Abstract
The Traveling Salesman Problem (TSP) is a well known problem in operations research with various studies and applications. In this paper, we address a variant of the TSP in which the customers are divided into several priority groups and the order of servicing groups can be flexibly changed with a rule called the d-relaxed priority rule. The problem is called the Clustered Traveling Salesman Problem with Relaxed Priority Rule (CTSP-d). We propose two new Mixed Integer Linear Programming (MILP) models for the CTSP-d and a metaheuristic based on Iterated Local Search (ILS) with operators designed for or adapted to the problem. The experimental results obtained on the benchmark instances show that two new models performs better than previous ones, and ILS also proves its performance with 13 new best known solutions found and significant stability compared to existing metaheuristics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The data used to support the findings of this study are included in the article.
References
Ahmed ZH (2014) The ordered clustered travelling salesman problem: a hybrid genetic algorithm. Sci World J 2014:1–13
Alsheddy A (2018) A two-phase local search algorithm for the ordered clustered travelling salesman problem. Int J Metaheir 7(1):80–92
Anily S, Bramel J, Hertz A (1999) 5/3-approximation algorithm for the clustered traveling salesman tour and path problems. Oper Res Lett 24(1):29–35
Applegate DL, Bixby RE, Chvatál V, Cook WJ (2006) The traveling salesman problem: a computational study. Princeton, Princeton University Press
Chisman JA (1975) The clustered traveling salesman problem. Comput Oper Res 2(2):115–119
Dam TT, Thinh Nguyen D, Bui QT, Kien Do T (2019) On the traveling salesman problem with hierarchical objective function. In: 2019 11th international conference on knowledge and systems engineering (KSE), pp 1–5
Doan TT, Bostel N, Hà MH (2021) The vehicle routing problem with relaxed priority rules. EURO J Transp Logist 10:100039
Gavish B, Graves S (1978) The travelling salesman problem and related problems (working paper). In: Operations Research Center, Massachusetts Institute of Technology
Golden BL, Kovacs AA, Wasil EA (2014) Chapter 14: vehicle routing applications in disaster relief. In: Vehicle routing, society for industrial and applied mathematics, pp 409–436
Gutin G, Punnen AP (eds) (2007) The traveling salesman problem and its variations, combinatorial optimization, vol 12. Springer, Boston
Hà MH, Nguyen Phuong H, Tran Ngoc Nhat H, Langevin A, Trépanier M (2022) Solving the clustered traveling salesman problem with d-relaxed priority rule. Int Trans Oper Res 29(2):837–853
Laporte G, Palekar U (2002) Some applications of the clustered travelling salesman problem. J Oper Res Soc 53(9):972–976
Matai R, Singh S, Mittal ML (2010) Traveling salesman problem: an overview of applications, formulations, and solution approaches. In: Davendra D (ed) Traveling salesman problem, theory and applications, IntechOpen, Rijeka, chap 1
Morais VW, Mateus GR, Noronha TF (2014) Iterated local search heuristics for the vehicle routing problem with cross-docking. Expert Syst Appl 41(16):7495–7506
Pacheco T, Martinelli R, Subramanian A, Toffolo TAM, Vidal T (2022) Exponential-size neighborhoods for the pickup-and-delivery traveling salesman problem. Transp Sci 57(2):463–481
Panchamgam K, Xiong Y, Golden B, Dussault B, Wasil E (2013) The hierarchical traveling salesman problem. Optim Lett 7(7):1517–1524
Panchamgam KV (2011) Essays in retail operations and humanitarian logistics. PhD thesis, Robert H.Smith School of Business, University of Maryland (College Park, Md.)
Penna PHV, Subramanian A, Ochi LS (2013) An iterated local search heuristic for the heterogeneous fleet vehicle routing problem. J Heurist 19(2):201–232
Potvin JY, Guertin F (1998) A genetic algorithm for the clustered traveling salesman problem with a prespecified order on the clusters. Springer, Boston, pp 287–299
Reinelt G (1991) TSPLIB: a traveling salesman problem library. ORSA J Comput 3(4):376–384
Ropke S, Pisinger D (2006) An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transp Sci 40(4):455–472
Vansteenwegen P, Souffriau W, Vanden Berghe G, Van Oudheusden D (2009) Iterated local search for the team orienteering problem with time windows. Comput Oper Res 36(12):3281–3290
Acknowledgements
This paper is dedicated to the memory of the last author Vu Hoang Vuong Nguyen, who sadly passed away in 2021.
Funding
The authors have not disclosed any funding.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have not disclosed any competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Doan, T.T., Bostel, N., Hà, M.H. et al. New mixed integer linear programming models and an iterated local search for the clustered traveling salesman problem with relaxed priority rule. J Comb Optim 46, 1 (2023). https://doi.org/10.1007/s10878-023-01066-x
Accepted:
Published:
DOI: https://doi.org/10.1007/s10878-023-01066-x