Abstract
We consider two approaches to formulation and solving of optimal recombination problems arising as supplementary problems in genetic algorithms for the Asymmetric Travelling Salesman Problem and the Makespan Minimization Problem on a Single Machine. All four optimal recombination problems under consideration are NP-hard but relatively fast exponential-time algorithms are known for solving them. The experimental evaluation carried out in this paper shows that the two approaches to optimal recombination are competitive with each other.
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References
Buriol, L.S., Franca, P.M., Moscato, P.: A new memetic algorithm for the asymmetric traveling salesman problem. J. Heuristics 10, 483–506 (2004)
Chvatal, V.: Probabilistic methods in graph theory. Ann. Oper. Res. 1, 171–182 (1984)
Cirasella, J., Johnson, D.S., McGeoch, L.A., Zhang, W.: The asymmetric traveling salesman problem: algorithms, instance generators, and tests. In: Buchsbaum, A.L., Snoeyink, J. (eds.) ALENEX 2001. LNCS, vol. 2153, pp. 32–59. Springer, Heidelberg (2001)
Cook, W., Seymour, P.: Tour merging via branch-decomposition. INFORMS J. Comput. 15(2), 233–248 (2003)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Cotta, C., Alba, E., Troya, J.M.: Utilizing dynastically optimal forma recombination in hybrid genetic algorithms. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 305–314. Springer, Heidelberg (1998)
Cotta, C., Troya, J.M.: Genetic forma recombination in permutation flowshop problems. Evol. Comput. 6(1), 25–44 (1998)
Dantzig, G., Fulkerson, R., Johnson, S.: Solution of a large-scale traveling salesman problem. Oper. Res. 2, 393–410 (1954)
Dongarra, J.J.: Performance of various computers using standard linear equations software. Technical Report No. CS-89-85, University of Manchester, 110 p. (2014)
Eppstein, D.: The traveling salesman problem for cubic graphs. J. Graph Algorithms Appl. 11(1) (2007)
Eremeev, A.V., Kovalenko, J.V.: Optimal recombination in genetic algorithms for combinatorial optimization problems: Part II. Yugoslav J. Oper. Res. 24(2), 165–186 (2014)
Fischetti, M., Toth, P.: An additive bounding procedure for the asymmetric travelling salesman problem. Math. Program. A 53, 173–197 (1992)
Fischetti, M., Toth, P.: A polyhedral approach to the asymmetric travelling salesman problem. Manage. Sci. 43, 1520–1536 (1997)
Fischetti, M., Toth, P., Vigo, D.: A branch and bound algorithm for the capacitated vehicle routing problem on directed graphs. Oper. Res. 42, 846–859 (1994)
Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-completeness. W.H. Freeman and Company, San Francisco (1979)
Goldberg, D., Thierens, D.: Elitist recombination: an integrated selection recombination GA. In: Proceedings of the First IEEE World Congress on Computational Intelligence. vol. 1, pp. 508–512. IEEE Service Center, Piscataway, New Jersey (1994)
Hazir, O., Günalay, Y., Erel, E.: Customer order scheduling problem: a comparative metaheuristics study. Int. Journ. Adv. Manuf. Technol. 37, 589–598 (2008)
Holland, J.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)
Mood, A.M., Graybill, F.A., Boes, D.C.: Introduction to the Theory of Statistics, 3rd edn. McGraw-Hill, New York (1973)
Nagata, Y., Soler, D.: A new genetic algorithm for the asymmetric travelling salesman problem. Expert Syst. Appl. 39(10), 8947–8953 (2012)
Radcliffe, N.J.: The algebra of genetic algorithms. Ann. Math. Artif. Intell. 10(4), 339–384 (1994)
Reinelt, G.: TSPLIB - a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)
Serdyukov, A.I.: On travelling salesman problem with prohibitions. Upravlaemye systemi 1, 80–86 (1978). (in Russian)
Tinós, R., Whitley, D., Ochoa, G.: Generalized asymmetric partition crossover (GAPX) for the asymmetric TSP. In: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation, pp. 501–508. ACM, New York (2014)
Whitley, D., Starkweather, T., Shaner, D.: The traveling salesman and sequence scheduling: quality solutions using genetic edge recombination. In: Handbook of Genetic Algorithms, pp. 350–372. Van Nostrand Reinhold, New York (1991)
Yagiura, M., Ibaraki, T.: The use of dynamic programming in genetic algorithms for permutation problems. Eur. Jour. Oper. Res. 92, 387–401 (1996)
Zhang, W.: Depth-first branch-and-bound versus local search: a case study. In: Proceedings of 17th National Conference on Artificial Intelligence, pp. 930–935. Austin, TX (2000)
Acknowledgements
This research is supported by the Russian Science Foundation grant 15-11-10009, except for Subsect. 3.2 which is supported by RFBI grant 15-01-00785.
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Eremeev, A.V., Kovalenko, J.V. (2016). Experimental Evaluation of Two Approaches to Optimal Recombination for Permutation Problems. In: Chicano, F., Hu, B., GarcÃa-Sánchez, P. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2016. Lecture Notes in Computer Science(), vol 9595. Springer, Cham. https://doi.org/10.1007/978-3-319-30698-8_10
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DOI: https://doi.org/10.1007/978-3-319-30698-8_10
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