Abstract
Derived from the well-known Traveling Salesman problem (TSP), the multiple-Traveling Salesman problem (multiple-TSP) with single depot is a straightforward generalization: several salesmen located in a given city (the depot) need to visit a set of interconnected cities, such that each city is visited exactly once (by a single salesman) while the total cost of their tours is minimized. Designed for shortest path problems and with proven efficiency for TSP, Ant Colony Systems (ACS) are a natural choice for multiple-TSP as well. Although several variations of ant algorithms for multiple-TSP are reported in the literature, there is no clear evidence on their comparative performance. The contribution of this paper is twofold: it provides a benchmark for single-depot-multiple-TSP with reported optima and performs a thorough experimental evaluation of several variations of the ACS on this problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
- 3.
The address where it can be visualized the multiple-TSP instances is www.infoiasi.ro/~mtsplib.
- 4.
- 5.
References
Bektas, T.: The multiple traveling salesman problem: an overview of formulations and solution procedures. Omega 34(3), 209–219 (2006)
Laporte, G.G., Nobert, Y.A.: Cutting planes algorithm for the m-salesmen problem. J. Oper. Res. Soc. 31, 1017–1023 (1980)
Ali, A., Kennington, J.L.: Exact solution of multiple traveling salesman problems. Discrete Appl. Math. 13, 259–276 (1986)
Russell, R.A.: An effective heuristic for the m-tour traveling salesman problem with some side conditions. Oper. Res. 25(3), 517–524 (1977)
Ryan, J.L., Bailey, T.G., Moore, J.T., Carlton, W.B.: Reactive Tabu search in unmanned aerial reconnaissance simulations. In: WSC 1998, pp. 873–880 (1998)
Yuan, S., Skinner, B., Huang, S., Liu, D.: A new crossover approach for solving the multiple travelling salesmen problem using genetic algorithms. EJOR 228, 72–82 (2013)
Singh, A., Baghel, A.S.: A new grouping genetic algorithm approach to the multiple traveling salesperson problem. Soft Comput. 13(1), 95–101 (2009)
Li, J., Sun, Q., Zhou, MC., Dai, X.: A new multiple traveling salesman problem and its genetic algorithm-based solution. In: SMC 2013, pp. 627–632 (2013)
Andrade, C.E., Miyazawa, F.K., Resende, M.G.C.: Evolutionary algorithm for the k-interconnected multi-depot multi-traveling salesmen problem. In: GECCO 2013, pp. 463–470 (2013)
Liu, W., Li, S., Zhao, F., Zheng, A.: An ant colony optimization algorithm for the multiple traveling salesmen problem. ICIEA 2009, 1533–1537 (2009)
Somhom, S., Modares, A., Enkawa, T.: Competition-based neural network for the multiple travelling salesmen problem with minmax objective. Comput. Oper. Res. 26, 395–407 (1999)
Venkatesh, P., Singh, A.: Two metaheuristic approaches for the multiple traveling salesperson problem. Appl. Soft. Comput. 26, 74–89 (2015)
Kivelevitch, E., Cohen, K., Kumar, M.: A market-based solution to the multiple traveling salesmen problem. JIRS J. 72(1), 21–40 (2013)
Junjie, P., Dingwei, W.: An ant colony optimization algorithm for multiple travelling salesman problem. In: ICICIC 2006, vol. 1, pp. 210–213 (2006)
Salas, Y.J.C., Ledn, R.A., Machado, N.I.C., Now, A.: Multi-type ant colony system for solving the multiple traveling salesman problem. Rev. Tc. Ing. Univ. Zulia 35(3), 311–320 (2012)
Ghafurian, S., Javadian, N.: An ant colony algorithm for solving fixed destination multi-depot multiple traveling salesmen problems. Appl. Soft. Comput. 11(1), 1256–1262 (2011)
Vallivaara, I.: A team ant colony optimization algorithm for the multiple travelling salesmen problem with minmax objective. In: MIC 2008, pp. 387–392 (2008)
Sofge, D.A., Schultz, A., De Jong, K.A.: Evolutionary computational approaches to solving the multiple traveling salesman problem using a neighborhood attractor schema. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds.) EvoIASP 2002, EvoWorkshops 2002, EvoSTIM 2002, EvoCOP 2002, and EvoPlan 2002. LNCS, vol. 2279, pp. 153–162. Springer, Heidelberg (2002)
Chandran, N., Narendran, T.T., Ganesh, K.: A clustering approach to solve the multiple traveling salesmen problem. IJISE 1(3), 372–387 (2006)
Kara, I., Bektas, T.: Integer linear programming formulations of multiple salesman problems and its variations. EJOR 174(3), 1449–1458 (2006)
Dorigo, M., Gambardella, L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1(1), 53–66 (1997)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Necula, R., Breaban, M., Raschip, M. (2015). Performance Evaluation of Ant Colony Systems for the Single-Depot Multiple Traveling Salesman Problem. In: Onieva, E., Santos, I., Osaba, E., Quintián, H., Corchado, E. (eds) Hybrid Artificial Intelligent Systems. HAIS 2015. Lecture Notes in Computer Science(), vol 9121. Springer, Cham. https://doi.org/10.1007/978-3-319-19644-2_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-19644-2_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19643-5
Online ISBN: 978-3-319-19644-2
eBook Packages: Computer ScienceComputer Science (R0)