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A Hybrid Approach GABC-LS to Solve mTSP

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Optimization, Learning Algorithms and Applications (OL2A 2022)

Abstract

The Multiple Traveling Salesman Problem (mTSP) is an interesting combinatorial optimization problem due to its numerous real-life applications. It is a problem where m salesmen visit a set of n cities so that each city is visited once. The primary purpose is to minimize the total distance traveled by all salesmen. This paper presents a hybrid approach called GABC-LS that combines an evolutionary algorithm with the swarm intelligence optimization ideas and a local search method. The proposed approach was tested on three instances and produced some better results than the best-known solutions reported in the literature.

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References

  1. Agarwala, R., Applegate, D., Maglott, D., Schuler, G.S.A.: A fast and scalable radiation hybrid map construction and integration strategy. Genome Res. 10, 350–364 (2000)

    Article  Google Scholar 

  2. Angel, R.D., Caudle, W., Noonan, R., Whinson, A.: Computer assisted school bus scheduling. Manag. Sci. 10, 279–288 (1972)

    Article  Google Scholar 

  3. Basu, S.: Tabu search implementation on traveling salesman problem and its variations: a literature survey. Am. J. Oper. Res. 2(2) (2012)

    Google Scholar 

  4. Calado, F., Ladeira, A.: Traveling salesman problem: a comparative approach by using artificial intelligence techniques. Centro Universitário de Belo Horizonte, Belo Horizonte, MG (2011)

    Google Scholar 

  5. Cheikhrouhou, O., Khoufi, I.: A comprehensive survey on the multiple traveling salesman problem: applications, approaches and taxonomy. Comput. Sci. Rev. 40, 100369 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  6. Conesa-Muñoz, J., Pajares, G., Ribeiro, A.: Mix-opt: a new route operator for optimal coverage path planning for a fleet in an agricultural environment. Expert Syst. Appl. 54, 364–378 (2016)

    Article  Google Scholar 

  7. Croes, G.A.: A method for solving traveling-salesman problems. Oper. Res. 6(6), 791–812 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  8. Darwin, C.: On the origin of species by means of natural selection, or the preservation of favoured races in the struggle for life, 6th edn. John Murray, London (1859). http://www.gutenberg.org/etext/1228

  9. Falkenauer, E.: Genetic Algorithms and Grouping Problems. Wiley, New York (1992)

    MATH  Google Scholar 

  10. Karapetyan, D., Gutin, G.: Lin-kernighan heuristic adaptations for the generalized traveling salesman problem. Eur. J. Oper. Res. 208(3), 221–232 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Katoch, S., Chauhan, S.S., Kumar, V.: A review on genetic algorithm: past, present, and future. Multimedia Tools Appl. 80(5), 8091–8126 (2020). https://doi.org/10.1007/s11042-020-10139-6

    Article  Google Scholar 

  12. Kitjacharoenchai, P., Ventresca, M., Moshref-Javadi, M., Lee, S., Tanchoco, J., Brunese, P.: Multiple traveling salesman problem with drones: mathematical model and heuristic approach. Comput. Ind. Eng. 129, 14–30 (2019). https://doi.org/10.1016/j.cie.2019.01.020

    Article  Google Scholar 

  13. Malik, W., Rathinam, S., Darbha, S.: An approximation algorithm for a symmetric generalized multiple depot, multiple travelling salesman problem. Oper. Res. Lett. 35(6), 747–753 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Malmborg, C.: A genetic algorithm for service level based vehicle scheduling. Eur. J. Oper. Res. 93(1), 121–134 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  15. Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. Evol. Comput. 4(1), 1–32 (1996)

    Article  Google Scholar 

  16. Morrison, D.R., Jacobson, S.H., Sauppe, J.J., Sewell, E.C.: Branch-and-bound algorithms: a survey of recent advances in searching, branching, and pruning. Discret. Optim. 19, 79–102 (2016). https://doi.org/10.1016/j.disopt.2016.01.005

    Article  MathSciNet  MATH  Google Scholar 

  17. Potvin, J., Lapalme, G., Rousseau, J.: A generalized k-opt exchange procedure for the MTSP. Inf. Syst. Oper. Res. 27(4), 474–481 (1989)

    Google Scholar 

  18. Rahbari, M., Jahed, A.: A hybrid simulated annealing algorithm for travelling salesman problem with three neighbor generation structures. In: 10th International Conference of Iranian Operations Research Society (ICIORS 2017) (2017)

    Google Scholar 

  19. Ratliff, H., Rosenthal, A.: Order-picking in a rectangular warehouse: a solvable case for the traveling salesman problem. Georgia Institute of Technology, PDRC Report Series, PDRC Report Series No. 81-10 (1981)

    Google Scholar 

  20. Reeves, C.: Modern Heuristic Techniques for Combinatorial Problems. Mcgraw-Hill transfer from Blackwell Scientific (1993)

    Google Scholar 

  21. Soylu, B.: A general variable neighborhood search heuristic for multiple traveling salesmen problem. Comput. Ind. Eng. 90, 390–401 (2015). https://doi.org/10.1016/j.cie.2015.10.010

    Article  Google Scholar 

  22. Tang, L., Liu, J., Rong, A., Yang, Z.: A multiple traveling salesman problem model for hot rolling scheduling in Shangai Baoshan iron & steel complex. Eur. J. Oper. Res. 124, 267–282 (2000)

    Article  MATH  Google Scholar 

  23. Trigui, S., Cheikhrouhou, O., Koubaa, A., Zarrad, A., Youssef, H.: An analytical hierarchy process-based approach to solve the multi-objective multiple traveling salesman problem. Intel. Serv. Robot. 11(4), 355–369 (2018). https://doi.org/10.1007/s11370-018-0259-8

    Article  Google Scholar 

  24. Violina, S.: Analysis of brute force and branch & bound algorithms to solve the traveling salesperson problem (TSP). Turkish J. Comput. Math. Educ. 12(8), 1226–1229 (2021)

    Google Scholar 

  25. Wichmann, A., Korkmaz, T.: Smooth path construction and adjustment for multiple mobile sinks in wireless sensor networks. Comput. Commun. 72, 93–106 (2015)

    Article  Google Scholar 

  26. Zhao, W., Meng, Q., Chung, P.: A heuristic distributed task allocation method for multivehicle multitask problems and its application to search and rescue scenario. IEEE Trans. Cybern. 46(4), 902–915 (2015)

    Article  Google Scholar 

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Acknowledgments

This work is financed by National Funds through the Portuguese funding agency, FCT – Fundação para a Ciência e a Tecnologia, within project UIDB/50014/2020.

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Correspondence to Sílvia de Castro Pereira .

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de Castro Pereira, S., Solteiro Pires, E.J., B. de Moura Oliveira, P. (2022). A Hybrid Approach GABC-LS to Solve mTSP. In: Pereira, A.I., Košir, A., Fernandes, F.P., Pacheco, M.F., Teixeira, J.P., Lopes, R.P. (eds) Optimization, Learning Algorithms and Applications. OL2A 2022. Communications in Computer and Information Science, vol 1754. Springer, Cham. https://doi.org/10.1007/978-3-031-23236-7_36

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  • DOI: https://doi.org/10.1007/978-3-031-23236-7_36

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