Abstract
This paper presents an evolutionary algorithm for multi-objective optimization problems, based on the Biased Random-Key Genetic Algorithms and on the Elitist Non-dominated Sorting Genetic Algorithm. Computational experiments applied to the Bi-Objective Travelling Salesman Problem compared our algorithm with other well-known multi-objective evolutionary algorithms from the literature. The results show that our methodology consistently outperformed the other approaches with respect to the hypervolumes from the obtained non-dominated fronts.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
References
Applegate, D.L., Bixby, R.E., Chvatál, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, Princeton (2007)
Bean, J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 6(2), 154–160 (1994)
Chagas, J.B., Blank, J., Wagner, M., Souza, M.J., Deb, K.: A non-dominated sorting based customized random-key genetic algorithm for the bi-objective traveling thief problem. J. Heurist. 27(3), 267–301 (2021)
Damm, R.B., Ronconi, D.P.: A multi-objective biased random-key genetic algorithm for service technician routing and scheduling problem. In: Mes, M., Lalla-Ruiz, E., Voß, S. (eds.) ICCL 2021. LNCS, vol. 13004, pp. 471–486. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-87672-2_31
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Gonçalves, J.F., Resende, M.G.: Biased random-key genetic algorithms for combinatorial optimization. J. Heurist. 17(5), 487–525 (2011)
Lacevic, B., Amaldi, E.: Ectropy of diversity measures for populations in Euclidean space. Inf. Sci. 181(11), 2316–2339 (2011)
Li, X.: A non-dominated sorting particle swarm optimizer for multiobjective optimization. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 37–48. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-45105-6_4
Lucena, M.L., Andrade, C.E., Resende, M.G., Miyazawa, F.K.: Some extensions of biased random-key genetic algorithms. In: Proceedings of the 46th Brazilian Symposium of Operational Research, pp. 1–12 (2014)
Lust, T., Jaszkiewicz, A.: Speed-up techniques for solving large-scale biobjective TSP. Comput. Oper. Res. 37(3), 521–533 (2010)
Shang, K., Ishibuchi, H., He, L., Pang, L.M.: A survey on the hypervolume indicator in evolutionary multiobjective optimization. IEEE Trans. Evol. Comput. 25(1), 1–20 (2021)
Shim, V.A., Tan, K.C., Chia, J.Y., Chong, J.K.: Evolutionary algorithms for solving multi-objective travelling salesman problem. Flex. Serv. Manuf. J. 23(2), 207–241 (2011)
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Pauleti Mendes, L.H., Usberti, F.L., San Felice, M.C. (2023). An Evolutionary Algorithm Applied to the Bi-Objective Travelling Salesman Problem. In: Di Gaspero, L., Festa, P., Nakib, A., Pavone, M. (eds) Metaheuristics. MIC 2022. Lecture Notes in Computer Science, vol 13838. Springer, Cham. https://doi.org/10.1007/978-3-031-26504-4_42
Download citation
DOI: https://doi.org/10.1007/978-3-031-26504-4_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-26503-7
Online ISBN: 978-3-031-26504-4
eBook Packages: Computer ScienceComputer Science (R0)