A Set-based Comprehensive Learning Particle Swarm Optimization with Decomposition for Multiobjective Traveling Salesman Problem

This paper takes the multiobjective traveling salesman problem (MOTSP) as the representative for multiobjective combinatorial problems and develop a set-based comprehensive learning particle swarm optimization (S-CLPSO) with decomposition for solving MOTSP. The main idea is to take advantages of both the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework and our previously proposed S-CLPSO method for discrete optimization. Consistent to MOEA/D, a multiobjective problem is decomposed into a set of subproblems, each of which is represented as a weight vector and solved by a particle. Thus the objective vector of a solution or the cost vector between two cities will be transformed into real fitness to be used in S-CLPSO for the exemplar construction, the heuristic information generation and the update of pBest. To validate the proposed method, experiments based on TSPLIB benchmark are conducted and the results indicate that the proposed algorithm can improve the solution quality to some degree.

[1]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[2]  Shuzhi Sam Ge,et al.  On parameter settings of Hopfield networks applied to traveling salesman problems , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  Yuefeng Li,et al.  Granule Based Intertransaction Association Rule Mining , 2007 .

[4]  Qingfu Zhang,et al.  Hybridization of Decomposition and Local Search for Multiobjective Optimization , 2014, IEEE Transactions on Cybernetics.

[5]  Alexander Schrijver,et al.  Combinatorial optimization. Polyhedra and efficiency. , 2003 .

[6]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[7]  Aimin Zhou,et al.  An estimation of distribution algorithm based on decomposition for the multiobjective TSP , 2012, 2012 8th International Conference on Natural Computation.

[8]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[9]  Bruce L. Golden,et al.  Solving the traveling salesman problem with annealing-based heuristics: a computational study , 2002, IEEE Trans. Syst. Man Cybern. Part A.

[10]  Moritoshi Yasunaga,et al.  Implementation of an Effective Hybrid GA for Large-Scale Traveling Salesman Problems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Kay Chen Tan,et al.  A Hybrid Estimation of Distribution Algorithm with Decomposition for Solving the Multiobjective Multiple Traveling Salesman Problem , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[12]  Salman Mohagheghi,et al.  Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems , 2008, IEEE Transactions on Evolutionary Computation.

[13]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[14]  José Ignacio Hidalgo,et al.  A hybrid heuristic for the traveling salesman problem , 2001, IEEE Trans. Evol. Comput..

[15]  Zbigniew Michalewicz,et al.  Benchmarking Optimization Algorithms: An Open Source Framework for the Traveling Salesman Problem , 2014, IEEE Computational Intelligence Magazine.

[16]  Qingfu Zhang,et al.  MOEA/D-ACO: A Multiobjective Evolutionary Algorithm Using Decomposition and AntColony , 2013, IEEE Transactions on Cybernetics.

[17]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[18]  Daniel Merkle,et al.  Bi-Criterion Optimization with Multi Colony Ant Algorithms , 2001, EMO.

[19]  Wei Pang,et al.  Modified particle swarm optimization based on space transformation for solving traveling salesman problem , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).

[20]  Francisco Herrera,et al.  A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP , 2007, Eur. J. Oper. Res..

[21]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[22]  Christine Solnon,et al.  Ant Colony Optimization for Multi-Objective Optimization Problems , 2007 .

[23]  Jun Zhang,et al.  A Novel Set-Based Particle Swarm Optimization Method for Discrete Optimization Problems , 2010, IEEE Transactions on Evolutionary Computation.

[24]  Mitsuo Gen,et al.  A Multiobjective Hybrid Genetic Algorithm for TFT-LCD Module Assembly Scheduling , 2014, IEEE Transactions on Automation Science and Engineering.