Abstract
In this research paper, we address the Bi-objective Traveling Salesman Problem (BTSP), which involves minimizing two conflicting objectives: travel time and monetary cost. To tackle this problem, we propose a novel three-Phase Hybrid Evolutionary Algorithm (3PHEA) that combines the Lin-Kernighan Heuristic, an enhanced Non-Dominated Sorting Genetic Algorithm, and a Pareto Variable Neighborhood Search. We conduct a comparative study comparing our approach with three existing methods specifically designed for solving BTSP. Our evaluation includes 14 instances of varying degrees of difficulty and different sizes. To assess the performance of the algorithms, we employ multi-objective performance indicators. The results of our study demonstrate that 3PHEA outperforms the existing approaches by a significant margin. It achieves coverage of up to 80% of the true Pareto fronts, indicating its superiority in solving the BTSP.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Agrawal, A., Ghune, N., Prakash, S., Ramteke, M.: Evolutionary algorithm hybridized with local search and intelligent seeding for solving MTSP. Expert Syst. Appl. 181, 115192 (2021)
Applegate, D., Bixby, R., Chvatal, V., Cook, W.: Concorde TSP solver (2006). http://www.tsp.gatech.edu/concorde
Bergel, A., Bergel, A.: The traveling salesman problem. Agile Artificial Intelligence in Pharo: Implementing Neural Networks, Genetic Algorithms, and Neuroevolution, pp. 209–224 (2020)
Blank, J., Deb, K., Mostaghim, S.: Solving the bi-objective traveling thief problem with multi-objective evolutionary algorithms. In: Trautmann, H., et al. (eds.) Evolutionary Multi-Criterion Optimization, pp. 46–60 (2017)
Cai, X., Wang, K., Mei, Y., Li, Z., Zhao, J., Zhang, Q.: Decomposition-based Lin-Kernighan heuristic with neighborhood structure transfer for multi/many-objective traveling salesman problem. IEEE Transactions on Evolutionary Computation, pp. 1 (2022). https://doi.org/10.1109/TEVC.2022.3215174
Cheikhrouhou, O., Khoufi, I.: A comprehensive survey on the multiple traveling salesman problem: applications, approaches and taxonomy. Comput. Sci. Rev. 40, 100369 (2021). https://doi.org/10.1016/j.cosrev.2021.100369
Dib, O., Moalic, L., Manier, M.A., Caminada, A.: An advanced GA-VNS combination for multicriteria route planning in public transit networks. Expert Syst. Appl. 72, 67–82 (2017). https://doi.org/10.1016/j.eswa.2016.12.009
Dib, O.: Novel hybrid evolutionary algorithm for bi-objective optimization problems. Sci. Rep. 13(1), 4267 (2023). https://doi.org/10.1038/s41598-023-31123-8
Dib, O., Caminada, A., Manier, M.A., Moalic, L.: A memetic algorithm for computing multicriteria shortest paths in stochastic multimodal networks. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 103–104 (2017)
Dib, O., Manier, M.A., Moalic, L., Caminada, A.: Combining VNS with genetic algorithm to solve the one-to-one routing issue in road networks. Comput. Oper. Res. 78, 420–430 (2017). https://doi.org/10.1016/j.cor.2015.11.010
Florios, K., Mavrotas, G.: Generation of the exact pareto set in MTSP and set covering problems. Appl. Math. Comput. 237, 1–19 (2014)
George, T., Amudha, T.: Genetic algorithm based multi-objective optimization framework to solve traveling salesman problem. In: Sharma, H., Govindan, K., Poonia, R.C., Kumar, S., El-Medany, W.M. (eds.) Advances in Computing and Intelligent Systems. AIS, pp. 141–151. Springer, Singapore (2020). https://doi.org/10.1007/978-981-15-0222-4_12
Jin, Z., Dib, O., Luo, Y., Hu, B.: A non-dominated sorting memetic algorithm for the multi-objective travelling salesman problem. In: 2021 4th International Conference on Algorithms, Computing and Artificial Intelligence, pp. 1–6 (2021)
Khan, I., Maiti, M.K., Basuli, K.: MTSP: an ABC approach. Appl. Intell. 50(11), 3942–3960 (2020)
Kumar, R.: A survey on memetic algorithm and machine learning approach to traveling salesman problem. Int. J. Emerg. Technol. 11(1), 500–503 (2020)
Lust, T., Teghem, J.: Two-phase pareto local search for the BTSP. J. Heuristics 16(3), 475–510 (2010)
Mandal, A.K., Kumar Deva Sarma, P.: Novel applications of ant colony optimization with the traveling salesman problem in DNA sequence optimization. In: 2022 IEEE 2nd International Symposium on Sustainable Energy, Signal Processing and Cyber Security (iSSSC), pp. 1–6 (2022). https://doi.org/10.1109/iSSSC56467.2022.10051206
Michalak, K.: Evolutionary algorithm using random immigrants for the MTSP. Procedia Comput. Sci. 192, 1461–1470 (2021)
Moraes, D.H., Sanches, D.S., da Silva Rocha, J., Garbelini, J.M.C., Castoldi, M.F.: A novel multi-objective evolutionary algorithm based on subpopulations for the BTSP. Soft Comput. 23(15), 6157–6168 (2019)
Riquelme, N., Von Lücken, C., Baran, B.: Performance metrics in multi-objective optimization. In: 2015 Latin American Computing Conference, pp. 1–11 (2015)
Zheng, J., He, K., Zhou, J., Jin, Y., Li, C.M.: Combining reinforcement learning with Lin-Kernighan-Helsgaun algorithm for the traveling salesman problem. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, pp. 12445–12452 (2021)
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
Dib, O. (2023). Three-Phase Hybrid Evolutionary Algorithm for the Bi-Objective Travelling Salesman Problem. In: El Ayachi, R., Fakir, M., Baslam, M. (eds) Business Intelligence. CBI 2023. Lecture Notes in Business Information Processing, vol 484 . Springer, Cham. https://doi.org/10.1007/978-3-031-37872-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-031-37872-0_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-37871-3
Online ISBN: 978-3-031-37872-0
eBook Packages: Computer ScienceComputer Science (R0)