Scientific and Technical Information of China (English)
江泽东; 蔡延光; 汤雅连; 杨军; 朱君
2014-01-01
针对传统的物流运输调度问题(Vehicle Routing Problem,VRP)中车辆之间不协作会造成资源浪费的情况,提出整合资源条件下的运输调度问题(Vehicle Routing Problem with Integration of resources,VRPIR),建立了相应的数学模型.由于混沌具有良好的遍历性,而粒子群优化算法(Particle Swarm Optimization,PSO)具有概念简单,参数少,容易实现等优点,将混沌优化方法引入到粒子群优化算法中,应用混沌粒子群优化算法(Chaos Particle Swarm Algorithm,CP-SO)求解VRPIR和VRP,并用CPSO和PSO分别求解VRPIR,实验结果证明该算法优于粒子群优化算法,也证明了提出的VRPIR模型优于VRP,能节省资源,且最小化成本.
Memettc algorithm for vehicle routing problem with time windows.%带时间窗车辆路径问题的文化基因算法
Institute of Scientific and Technical Information of China (English)
王君; 李波
2012-01-01
针对物流配送中带时问窗的车辆路径问题(Vehicle Routing Problem with Time Windows,VRPTW),建立了数学模型,并设计了求解VRPTW的文化基因算法.种群搜索采用遗传算法的进化模式,局部搜索采用禁忌搜索机制,并结合可行邻域结构避免对不可行解的搜索,以提高搜索效率.与单纯的遗传算法和禁忌搜索算法进行对比实验,表明该算法是求解VRPTW的一种有效方法.%The Vehicle Routing Problem with Time Windows(VRPTW) is addressed in this paper. A mathematical model is designed and a memetic algorithm is proposed for VRPTW. The pattern of population search is genetic algorithm and the local search used tabu. The feasible neighborhoods are integrated into the algorithm to avoid the search for infeasible solutions, thus it improves search efficiency. Compared with the pure genetic algorithm and the tabu search, computational experiments on Solomon benchmarks show the effectiveness of the proposed memetic algorithm for VRPTW.
Hybrid Algorithm for Open Vehicle Routing Problem%开放式车辆路径问题的混合算法
Institute of Scientific and Technical Information of China (English)
钟雪灵; 王雄志
2011-01-01
为研究开放式车辆路径问题(Open Vehicle Routing Problem,OVRP),建立了数学模型.针对遗传算法(Genetic Algorithm,GA)与禁忌搜索算法(Tabu Search Algorithm,TSA)的不足,提出了一个采用GA和TSA相结合的混合算法求解OVRP.混合算法中以GA为主,把TSA用在GA的变异操作中,增强算法的爬山能力.通过仿真,将提出的混合算法与文献中其它算法比较,结果表明它可以快速、有效求得最优解或近似解.%This paper studies the open vehicle routing problem(OVRP). First, the mathematics model of OVRP is described. Then hybrid algorithm of genetic algorithm (GA) and tabu search algorithm (TSA) are proposed on the basis of analyzing the weakness of GA and TSA. The GA is taken as the main part, and the TSA is used in the big cycle of the GA. So, the hill - climbing power of the algorithm is increased, and the probability of obtaining the optimal solution is increased. Finally, the proposed hybrid algorithm is compared with other algorithms with simulation results, which demonstrates that it is an efficient and effective method for finding the optimum or approximate solution.
Directory of Open Access Journals (Sweden)
Yu Lin
2015-01-01
Full Text Available In recent years, logistics systems with multiple suppliers and plants in neighboring regions have been flourishing worldwide. However, high logistics costs remain a problem for such systems due to lack of information sharing and cooperation. This paper proposes an extended mathematical model that minimizes transportation and pipeline inventory costs via the many-to-many Milk-run routing mode. Because the problem is NP hard, a two-stage heuristic algorithm is developed by comprehensively considering its characteristics. More specifically, an initial satisfactory solution is generated in the first stage through a greedy heuristic algorithm to minimize the total number of vehicle service nodes and the best insertion heuristic algorithm to determine each vehicle’s route. Then, a simulated annealing algorithm (SA with limited search scope is used to improve the initial satisfactory solution. Thirty numerical examples are employed to test the proposed algorithms. The experiment results demonstrate the effectiveness of this algorithm. Further, the superiority of the many-to-many transportation mode over other modes is demonstrated via two case studies.
PNW River Reach Files -- 1:100k LLID Routed Streams (routes)
Pacific States Marine Fisheries Commission — This feature class includes the ROUTE features from the 2001 version of the PNW River Reach files Arc/INFO coverage. Separate, companion feature classes are also...
Institute of Scientific and Technical Information of China (English)
李建波
2009-01-01
The reasons for gap occurrence in forestry cartography using ArcGIS 9 were analyzed, the methods for checking and removing the gap in cartography were described. It was suggested that the software user should cultivate good habit, in the course of feature selection, using the tool of "selected by features" instead of "edit" could significantly decrease the occurrence of gap.%分析了基于ArcGIS 9软件的林业制图中出现面层缝隙的原因,对面层缝隙的检查和去除方法进行了论述,建议软件使用者养成良好的制图习惯,在选择要素时尽量不使用"编辑"工具,而是用"选自要素"工具则可极大地减少面层缝隙的产生.
A novel methodology for determining low-cost fine particulate matter street sweeping routes.
Blazquez, Carola A; Beghelli, Alejandra; Meneses, Veronica P
2012-02-01
This paper addresses the problem of low-cost PM10 (particulate matter with aerodynamic diameter arc routing problem into a node routing problem is proposed in this paper. This is accomplished by building a graph that represents the area to sweep in such a way that the problem can be solved by applying any known solution to the Traveling Salesman Problem (TSP). As a way of illustration, the proposed method was applied to the northeast area of the Municipality of Santiago (Chile). Results show that the proposed methodology achieved up to 37% savings in kilometers traveled by the sweeping vehicle when compared to the solution obtained by solving the TSP problem with Geographic Information Systems (GIS)--aware tools.
A branch-and-cut-and-price approach for the pickup and delivery problem with shuttle routes
DEFF Research Database (Denmark)
Masson, Renaud; Røpke, Stefan; Lehuédé, Fabien;
2014-01-01
delivery point. The second leg is a direct trip – called a shuttle – between two delivery points. This optimization problem has practical applications in the transportation of people between a large set of pickup points and a restricted set of delivery points.This paper proposes three mathematical models...... for the PDPS and a branch-and-cut-and-price algorithm to solve it. The pricing sub-problem, an Elementary Shortest Path Problem with Resource Constraints (ESPPRC), is solved with a labeling algorithm enhanced with efficient dominance rules. Three families of valid inequalities are used to strengthen...
车辆路径问题的连接点选择节约算法%Connection Point Selection Saving Algorithm Solving the Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
邵俊岗; 郑芳瑜
2015-01-01
为了深入研究车辆路径问题中节约算法的应用，通过具体数据比较与分析了传统CW算法和改进后的分割节约算法得出的配送方案．发现针对C－W算法下运输车辆数目已经最优的情况，允许分割配送的节约算法反而增加了配送里程，路径交叉的情况却没有得到改善，因此此方法不再适用．因此，基于传统Clarke－Wright节约算法，对连接点进行选择来解决这一问题．通过matlab7．0对具体的实例进行了对比计算，用专业的制图和数据分析软件OriginPro 8．0画出配送路径图．结果表明，对连接点选择进行优化的节约算法不仅避免了路线交叉，且计算结果优于传统节约法．%In order to study the saving algorithm in the application of vehicle routing problem , the paper analyzed the instance data of traditional savings algorithm and improved saving segmentation algorithm .Under the CW algorithm for the case , saving segmentation algorithm actually increases the distribution mileage and route crossed is not improved when the number of transport vehicles have been optimized to allow the distribution , so saving segmentation algorithm is no longer applicable .In this paper , the connection point selection saving algo-rithm approach to solving this problem .The calculation of specific examples was compared by matlab 7.0 and the distribution route map was drawn by a professional graphics and data analysis software OriginPro 8.0.The results show that the connection point selection saving algorithm can not only avoid the route cross , but also optimize the calculation results .
Clustering algorithm for split delivery vehicle routing problem%需求可拆分车辆路径问题的聚类求解算法
Institute of Scientific and Technical Information of China (English)
刘旺盛; 杨帆; 李茂青; 陈培芝
2012-01-01
In the traditional vehicle routing problems, customer demands are usually assumed that they can not be split. That is to say, a customer can only be severed by a vehicle. In fact, split delivery requires fewer vehicles, which reduces transportation costs. This paper analyzes the solution＇s characteristics of split delivery vehicle routing problem, and also proves the situations that customers＇ demands can not be split. A clustering algorithm meeting the solution＇s characteristics is designed to solve this problem. Compared with ant colony algorithm and tabu search algorithm, the proposed algorithm is demonstrated to obtain optimal solution more effectively through the simulation, and it is an effective method to solve split delivery vehicle routing problem.%针对传统的车辆路径问题通常假设客户的需求不能拆分，即客户的需求由一辆车满足，而实际上通过需求的拆分可使需要的车辆数更少，从而降低配送成本的问题，分析了需求可拆分的车辆路径问题的解的特征，证明了客户需求不宜拆分应满足的条件，设计了符合解的特征的聚类算法，并对其求解．通过实验仿真，将所提出的聚类算法与蚁群算法和禁忌搜索算法进行比较，所得结果表明了所提出的算法可以更有效地求得需求可拆分车辆路径问题的优化解，是解决需求町拆分车辆路径问题的有效方法．
Solution to a two-phase tabu algorithm for location routing problem%定位路线问题的两阶段禁忌搜索算法研究
Institute of Scientific and Technical Information of China (English)
徐丽蕊; 李静
2011-01-01
Location routing problem is the integrated decision of location allocation problem and vehicle routing problem. This paper describes the location routing problem, sets up the mathematical model of this problem, and validates the model by Lingo 10. 0. Because this model is a NP-hard problem, to solve this problem, a two-phase tabu search algorithms was designed. At the first phase, the problems of location allocation to fix on the facility and custom allocation were solved by tabu search algorithms; at the second phase, the vehicle routing problem was solved by tabu search algorithms; by a large number of iterative from location to routing phases, the optimizing solution to the location routing can be obtained. Comparing with the related literature , the computing result shows that the designed algorithm is practicable and effective to solve this problem.%定位路线问题是定位配给和车辆路线问题的集成.分析了定位路线问题的含义,建立了此问题的数学模型,并用Lingo 10.0验证了模型的正确性.由于该模型属于NP-hard问题,设计了两阶段禁忌搜索算法:第一阶段用禁忌搜索算法求解定位配给问题,确定设施定位及客户分配;第二阶段用禁忌搜索算法求解车辆路线问题,经过两个阶段的多次迭代求得定位路线问题的优化解,通过实例计算验证该算法的可行性和有效性.
Using Genetic Algorithm For Winter Maintenance Operations: Multi Depot K-Chinese Postman Problem
Directory of Open Access Journals (Sweden)
İbrahim Zeki Akyurt
2015-02-01
Full Text Available In this study, the assignment and routing problem of one of Istanbul’s winter maintenance activities, salt pouring, was scrutinized. The starting point of the study considers the high cost of winter maintenance work, a shrinking assigned budget, high numbers of vehicles and streets to service that the increase in difficulty to solve the problem due to their high numbers. In this respect, the problem was modeled as multi depot k-Chinese postman problem, a type of arc routing problem. This mathematical model was solved by genetic algorithm. For comparison, the current solution, Clarke and Wright Algorithm and Sweep Algorithm were used.
VMI&TPL供应链下的VRP问题研究%Vehicle Routing Problem in Integrated Supply Chain of VMI and TPL
Institute of Scientific and Technical Information of China (English)
汤中明
2013-01-01
Based on the background of supply chain which integrates VMI and TPL, a new vehicle routing problem model is built. The model proposes a supply chain network which contains many vendors, one TPL and one manufacture, and TPL is responsible for the decision of vehicle routing problem. The solution strategy is divided into two courses. Firstly, basic data of Travelling Salesman Problem (TSP) is built by saving algorithm. Secondly, based on the basic data of TSP, a VRP model is built and solved by simulation annealing genetic algorithm. At last, the algorithm and its effectiveness are explained by a numerical example.%提出供应商管理库存(VMI)与第三方物流(TPL)集成供应链管理模式,构建VMI&TPL模式下的VRP优化模型.模型考虑“多供应商,单TPL,单制造商”的供应链网络,TPL负责统一为所有供应商配送货物.为提高求解效率,将求解过程分为两个部分:TPL首先基于节约法建立旅行商问题(TSP)基础数据,然后通过调用TSP基础数据来安排车辆分配与路线计划.VRP模型采用模拟退火遗传算法进行求解,通过算例对模型的求解策略及其有效性进行了说明.
物流配送车辆调度问题算法综述%Research on Algorithm of Delivery Vehicle Routing Problems
Institute of Scientific and Technical Information of China (English)
陈君兰; 叶春明
2012-01-01
Delivery vehicle routing problems （VRP） is a kind of optimization problems, aiming at solving the vehicle routing problems in delivery section. And they have been a focus of research in logistics control optimization recently. After summarize different kinds of VRP, the article gives the relevant general models. The character and the application of genetic algorithm, simulated annealing, tabu search, ant colony algorithm, particle swarm optimization are analyzed and the current possibilities to solve VRP are also discussed. Finally, the development of VRP solution is presented, and point out that improved combined algorithm as well as new algorithm will be important measures to solve VRP.%配送车辆调度优化问题旨在解决配送中路径和车辆调度问题的一类组合优化问题，是近年来物流控制优化领域的研究热点。文章对运输调度问题进行了分类总结，给出总体模型的概括描述，分析遗传算法、模拟退火算法、禁忌搜索算法、蚁群算法和微粒群算法的特点及其在求解配送车辆调度优化问题中的求解思路，并讨论了其求解现状，对未来研究方向进行展望，指出改进混合现有算法，开拓新算法将是更有效解决配送车辆调度问题的好方法。
需求可拆分的开放式车辆路径问题研究%Research on Split Delivery Open Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
李三彬; 柴玉梅; 王黎明
2011-01-01
The traditional Open Vehicle Routing Problem(OVRP) assumes that the demand of the clients can not be split and the type of vehicles is the same, but in the practical logistics distribution, the type of vehicles is not exactly the same, sometimes the transportation cost can be reduced by splitting the demand of clients to make the best of the loading capacity of vehicles.This paper proposes the Split Delivery Open Vehicle Routing Problem with Heterogeneous Vehicles(SDOVRPHV), presents mathematic model of the integer programming of the problem, solves it with Tabu search algorithm and improves the generation of the initial solution and neighborhood structure in the algorithm.By experiments, the validity of the model is validated, and the results are compared with the traditional OVRP which indicates that the algorithm can reduce effectively the transportation cost.%传统的开放式车辆路径问题假设客户的需求不可拆分、车辆类型相同,但在实际的物流配送中,车辆类型不完全相同,对需求的拆分能充分利用车辆的装载能力,降低运输成本.为此,提出需求可拆分的不同种车辆的开放式车辆路径问题,给出整数规划的数学模型,利用禁忌搜索算法对该问题求解,改进算法中初始解和邻域结构的产生过程.通过实验验证模型的有效性,并将结果与传统的开放式车辆路径问题进行比较,表明该算法可有效减少运输成本.
Simulation Analysis of Logistics Distribution Vehicle Routing Problem%物流配送车辆路径优化的仿真分析
Institute of Scientific and Technical Information of China (English)
张玲雅
2015-01-01
The current development of the logistics industry,based on the development needs of the industry,as well as traditional logistics short board to reduce logistics costs can not be overcome,the urgent need for logistics distribution vehicle routing optimization,thus effectively reducing logistics costs,based on this,propose an ant colony algorithm for logistics distribution vehicle routing optimization algorithm,aimed at establishing a basis for the mathematical model,the logistics vehicle routing problem using ant colony optimization algorithm to solve subsequent experiments concluded that the algorithm achieved significant results,conducive to the logistics and distribution reduce costs for the development of the current logistics enterprises of great significance.%当前物流行业发展中，基于行业的发展需要，以及传统物流在降低物流运输成本方面无法克服的短板，急需进行物流配送车辆路径优化，从而有效地降低物流配送成本，基于此，文中提出一种蚁群算法的物流配送车辆路径优化算法，旨在建立数学模型的基础上，对物流车辆路径的问题采用蚁群算法进行求解优化，后续实验得出，该算法效果显著，利于对物流配送成本的降低，对于当前物流企业的发展意义重大。
Research on the Open Incident Vehicle Routing Problems%开放式关联运输调度问题的研究
Institute of Scientific and Technical Information of China (English)
汤雅连; 蔡延光; 黄刚
2013-01-01
Aiming at Open Incident Vehicle Routing Problem with Soft Time Windows ( OIVRPSTW) and relating to the VRP( Vehicle Routing Problem ) of goods supply in chain stores , this paper introduces the fundamental principle of PSO ( Particle Swarm Optimization ) , adopting the nonlinear dynamic self -adapting method to adjust inertia weight factor , so that the weight factor can change along with the target value , combined with the advantage of using chaos to generate initial population and design a kind of CPSO(Chaos Particle Swarm Optimizaton).Meanwhile, SA (simulated annealing) mechanism is brought in the CGA (Chaos Genetic Algorithm), adjusting crossover probability and mutation probability adaptively .At last, both of the modified algorithms are applied to solve OIVRPSTW , so does GA ( Genetic Algorithm ) .The result shows that the advantage of using chaos to generate ini-tial population is flexible to solve this kind of OIVRP and can obtain the satisfied result .%针对带软时间窗的开放式关联运输调度问题（ Open Incident Vehicle Routing Problem with Soft Time Windows， OIVRPSTW），联系实际应用中连锁店超市中货物供应的车辆路径问题，介绍了粒子群算法的基本原理，采用一种非线性动态自适应调节惯性权重因子的方法，使得惯性系数会随着粒子目标值的变化而自动改变，结合混沌搜索产生初始种群的方法，设计了一种混沌粒子群优化算法。同时也设计了引入了模拟退火机制的混沌遗传算法，自适应地调整交叉概率和变异概率。并用这两种算法来对OIVRPSTW求解，然后与基本的遗传算法求解此模型的结果相比较。实例证明用混沌搜索产生初始种群的方法在求解此类开放式关联运输调度问题是可行的，能取得令人满意的效果。
物流配送车辆路径的优化方法分析%Analysis on Optimizing Methods of Logistics Distribution Vehicles Routing Problem
Institute of Scientific and Technical Information of China (English)
张志强
2013-01-01
随着经济全球化的不断发展，各区域的经济交流不断加强，物流行业迅速发展起来，同时配送成本在物流行业发展过程中显得越来越重要。物流企业要想在激烈的社会竞争中不被淘汰，就必须考虑如何降低随着社会结构改变而出现复杂化的物流配送成本，不断提高自身的综合竞争力。文中主要介绍了有关计算和改进物流配送车辆路径优化方面的问题，着重论述了对蚁群算法在降低物流配送成本，以及物流配送车辆在路径优化上中的应用，从而选择出对配送车辆路径进行最好的优化的方法。%With the continuing development of economic globalization and increasingly closer link between regional economies,the logistics industry grows with a high speed.The cost on distribution is thus,being attached more and more attention in the development of logistics industry.The issues on how to reduce the more complicated cost of distribution as the social structure is undertaking profound changes and how to improve their overall strength must be taken into account by the logistics enterprises in order not to be eliminated in the fierce competition.The paper introduced algorithms and methods for optimizing logistics distribution vehicles routing problem.Ant Colony Algorithm (ACA)was given particular attention to illustrate its role in reducing distribution cost and optimizing the routing problem so as to select the best method for the routing of distribution vehicles.
The research on multi-depot and multi-vehicle-type related vehicle routing problem%类电磁机制算法的应用研究
Institute of Scientific and Technical Information of China (English)
段熙鹏; 蔡延光; 汤雅连
2012-01-01
The iwproved electromagnetism-like mechanism algorithm （EMA） was introduced, and this algorithm was applied to solve multi-depot and multi-vehicle-type related vehicle routing problem. Local search can improve the ability of fine search in the local area, moreover, mobile coefficient can improve the convergence rate. The results show that improved EMA is feasible and flexible to solve this type of RVRP and its better than traditional EMA.%摘要：针对多车场多车型的关联运输调度问题（Multi-depot and Multi—vehicle—type Related Vehi—cle Routing Problem），对传统的类电磁机制算法进行改进，局部搜索可以提高算法在局部区域精细搜索的能力，并引入了移动系数来提高算法的收敛速度。实验结果证明，改进的算法有效地解决了此类问题且优于传统类电磁机制算法。
Graph theoretic approach for routing problem in VLSI%基于图论模型的一类集成电路布线算法
Institute of Scientific and Technical Information of China (English)
耿显亚; 许峰
2015-01-01
针对具有曼哈顿模型的一类通道布线，提出了一个依据图论模型的最优轨道高度布线算法。算法根据通道上结点的水平约束图和垂直约束图，依次安排好每一个结点的布线轨道，进而通过通孔可以把所有的结点在2层轨道上布线完成。通过计算分析，该算法相对以前的算法能够达到更优的布线高度，并且其复杂性保持不变。%For a channel in 2-layer Manhattan model, this paper aims at interconnecting the terminals of each net by wires such that the circuit elements and the interconnecting wires are embedded into two planar layers by the methods of graph theory. Furthermore, the width(number of tracks required for routing)of a channel should be minimized. The constraints of a channel routing problem can be represented by a Horizontal Constraint Graph(HCG)and a Vertical Constraint Graph (VCG). Considering the two constraints, the paper improves the upper bound, it shows that this algorithm is better than the best known algorithm.
Allocation and Routing of CRAF MD80 Aircraft
1990-03-01
5 II. Literature Review...................7 Formal Statement of the Vehicle Routing Problem ............ .. . .. .. ....... Vehicle...83 Appendix H: Example Vehicle Routing Problem Input 84 Appendix I: Example Vehicle Routing Problem Output 85 Appendix J: Spacefilling Curve...this problem is a stochastic vehicle routing problem with multiple depots. In this case, there are nine depots and 30 vehicles corresponding to nine
Research of Vehicle Routing Problem Based on Fuzzy Time Windows%基于模糊时间窗的车辆调度问题研究
Institute of Scientific and Technical Information of China (English)
王旭坪; 张凯; 胡祥培
2011-01-01
An increasing number of enterprises are focusing on the vehicle routing problems (VRP) because of expanded logistics support. VRP belongs to typical NP-Hard problems. An enterprise typically spends 25% to 30% of total expenses on vehicle routing problems because they can affect economic efficiency and customer benefits. Therefore, it is important to research VRP and optimize logistics activities.Exiting literature has focused on the vehicle routing problem with hard time and soft time windows. In the VRP with hard time window, the service time must fall within each customer' s time window. Due to the limitation of hard time window and the number of available vehicles, it is often unable to find feasible schedules. To deal with issues pertaining to the violation of time window, researchers have proposed the concept of "soft time window". In the VRP with soft time window, a penalty cost is added once a time window is violated, and the penalty cost is often assumed to be linear with the degree of violation. In some cases, violation of time window does not directly incur any penalty cost, although the satisfaction levels of customers may drop and lead to benefit loss in the long term. In many realistic applications, the hard time window or soft time window does represent customer requirements very well. Under these circumstances, the fuzzy processing of time window can reflect customers' requirements well and truly. Until now, few studies have addressed VRP-with fuzzy time window when the number of vehicle is limited. There are many real-life situations where the number of vehicle is limited, such as logistics distribution, post express and so on. Thus, this paper proposes and solves vehicle routing problems based on the fuzzy time window and a definite number of vehicles. In this paper, a fuzzy membership function is used to characterize customers' satisfaction levels by analyzing customers' practical requirements of the service time window.A multi-objective model
Institute of Scientific and Technical Information of China (English)
陆琳; 谭清美
2006-01-01
针对一类随机需求车辆路径问题(stochastic vehicle routing problem,SVRP),结合现实生活中长期客户服务记录所隐含的统计性知识构建新的统计学模型,并将种群搜索与轨迹搜索算法相结合提出了一种新的混合粒子群优化算法.该算法通过引入导引式局部搜索,来减小粒子群搜索陷入局优的可能性以获得更优化解.仿真计算证明混合粒子群优化算法的有效性.同时,该算法也拓展了VRP的算法空间.
车辆路径问题的模拟退火算法%Simulated Annealing Algorithm for Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
胡大伟; 朱志强; 胡勇
2006-01-01
在构造车辆路径问题(Vehicle Routing Problem,VRP)数学模型后,采用路径间调整和路径内优化方法,结合模拟退火算法策略对该问题进行求解.重点阐述了VRP模拟退火算法的设计思路,详细分析和编制了求解程序框图,并实现了计算机求解.仿真测试结果表明:采用模拟退火算法求解VRP效果显著,计算速度较快,与有关算法对比显示了较强的实用性和可操作性,为解决大规模VRP提供了一种有效算法.
车辆路径安排问题算法研究综述%Algorithmic Review on the Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
陈文兰; 戴树贵
2007-01-01
车辆路径安排是决定物流配送费用的主要因素.车辆路径安排问题(Vehicle Routing Problem,VRP)是近年来应用数学、计算机科学和物流科学研究的一个热点问题,产生了众多的研究成果.本文首先讨论了VRP的分类,然后基于VRP算法构造方法的分类,概要介绍了近五年来VRP算法研究的主要成果,并对研究方法进行了分析,最后对全文进行了总结,并探讨了该问题未来的研究方法.
多车场车辆路径问题及混合遗传算法%Multi-depot Vehicle Routing Problem with Hybrid Genetic Algorithm
Institute of Scientific and Technical Information of China (English)
党立伟; 孙小明
2012-01-01
在多车场车辆路径问题中,综合考虑车辆的行驶路程和使用车辆的数量能有效降低配送成本,考虑了这两方面的因素建立了相应的数学模型,运用混合遗传算法进行了求解,并通过实例证明了模型和算法的有效性.%About the multi-depot vehicle routing problem, considering the distance traveled by the vehicle and the number of vehicles together can effectively reduce distribution costs. The corresponding mathematical model by taking the two factors into account is established, solved the model by using genetic algorithms and demonstrate the effectiveness of the model and algorithm by example.