Target aiming Pareto search and its application to the vehicle routing problem with route balancing

Abstract In this paper, we present a solution method for a bi-objective vehicle routing problem, called the vehicle routing problem with route balancing (VRPRB), in which the total length and balance of the route lengths are the objectives under consideration. The method, called Target Aiming Pareto Search, is defined to hybridize a multi-objective genetic algorithm for the VRPRB using local searches. The method is based on repeated local searches with their own appropriate goals. We also propose an implementation of the Target Aiming Pareto Search using tabu searches, which are efficient meta-heuristics for the vehicle routing problem. Assessments with standard metrics on classical benchmarks demonstrate the importance of hybridization as well as the efficiency of the Target Aiming Pareto Search.

[1]  Samy Bengio,et al.  The Vehicle Routing Problem with Time Windows Part II: Genetic Search , 1996, INFORMS J. Comput..

[2]  Nicolas Jozefowiez,et al.  Parallel and Hybrid Models for Multi-objective Optimization: Application to the Vehicle Routing Problem , 2002, PPSN.

[3]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[4]  Hisao Ishibuchi,et al.  Balance Between Genetic Search And Local Search In Hybrid Evolutionary Multi-criterion Optimization Algorithms , 2002, GECCO.

[5]  Paolo Toth,et al.  Models, relaxations and exact approaches for the capacitated vehicle routing problem , 2002, Discret. Appl. Math..

[6]  J. K. Lenstra,et al.  Complexity of vehicle routing and scheduling problems , 1981, Networks.

[7]  Xavier Gandibleux,et al.  A survey and annotated bibliography of multiobjective combinatorial optimization , 2000, OR Spectr..

[8]  Yves Rochat,et al.  Probabilistic diversification and intensification in local search for vehicle routing , 1995, J. Heuristics.

[9]  Ángel Corberán,et al.  Heuristic solutions to the problem of routing school buses with multiple objectives , 2002, J. Oper. Res. Soc..

[10]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[11]  Kazuho Yoshimoto,et al.  納期に対する満足度を考慮した多目的配送計画に関する研究 : Hybrid GAを用いたパレート最適集合の生成 , 1998 .

[12]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[13]  Joshua D. Knowles,et al.  On metrics for comparing nondominated sets , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[14]  Andrzej Jaszkiewicz,et al.  Genetic local search for multi-objective combinatorial optimization , 2022 .

[15]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[16]  F. Abdelaziz,et al.  A Hybrid Heuristic for Multiobjective Knapsack Problems , 1999 .

[17]  Gilbert Laporte,et al.  A unified tabu search heuristic for vehicle routing problems with time windows , 2001, J. Oper. Res. Soc..

[18]  John R. Current,et al.  Multiobjective transportation network design and routing problems: Taxonomy and annotation , 1993 .

[19]  Yang-Byung Park,et al.  A heuristic for bi-objective vehicle routing with time window constraints , 1999 .

[20]  Joshua D. Knowles.  Local-search and hybrid evolutionary algorithms for Pareto optimization , 2002 .

[21]  Joel N. Morse,et al.  Reducing the size of the nondominated set: Pruning by clustering , 1980, Comput. Oper. Res..

[22]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[23]  Kalyanmoy Deb,et al.  A Hybrid Multi-objective Evolutionary Approach to Engineering Shape Design , 2001, EMO.

[24]  Helena Ramalhinho-Lourenço,et al.  A Multi-Objective Model For A Multi-Period Distribution Management Problem , 2001 .

[25]  Shen Lin.  Computer solutions of the traveling salesman problem , 1965 .

[26]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem , 1991 .

[27]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[28]  Tzong-Ru Lee,et al.  A study of vehicle routing problems with load‐balancing , 1999 .

[29]  G. Laporte,et al.  A tabu search heuristic for periodic and multi-depot vehicle routing problems , 1997, Networks.

[30]  Christian Prins,et al.  A simple and effective evolutionary algorithm for the vehicle routing problem , 2004, Comput. Oper. Res..