Solving the Traveling Salesman Problem with EDAs

In this chapter we present an approach for solving the Traveling Sales man Problem using Estimation of Distribution Algorithms (EDAs). This approach is based on using discrete and continuous EDAs to find the best possible solution. We also present a method in which domain knowledge (based on local search) is combined with EDAs to find better solutions. We show experimental results obtained on several standard examples for discrete and continuous EDAs both alone and combined with a heuristic local search.

[1]  Pablo Moscato,et al.  Memetic algorithms: a short introduction , 1999 .

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

[3]  G. Croes A Method for Solving Traveling-Salesman Problems , 1958 .

[4]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[5]  C. N. Liu,et al.  Approximating discrete probability distributions with dependence trees , 1968, IEEE Trans. Inf. Theory.

[6]  G. Syswerda,et al.  Schedule Optimization Using Genetic Algorithms , 1991 .

[7]  Lawrence Davis,et al.  Applying Adaptive Algorithms to Epistatic Domains , 1985, IJCAI.

[8]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[9]  Richard Spillman,et al.  Use of a genetic algorithm in the crypt-analysis of simple substitution ciphers , 1993 .

[10]  Pedro Larrañaga,et al.  Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators , 1999, Artificial Intelligence Review.

[11]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[12]  Robert A. J. Matthews,et al.  The Use of Genetic Algorithms in Cryptanalysis , 1993, Cryptologia.

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

[14]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[15]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[16]  M. E. Muller,et al.  A Note on the Generation of Random Normal Deviates , 1958 .

[17]  Jon Jouis Bentley,et al.  Fast Algorithms for Geometric Traveling Salesman Problems , 1992, INFORMS J. Comput..

[18]  Paul A. Viola,et al.  MIMIC: Finding Optima by Estimating Probability Densities , 1996, NIPS.

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

[20]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[21]  L. Darrell Whitley,et al.  Genetic Operators, the Fitness Landscape and the Traveling Salesman Problem , 1992, PPSN.

[22]  Heinz Mühlenbein,et al.  The Equation for Response to Selection and Its Use for Prediction , 1997, Evolutionary Computation.

[23]  Nicos Christofides Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem , 1976, Operations Research Forum.

[24]  C. Reeves Modern heuristic techniques for combinatorial problems , 1993 .

[25]  Bernd Freisleben,et al.  A genetic local search algorithm for solving symmetric and asymmetric traveling salesman problems , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[26]  Cecilia R. Aragon,et al.  Optimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning , 1989, Oper. Res..

[27]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .