Chaotic ant swarm for the traveling salesman problem

Chaotic ant swarm (CAS) is an optimization algorithm based on swarm intelligence theory, which has been applied to find the global optimum solution in continuous search space. However, it is not able to solve the combinational optimization problem directly, e.g., the traveling salesman problem (TSP). To tackle this problem, we propose a new method to solve the traveling salesman problem based on chaotic ant swarm, CAS-TSP for short. The CAS-TSP is developed by introducing a mapping from continuous space to discrete space, reverse operator and crossover operator into the CAS. Computer simulations demonstrate that the CAS-TSP is capable of generating optimal solution to instances of the TSPLIB in almost all test problems of sizes up to 150. Also a comparative computational study shows that this CAS-TSP algorithm is an efficient tool for solving TSP and this heuristic is competitive also with other heuristics.

[1]  Zbigniew Michalewicz,et al.  Inver-over Operator for the TSP , 1998, PPSN.

[2]  David S. Johnson,et al.  The Traveling Salesman Problem: A Case Study in Local Optimization , 2008 .

[3]  S. Chatterjee,et al.  Genetic algorithms and traveling salesman problems , 1996 .

[4]  Cong Wang,et al.  CAS based clustering algorithm for Web users , 2010 .

[5]  John J. Grefenstette,et al.  Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application , 1987 .

[6]  Marimuthu Palaniswami,et al.  Neural techniques for combinatorial optimization with applications , 1998, IEEE Trans. Neural Networks.

[7]  Haipeng Peng,et al.  Chaotic ant swarm optimization to economic dispatch , 2007 .

[8]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

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

[10]  P. W. Poon,et al.  Genetic algorithm crossover operators for ordering applications , 1995, Comput. Oper. Res..

[11]  M. Padberg,et al.  Addendum: Optimization of a 532-city symmetric traveling salesman problem by branch and cut , 1990 .

[12]  J. K. Lenstra,et al.  Local Search in Combinatorial Optimisation. , 1997 .

[13]  Chunguang Zhou,et al.  Particle swarm optimization for traveling salesman problem , 2003, Proceedings of the 2003 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.03EX693).

[14]  Lixiang Li,et al.  Fuzzy system identification via chaotic ant swarm , 2009 .

[15]  Laura I. Burke,et al.  Neural methods for the traveling salesman problem: Insights from operations research , 1994, Neural Networks.

[16]  Haipeng Peng,et al.  Parameter estimation of dynamical systems via a chaotic ant swarm. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  J. P. Secrétan,et al.  Der Saccus endolymphaticus bei Entzündungsprozessen , 1944 .

[18]  Yanchun Liang,et al.  Particle swarm optimization-based algorithms for TSP and generalized TSP , 2007, Inf. Process. Lett..

[19]  Jean-Yves Potvin,et al.  Genetic Algorithms for the Traveling Salesman Problem , 2005 .

[20]  Luca Maria Gambardella,et al.  Ant Algorithms for Discrete Optimization , 1999, Artificial Life.

[21]  Kazuyuki Aihara,et al.  Chaotic simulated annealing by a neural network model with transient chaos , 1995, Neural Networks.

[22]  James R. Evans,et al.  Optimizing tabu list size for the traveling salesman problem , 1998, Comput. Oper. Res..

[23]  Chee-Kit Looi,et al.  Neural network methods in combinatorial optimization , 1992, Comput. Oper. Res..

[24]  Kate A. Smith,et al.  Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research , 1999 .

[25]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[26]  John Knox,et al.  Tabu search performance on the symmetric traveling salesman problem , 1994, Comput. Oper. Res..

[27]  Qiaoyan Wen,et al.  Hybrid chaotic ant swarm optimization , 2009 .

[28]  D. J. Smith,et al.  A Study of Permutation Crossover Operators on the Traveling Salesman Problem , 1987, ICGA.

[29]  R. Bixby,et al.  On the Solution of Traveling Salesman Problems , 1998 .

[30]  Gábor Pataki,et al.  Teaching Integer Programming Formulations Using the Traveling Salesman Problem , 2003, SIAM Rev..

[31]  G. Reinelt.  The traveling salesman: computational solutions for TSP applications , 1994 .

[32]  Lixiang Li,et al.  An Optimization Method Inspired by "chaotic" Ant Behavior , 2006, Int. J. Bifurc. Chaos.

[33]  Lawrence J. Schmitt,et al.  Performance characteristics of alternative genetic algorithmic approaches to the traveling salesman problem using path representation: An empirical study , 1998, Eur. J. Oper. Res..

[34]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.