# Genetic algorithms for the traveling salesman problem

Genetic Algorithms

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## Abstract

This paper is a survey of genetic algorithms for the traveling salesman problem. Genetic algorithms are randomized search techniques that simulate some of the processes observed in natural evolution. In this paper, a simple genetic algorithm is introduced, and various extensions are presented to solve the traveling salesman problem. Computational results are also reported for both random and classical problems taken from the operations research literature.

### Keywords

Traveling salesman problem genetic algorithms stochastic search## Preview

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### References

- [1]E.H.L. Aarts, J.H.M. Korst and P.J.M. van Laarhoven, A quantitative analysis of the simulated annealing algorithm: A case study for the traveling salesman problem, J. Statist. Phys. 50(1988)189–206.CrossRefGoogle Scholar
- [2]J.D. Bagley, The behavior of adaptive systems which employ genetic and correlation algorithms, Doctoral Dissertation, University of Michigan, Dissertation Abstracts International 28(12), 5106B (1967).Google Scholar
- [3]J. Bentley, Fast algorithms for geometric salesman problems, ORSA J. Comp. 4(1992)387–411.Google Scholar
- [4]J.L. Blanton and R.L. Wainwright, Multiple vehicle routing with time and capacity constraints using genetic algorithms, in:
*Proc. 5th Int. Conf. on Genetic Algorithms (ICGA '93)*, University of Illinois at Urbana-Champaign, Champaign, IL (1993) pp. 452–459.Google Scholar - [5]L. Bodin, B.L. Golden, A. Assad and M. Ball, Routing and scheduling of vehicles and crews: The state of the art, Comp. Oper. Res. 10(1983)63–211.CrossRefGoogle Scholar
- [6]R.M. Brady, Optimization strategies gleaned from biological evolution, Nature 317(1985)804–806.CrossRefGoogle Scholar
- [7]H. Braun, On solving travelling salesman problems by genetic algorithms, in:
*Parallel Problem-Solving from Nature*, ed. H.P. Schwefel and R. Manner, Lecture Notes in Computer Science 496 (Springer) pp. 129–133.Google Scholar - [8]V. Cerny, Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm, J. Optim. Theory Appl. 45(1985)41–55.CrossRefGoogle Scholar
- [9]L. Davis, Applying adaptive algorithms to epistactic domains, in:
*Proc. Int. Joint Conf. on Artificial Intelligence*(*IJCAI '85*), Los Angeles, CA (1985) pp. 162–164.Google Scholar - [10]K.A. De Jong, An analysis of the behavior of a class of genetic adaptive systems, Doctoral Dissertation, University of Michigan, Dissertation Abstracts International 36(10), 5140B (1975).Google Scholar
- [11]C.N. Fiechter, A parallel tabu search algorithm for large scale traveling salesman problems, Working paper 90/1, Department of Mathematics, Ecole Polytechnique Fédérale de Lausanne, Switzerland (1990).Google Scholar
- [12]L.J. Fogel, A.J. Owens and M.J. Walsh,
*Artificial Intelligence through Simulated Evolution*(Wiley, 1966).Google Scholar - [13]B.R. Fox and M.B. McMahon, Genetic operators for sequencing problems, in:
*Foundations of Genetic Algorithms*, ed. J.E. Rawlins (Morgan Kaufmann, 1991) pp. 284–300.Google Scholar - [14]P.S. Gabbert, D.E. Brown, C.L. Huntley, B.P. Markowitz and D.E. Sappington, A system for learning routes and schedules with genetic algorithms, in:
*Proc. 4th Int. Conf. on Genetic Algorithms (ICGA '91)*, University of California at San Diego, San Diego, CA (1991) pp. 430–436.Google Scholar - [15]M. Gendreau, A. Hertz and G. Laporte, New insertion and post-optimization procedures for the traveling salesman problem, Oper. Res. 40(1992)1086–1094.Google Scholar
- [16]F. Glover, Tabu search, Part I, ORSA J. Comp. 1(1989)190–206.Google Scholar
- [17]F. Glover, Tabu Search, Part II, ORSA J. Comp. 2(1990)4–32.Google Scholar
- [18]D.E. Goldberg and R. Lingle, Alleles, loci and the traveling salesman problem, in:
*Proc. Ist Int. Conf. on Genetic Algorithms (ICGA '85)*, Carnegie-Mellon University, Pittsburg, PA (1985) pp. 154–159.Google Scholar - [19]B.L. Golden and W.R. Stewart, Empirical analysis of heuristics, in:
*The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization*, ed. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys (Wiley, 1985).Google Scholar - [20]D.E. Goldberg,
*Genetic Algorithms in Search, Optimization and Machine Learning*(Addison-Wesley, 1989).Google Scholar - [21]M. Gorges-Schleuter, ASPARAGOS: An asynchronous parallel genetic optimization strategy, in:
*Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89)*, George Mason University, Fairfax, VA (1989) pp. 422–427.Google Scholar - [22]J. Grefenstette, R. Gopal, B.J. Rosmaita and D.V. Gucht, Genetic algorithms for the traveling salesman problem, in:
*Proc. 1st. Int. Conf. on Genetic Algorithms (ICGA '85)*, Carnegie-Mellon University, Pittsburgh, PA (1985) pp. 160–168.Google Scholar - [23]J. Grefenstette, Incorporating problem specific knowledge into genetic algorithms, in:
*Genetic Algorithms and Simulated Annealing*, ed. L. Davis (Morgan Kaufmann, 1987) pp. 42–60.Google Scholar - [24]M. Grötschel and O. Holland, Solution of large-scale symmetric traveling salesman problems, Report 73, Institut für Mathematik, Universität Augsburg (1988).Google Scholar
- [25]M. Held and R.M. Karp, The traveling salesman problem and minimum spanning trees, Oper. Res. 18(1970)1138–1162.Google Scholar
- [26]J.H. Holland,
*Adaptation in Natural and Artificial Systems*(The University of Michigan Press, Ann Arbor, 1975); reprinted by MIT Press, 1992.Google Scholar - [27]A. Homaifar, S. Guan and G. Liepins, A new approach to the traveling salesman problem by genetic algorithms, in:
*Proc. 5th Int. Conf. on Genetic Algorithms (ICGA '93)*, University of Illinois at Urbana-Champaign, Champaign, IL (1993) pp. 460–466.Google Scholar - [28]J.J. Hopfield and D.W. Tank, Neural computation of decisions in optimization problems, Biol. Cybern. 52(1985)141–152.PubMedGoogle Scholar
- [29]P. Jog, J.Y. Suh and D.V. Gucht, The effects of population size, heuristic crossover and local improvement on a genetic algorithm for the traveling salesman problem, in:
*Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89)*, George Mason University, Fairfax, VA (1989) pp. 110–115.Google Scholar - [30]D.S. Johnson, Local optimization and the traveling salesman problem, in:
*Automata, Languages and Programming*, ed. G. Goos and J. Hartmanis, Lecture Notes in Computer Science 443 (Springer, 1990) pp. 446–461.Google Scholar - [31]R.L. Karg and G.L. Thompson, A heuristic approach to solving traveling salesman problems, Manag. Sci. 10(1964)225–248.Google Scholar
- [32]S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, Optimization by simulated annealing, Science 220(1983)671–680.Google Scholar
- [33]P.D. Krolak, W. Felts and G. Marble, A man-machine approach toward solving the traveling salesman problem, Commun. ACM 14(1971)327–334.CrossRefGoogle Scholar
- [34]G. Laporte, The traveling salesman problem: An overview of exact and approximate algorithms, Euro. J. Oper. Res. 59(1992)231–247.CrossRefGoogle Scholar
- [35]E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys,
*The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization*(Wiley, 1985).Google Scholar - [36]G.E. Liepins, M.R. Hilliard, M. Palmer and M. Morrow, Greedy genetics, in:
*Proc. 2nd Int. Conf. on Genetic Algorithms (ICGA '87)*, Massachusetts Institute of Technology, Cambridge, MA (1987) pp. 90–99.Google Scholar - [37]G.E. Liepins, M.R. Hilliard, J. Richardson and M. Palmer, Genetic algorithm applications to set covering and traveling salesman problems, in:
*Operations Research and Artificial Intelligence: The Integration of Problem Solving Strategies*, ed. Brown and White (Kluwer Academic, 1990) pp. 29–57.Google Scholar - [38]S. Lin, Computer solutions of the traveling salesman problem, Bell Syst. Tech. J. 44(1965) 2245–2269.Google Scholar
- [39]S. Lin and B. Kernighan, An effective heuristic algorithm for the traveling salesman problem, Oper. Res. 21(1973)498–516.Google Scholar
- [40]M. Malek, M. Guruswamy, M. Pandya and H. Owens, Serial and parallel simulated annealing and tabu search algorithms for the traveling salesman problem, Ann. Oper. Res. 21(1989)59–84.CrossRefGoogle Scholar
- [41]Z. Michalewicz and C.Z. Janikow, Handling constraints in genetic algorithms, in:
*Proc. 4th Int. Conf. on Genetic Algorithms (ICGA '91)*, University of California at San Diego, San Diego, CA (1991) pp. 151–157.Google Scholar - [42]Z. Michalewicz, G.A. Vigaux and M. Hobbs, A nonstandard genetic algorithm for the nonlinear transportation problem, ORSA J. Comp. 3(1991)307–316.Google Scholar
- [43]H. Mulhenbein, M. Gorges-Schleuter and O. Kramer, New solutions to the mapping problem of parallel systems — the evolution approach, Parallel Comp. 4(1987)269–279.CrossRefGoogle Scholar
- [44]H. Mulhenbein, M. Gorges-Schleuter and O. Kramer, Evolution algorithms in combinatorial optimization, Parallel Comp. 7(1988)65–85.CrossRefGoogle Scholar
- [45]H. Mulhenbein, Evolution in time and space — the parallel genetic algorithm, in:
*Foundations of genetic algorithms*, ed. G.J.E. Rawlins (Morgan Kaufmann, 1991) pp. 316–337.Google Scholar - [46]K.E. Nygard and C.H. Yang, Genetic algorithms for the traveling salesman problem with time windows, in:
*Computer Science and Operations research: New Developments in their Interfaces*, ed. O. Balci, R. Sharda and S.A. Zenios (Pergamon, 1992) pp. 411–423.Google Scholar - [47]I.M. Oliver, D.J. Smith and J.R.C. Holland, A study of permutation crossover operators on the traveling salesman problem, in:
*Proc. 2nd Int. Conf. on Genetic Algorithms (ICGA '87)*, Massachusetts Institute of Technology, Cambridge, MA (1987) pp. 224–230.Google Scholar - [48]I. Or, Traveling salesman-type combinatorial optimization problems and their relation to the logistics of regional blood banking, Ph.D. Dissertation, Northwestern University, Evanston, IL (1976).Google Scholar
- [49]M. Padberg and G. Rinaldi, Optimization of a 532-city symmetric traveling salesman problem by branch-and-cut, Oper. Res. Lett. 6(1987)1–7.CrossRefMathSciNetGoogle Scholar
- [50]M. Padberg and G. Rinaldi, A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems, Technical Report R-247, Instituto di Analisi dei Sistemi ed Informatica. Consiglio Nazionale delle Ricerche, Roma (1988).Google Scholar
- [51]M. Padberg and G. Rinaldi, Facet identification for the symmetric traveling salesman problem, Math. Progr. 47(1990)219–257.CrossRefGoogle Scholar
- [52]J.T. Richardson, M. Palmer, G.E. Liepins and M. Hilliard, Some guidelines for genetic algorithms with penalty functions, in:
*Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89)*, George Mason University, Fairfax, VA (1989) pp. 191–197.Google Scholar - [53]D. Rosenkrantz, R. Sterns and P. Lewis, An analysis of several heuristics for the traveling salesman problem, SIAM J. Comp. 6(1977)563–581.CrossRefGoogle Scholar
- [54]W. Siedlecki and J. Sklansky, Constrained genetic optimization via dynamic reward-penalty balancing and its use in pattern recognition, in:
*Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89)*, George Mason University, Fairfax, VA (1989) pp. 141–150.Google Scholar - [55]T. Starkweather, S. McDaniel, K. Mathias, D. Whitley and C. Whitley, A comparison of genetic sequencing operators, in:
*Proc. 4th Int. Conf. on Genetic Algorithms (ICGA '91)*, University of California at San Diego, San Diego, CA (1991) pp. 69–76.Google Scholar - [56]J.Y. Suh and D.V. Gucht, Incorporating heuristic information into genetic search, in:
*Proc. 2nd Int. Conf. on Genetic Algorithms (ICGA '87)*, Massachusetts Institute of Technology, Cambridge, MA (1987) pp. 100–107.Google Scholar - [57]G. Syswerda, Uniform crossover in genetic algorithms, in:
*Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89)*, George Mason University, Fairfax, VA (1989) pp. 2–9.Google Scholar - [58]G. Syswerda, Schedule optimization using genetic algorithms, in:
*Handbook of Genetic Algorithms*, ed. L. Davis (Van Nostrand Reinhold, 1990) pp. 332–349.Google Scholar - [59]S.R. Thangiah, K.E. Nygard and P. Juell, GIDEON: A genetic algorithm system for vehicle routing problems with time windows, in:
*Proc. 7th IEEE Conf. on Applications of Artificial Intelligence*, Miami, FL (1991) pp. 322–328.Google Scholar - [60]S.R. Thangiah and K.E. Nygard, School bus routing using genetic algorithms, in:
*Proc. Applications of Artificial Intelligence X: Knowledge Based Systems*, Orlando, FL (1992) pp. 387–397.Google Scholar - [61]S.R. Thangiah and A.V. Gubbi, Effect of genetic sectoring on vehicle routing problems with time windows, in:
*Proc. IEEE Int. Conf. on Developing and Managing Intelligent System Projects*, Washington, DC (1993) pp. 146–153.Google Scholar - [62]S.R. Thangiah and K.E. Nygard, Dynamic trajectory routing using an adaptive search strategy, in:
*Proc. ACM Symp. on Applied Computing*, Indianapolis, IN (1993) pp. 131–138.Google Scholar - [63]S.R. Thangiah, R. Vinayagamoorty and A.V. Gubbi, Vehicle routing and time deadlines using genetic and local algorithms, in:
*Proc. 5th Int. Conf. on Genetic Algorithms (ICGA '93)*, University of Illinois at Urbana-Champaign, Champaign, IL (1993) pp. 506–515.Google Scholar - [64]N.L.J. Ulder, E.H.L. Aarts, H.J. Bandelt, P.J.M. van Laarhoven and E. Pesch, Genetic local search algorithms for the traveling salesman problem, in:
*Parallel Problem-Solving from Nature*, ed. H.P. Schwefel and R. Manner, Lecture Notes in Computer Science 496 (Springer, 1991) pp. 109–116.Google Scholar - [65]G.A Vigaux and Z. Michalewicz, A genetic algorithm for the linear transportation problem, IEEE Trans. Syst., Man, Cybern. 21(1991)445–452.Google Scholar
- [66]D. Whitley, The genitor algorithm and selection pressure: Why rankbased allocation of reproductive trials is best, in:
*Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89)*, George Mason University, Fairfax, VA (1989) pp. 116–121.Google Scholar - [67]D. Whitley, T. Starkweather and D. Fuquay, Scheduling problems and traveling salesmen: The genetic edge recombination operator, in:
*Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89)*, George Mason University, Fairfax, VA (1989) pp. 133–140.Google Scholar - [68]D. Whitley, T. Starkweather and D. Shaner, Traveling saleman and sequence scheduling: Quality solutions using genetic edge recombination, in:
*Handbook of Genetic Algorithms*, ed. L. Davis (Van Nostrand Reinhold, 1990) pp. 350–372.Google Scholar

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© J.C. Baltzer AG, Science Publishers 1996