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Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators

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Abstract

This paper is the result of a literature study carried out by the authors. It is a review of the different attempts made to solve the Travelling Salesman Problem with Genetic Algorithms. We present crossover and mutation operators, developed to tackle the Travelling Salesman Problem with Genetic Algorithms with different representations such as: binary representation, path representation, adjacency representation, ordinal representation and matrix representation. Likewise, we show the experimental results obtained with different standard examples using combination of crossover and mutation operators in relation with path representation.

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References

  • Ackley, D. H. (1987). A Connectionist Machine for Genetic Hillclimbing. Kluwer Academic Publishers.

  • Ambati, B. K., Ambati, J. & Mokhtar, M.M. (1991). Heuristic Combinatorial Optimization by Simulated Darwinian Evolution: A Polynomial Time Algorithm for the Traveling Salesman Problem. Biological Cybernetics 65: 31-35.

    Google Scholar 

  • Banzhaf, W. (1990). The “Molecular” Traveling Salesman. Biological Cybernetics 64: 7-14.

    Google Scholar 

  • Beyer, H. G. (1992). Some Aspects of the 'Evolution Strategy' for Solving TSP-Like Optimization Problems Appearing at the Design Studies of the 0.5 TeVe + e −-Linear Collider. In Männer, R. & Manderick, B. (eds.) Parallel Problem Solving from Nature 2, 361-370. Amsterdam: North-Holland.

    Google Scholar 

  • Brady, R.M. (1985). Optimization Strategies Gleaned from Biological Evolution. Nature 317: 804-806.

    Google Scholar 

  • Bremermann, H. J., Rogson, M. & Salaff, S. (1965). Search by Evolution. In Maxfield, M., Callahan A. & Fogel, L. J. (eds.) Biophysics and Cyberntic Systems, 157-167. Washington: Spartan Books.

    Google Scholar 

  • Davis, L. (1985). Applying Adaptive Algorithms to Epistatic Domains. Proceedings of the International Joint Conference on Artificial Intelligence, 162-164.

  • Davis, L. (ed.) (1991). Handbook of Genetic Algorithms. New York: Van Nostrand Reinhold.

    Google Scholar 

  • Fogel, L. J. (1962). Atonomous Automata. Ind. Res. 4: 14-19.

    Google Scholar 

  • Fogel, D. B. (1988). An Evolutionary Approach to the Traveling Salesman Problem. Biological Cybernetics 60: 139-144.

    Google Scholar 

  • Fogel, D. B. (1990). A Parallel Processing Approach to a Multiple Traveling Salesman Problem Using Evolutionary Programming. In Canter, L. (ed.) Proceedings on the Fourth Annual Parallel Processing Symposium, 318-326. Fullterton, CA.

  • Fogel, D. B. (1993). Applying Evolutionary Programming to Selected Traveling Salesman Problems. Cybernetics and Systems 24: 27-36.

    Google Scholar 

  • Fox, M. S. & McMahon, M. B. (1987). Genetic Operators for Sequencing Problems. In Rawlings, G. (ed.) Foundations of Genetic Algorithms: First Workshop on the Foundations of Genetic Algorithms and Classifier Systems, 284-300. Los Altos, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Gunnels, J., Cull, P. & Holloway, J. L. (1994). Genetic Algorithms and Simulated Annealing for Gene Mapping. In Grefenstette, J. J. (ed.) Proceedings of the First IEEE Conference on Evolutionary Computation, 385-390. Florida: IEEE.

    Google Scholar 

  • Goldberg, D. E. & Lingle, Jr., R. (1985). Alleles, Loci and the TSP. In Grefenstette, J. J. (ed.) Proceedings of the First International Conference on Genetic Algorithms and Their Applications, 154-159. Hillsdale, New Jersey: Lawrence Erlbaum.

    Google Scholar 

  • Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Gorges-Schleuter, M. (1989). ASPARAGOS An Asynchronous Parallel Genetic Optimization Strategy. In Schaffer, J. (ed.) Proceedings on the Third International Conference on Genetic Algorithms, 422-427. Los Altos, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Grefenstette, J., Gopal, R., Rosmaita, B. & Van Gucht, D. (1985). Genetic Algorithms for the TSP. In Grefenstette, J. J. (ed.) Proceedings of the First International Conference on Genetic Algorithms and Their Applications, 160-165. Hillsdale, New Jersey: Lawrence Erlbaum.

    Google Scholar 

  • Grefenstette, J. J. (ed.) (1987a). Genetic Algorithms and Their Applications: Proceedings of the Second International Conference. Hillsdale, New Jersey: Lawrence Erlbaum.

    Google Scholar 

  • Grefenstette, J. J. (1987b). Incorporating Problem Specific Knowledge into Genetic Algorithms. In Davis, L. (ed.) Genetic Algorithms and Simulated Annealing, 42-60. Los Altos, CA: Morgan Kaufmann.

    Google Scholar 

  • Holland, J. (1975). Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan Press.

    Google Scholar 

  • Homaifar, A. & Guan, S. (1991). A New Approach on the Traveling Salesman Problem by Genetic Algorithm. Technical Report, North Carolina A&T State University.

  • Homaifar, A., Guan, S. & Liepins, G. E. (1993). A New Approach on the Traveling Salesman Problem by Genetic Algorithms. In Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms, 460-466.

  • Jog, P., Suh, J. Y. & Van Gucht, D. (1989). The Effects of Population Size, Heuristic Crossover and Local Improvement on a Genetic Algorithm for the Traveling Salesman Problem. In Schaffer, J. (ed.) Proceedings on the Third International Conference on Genetic Algorithms, 110-115. Los Altos, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Johnson, D. S. (1990). Local Optimization and the Traveling Salesman Problem. Proc. 17th Colloq. Automata, Languages and Programming. Springer-Verlag.

  • Kirkpatrick, S., Gelatt, C. D. & Vecchi, M. P. (1983). Optimization by Simulated Annealing. Science 220: 671-680.

    Google Scholar 

  • Koza, J. R. (1992). Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press.

  • Larrañaga, P., Kuijpers, C. M. H., Poza, M. & Murga, R. H. (1996a) Decomposing Bayesian Networks: Triangulation of the Moral Graph with Genetic Algorithms. Statistics and Computing (to be published).

  • Larrañaga, P., Kuijpers, C. M. H., Murga, R. H. & Yurramendi, Y. (1996b). Searching for the Best Ordering in the Structure Learning of Bayesian Networks. IEEE Transactions on Systems, Man and Cybernetics 26(4): 487-493.

    Google Scholar 

  • Larrañaga, P., Inza, I., Kuijpers, C. M. H., Graña, M. & Lozano, J. A. (1996c). Algoritmos Genéticos en el Problema del Viajante de Comercio. Informatica y Automatica (submitted).

  • Lauritzen, S. L. & Spiegelhalter, D. J. (1988). Local Computations with Probabilities on Graphic Structures and Their Application on Expert Systems. Journal of the Royal Statistical Society, Series B 50(2): 157-224.

    Google Scholar 

  • Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G. & Shmoys, D. B. (eds.) (1985). The Travelling Salesman Problem: A Guided Tour of Combinatorial Optimization. Chichester: Wiley.

    Google Scholar 

  • Lidd, M. L. (1991). The Travelling Salesman Problem Domain Application of a Fundamentally New Approach to Utilizing Genetic Algorithms. Technical Report, MITRE Corporation.

  • Liepins, G. E., Hilliard, M. R., Palmer, M. & Morrow, M. (1987). Greedy Genetics. In Grefenstette, J. J. (ed.) Genetic Algorithms and Their Applications: Proceedings of the Second International Conference, 90-99. Hillsdale, New Jersey: Lawrence Erlbaum.

    Google Scholar 

  • Lin, S. (1965). Computer Solutions on the Travelling Salesman Problem. Bell Systems Techn. J. 44: 2245-2269.

    Google Scholar 

  • Lin, S. & Kernighan, B. W. (1973). An Effective Heuristic Algorithm for the Traveling Salesman Problem. Operations Research 21: 498-516.

    Google Scholar 

  • Lin, F.-T., Kao, C.-Y. & Hsu, C.-C. (1993). Applying the Genetic Approach to Simulated Annealing in Solving NP-Hard Problems. IEEE Transactions on Systems, Man, and Cybernetics 23(6): 1752-1767.

    Google Scholar 

  • Lozano, J. A., Larrañaga, P. & Graña, M. (1996). Partitional Cluster Analysis with Genetic Algorithms: Searching for the Number of Clusters. Fifth Conference of International Federation of Classification Societies, 251-252. Kobe, Japan.

  • Matthews, R. A. J. (1993). The Use of Genetic Algorithms in Cryptanalysis. Cryptologia XVII(2): 187-201.

    Google Scholar 

  • Michalewicz, Z. (1992). Genetic Algorithms + Data Structures = Evolution Programs. Berlin Heidelberg: Springer Verlag.

    Google Scholar 

  • Mühlenbein, H., Gorges-Schleuter, M. & Krämer, O. (1987). New Solutions to the Mapping Problem of Parallel Systems: The Evolution Approach. Parallel Computing 4: 269-279.

    Google Scholar 

  • Mühlenbein, H., Gorges-Schleuter, M. & Krämer, O. (1988). Evolution Algorithms in Combinatorial Optimization. Parallel Computing 7: 65-85.

    Google Scholar 

  • Mühlenbein, H. (1989). Parallel Genetic Algorithms, Population Genetics and Combinatorial Optimization. In Schaffer, J. (ed.) Proceedings on the Third International Conference on Genetic Algorithms, 416-421. Los Altos, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Mühlenbein, H. & Kindermann, J. (1989). The Dynamics of Evolution and Learning — Towards Genetic Neural Networks. In Pfeiffer, J. (ed.) Connectionism in Perspectives.

  • Mühlenbein, H. (1991). Evolution in Time and Space — The Parallel Genetic Algorithm. In Rawlins, G. (ed.) Foundations of Genetic Algorithms. Los Altos, CA: Morgan Kaufmann.

    Google Scholar 

  • Oliver, I. M., Smith, D. J. & Holland, J. R. C. (1987). A Study of Permutation Crossover Operators on the TSP. In Grefenstette, J. J. (ed.) Genetic Algorithms and Their Applications: Proceedings of the Second International Conference, 224-230. Hillsdale, New Jersey: Lawrence Erlbaum.

    Google Scholar 

  • Or, I. (1976). Travelling Salesman-Type Combinatorial Problems and Their Relation to the Logistics of Regional Blood Banking. PhD Thesis, Northwestern University.

  • Prinetto, P., Rebaudengo, M. & Sonza Reorda, M. (1993). Hybrid Genetic Algorithms for the Traveling Salesman Problem. In Albrecht, R. F., Reeves, C. R. & Steele, N. C. (eds.) Artificial Neural Nets and Genetic Algorithms, 559-566. Wien: Springer-Verlag.

    Google Scholar 

  • Rechenberg, I. (1973). Optimierung Technischer Systeme Nach Prinzipien der Biologischen Information. Stuttgart: Frommann Verlag.

    Google Scholar 

  • Reinelt, G. (1991). TSPLIB — A Traveling Salesman Library. ORSA Journal on Computing 3(4): 376-384.

    Google Scholar 

  • Schaffer, J. (ed.) (1989). Proceedings on the Third International Conference on Genetic Algorithms. Los Altos, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Schwefel, H.P. (1975). Evolutionsstrategie und Numerische Optimierung. Doctoral Thesis Diss. D 83, TU Berlin.

  • Seniw, D. (1991). A Genetic Algorithm for the Traveling Salesman Problem. MSc Thesis, University of North Carolina at Charlotte.

  • Spillman, R., Janssen, M., Nelsonn B. & Kepner, M. (1993). Use of a Genetic Algorithm in the Cryptanalysis Simple Substitution Ciphers. Cryptologia XVII(1): 31-44.

    Google Scholar 

  • SPSS-X, User's Guide (1988). 3rd Edition.

  • Starkweather, T., McDaniel, S., Mathias, K., Whitley, C. & Whitley, D. (1991). A Comparison of Genetic Sequencing Operators. In Belew, R. & Booker, L. (eds.) Proceedings on the Fourth International Conference on Genetic Algorithms, 69-76. Los Altos, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Suh, J. Y. & Van Gucht, D. (1987). Incorporating Heuristic Information into Genetic Search. In Grefenstette, J. J. (ed.) Genetic Algorithms and Their Applications: Proceedings of the Second International Conference, 100-107. Hillsdale, New Jersey: Lawrence Erlbaum.

    Google Scholar 

  • Syswerda, G. (1991). Schedule Optimization Using Genetic Algorithms. In Davis, L. (ed.) Handbook of Genetic Algorithms, 332-349. New York: Van Nostrand Reinhold.

    Google Scholar 

  • Ulder, N. L. J., Aarts, E. H. L., Bandelt, H.-J., Van Laarhoven, P. J. M. & Pesch, E. (1990). Genetic Local Search Algorithms for the Traveling Salesman Problem. In Parallel Problem Solving from Nature, 106-116. Berlin Heidelberg: Springer-Verlag.

    Google Scholar 

  • Whitley, D., Starkweather, T. & D'Ann Fuquay (1989). Scheduling Problems and Travelling Salesman: The Genetic Edge Recombination Operator. In Schaffer, J. (ed.) Proceedings on the Third International Conference on Genetic Algorithms, 133-140. Los Altos, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Whitley, D., Starkweather, T. & Shaner, D. (1991). The Traveling Salesman and Sequence Scheduling: Quality Solutions Using Genetic Edge Recombination. In Davis, L. (ed.) Handbook of Genetic Algorithms, 350-372. New York: Van Nostrand Reinhold.

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Computer Science and Artificial Intelligence, University of the Basque Country, P.O. Box 649, E-20080, San Sebastián, The Basque Country, Spain

    P. Larrañaga, C.M.H. Kuijpers, R.H. Murga, I. Inza & S. Dizdarevic

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  1. P. Larrañaga
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  2. C.M.H. Kuijpers
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  3. R.H. Murga
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  4. I. Inza
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  5. S. Dizdarevic
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Larrañaga, P., Kuijpers, C., Murga, R. et al. Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators. Artificial Intelligence Review 13, 129–170 (1999). https://doi.org/10.1023/A:1006529012972

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