A genetic algorithm for traveling salesman problems

This paper proposes an evolutionary approach for the traveling salesman problem. The proposed approach consists of global and local strategies by incorporating the family competition into edge assembly crossover and near 2-opt mutation. The method is applied to six well-known problems, including the eil101, lin318, pcb442, att532, rat575, and u724. The experimental results indicate that the proposed approach performs robustly and is very competitive with the other approaches surveyed in this paper. As our approach, although somewhat slower, executes 50 independent runs for the att532 problem, it is able to find the optimum solution in 23 runs and the average value of solution quality is 27691.3 To the best of our knowledge, the solution quality is the best in our surveys for this problem.

[1]  Shigenobu Kobayashi,et al.  Edge Assembly Crossover: A High-Power Genetic Algorithm for the Travelling Salesman Problem , 1997, ICGA.

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

[3]  David B. Fogel,et al.  Multi-operator Evolutionary Programming: A Preliminary Study on Function Optimization , 1997, Evolutionary Programming.

[4]  Lee Aaron Newberg,et al.  Physical mapping of chromosomes: A combinatorial problem in molecular biology , 1995, SODA '93.

[5]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[6]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[7]  Zbigniew Michalewicz,et al.  Adaptive evolutionary planner/navigator for mobile robots , 1997, IEEE Trans. Evol. Comput..

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

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

[10]  Byung-Ro Moon,et al.  The natural crossover for the 2D Euclidean TSP , 2000 .

[11]  Bernd Freisleben,et al.  New Genetic Local Search Operators for the Traveling Salesman Problem , 1996, PPSN.

[12]  John Yen,et al.  A hybrid approach to modeling metabolic systems using a genetic algorithm and simplex method , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[13]  Gaston H. Gonnet,et al.  Using traveling salesman problem algorithms for evolutionary tree construction , 2000, Bioinform..

[14]  D. J. Cavicchio,et al.  Adaptive search using simulated evolution , 1970 .

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

[16]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

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

[18]  M. Al-Mulhem,et al.  Efficient convex-elastic net algorithm to solve the Euclidean traveling salesman problem , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[19]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[20]  Jinn-Moon Yang,et al.  Flexible ligand docking using a robust evolutionary algorithm , 2000 .

[21]  Chengjian Wei,et al.  A new population-based incremental learning method for the traveling salesman problem , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[22]  W. Hart.  Adaptive global optimization with local search , 1994 .

[23]  Cheng-Yan Kao,et al.  An evolutionary algorithm for the synthesis of multilayer coatings at oblique light incidence , 2001 .

[24]  Thomas Bäck,et al.  Evolutionary computation: comments on the history and current state , 1997, IEEE Trans. Evol. Comput..