Abstract
The Prize Collecting Traveling Salesman Problem (PCTSP) can be associated to a salesman that collects a prize in each city visited and pays a penalty for each city not visited, with travel costs among the cities. The objective is to minimize the sum of travel costs and penalties, while including in the tour enough cities to collect a minimum prize. This paper presents one solution procedure for the PCTSP, using a hybrid metaheuristic known as Clustering Search (CS), whose main idea is to identify promising areas of the search space by generating solutions and clustering them into groups that are then explored further. The validation of the obtained solutions was through the comparison with the results found by CPLEX.
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References
Oliveira, A.C.M., Lorena, L.A.N.: Detecting promising areas by evolutionary clustering search. In: Bazzan, A.L.C., Labidi, S. (eds.) SBIA 2004. LNCS (LNAI), vol. 3171, pp. 385–394. Springer, Heidelberg (2004)
Feo, T., Resende, M.: Greedy randomized adaptive search procedures. Journal of Global Optimization 6, 109–133 (1995)
Mladenovic, N., Hansen, P.: Variable neighborhood search. Computers and Operations Research 24, 1097–1100 (1997)
ILOG France: ILOG CPLEX 10.0 - User’s Manual (2006)
Balas, E.: The prize collecting travelling salesman problem. In: Anais..., ORSA/TIMS Meeting (1986)
Balas, E.: The prize collecting travelling salesman problem. Networks 19, 621–636 (1989)
Fischetti, M., Toth, P.: An additive approach for the optimal solution of the prize collecting traveling salesman problem. In: Vehicle Routing: Methods and Studies, 319–343 (1988)
Goemans, M.X., Williamson, D.P.: A general aproximation technique for constrained forest problems. SIAM Journal on Computing 24(2), 296–317 (1995)
Dell’Amico, M., Maffioli, F., Sciomanchen, A.: A lagrangian heuristic for the prize collecting travelling salesman problem. Annals of Operations Research 81, 289–305 (1998)
Chaves, A.A., Lorena, L.A.N.: Hybrid algorithms with detection of promising areas for the prize collecting traveling salesman problem. In: Proceedings of International Conference on Hybrid Intelligent Systems, pp. 49–54. IEEE Computer Society, Los Alamitos, California (2005)
Feillet, D., Dejax, P., Gendreau, M.: Traveling salesman problems with profits. Transportation Science 2(39), 188–205 (2005)
Oliveira, A.C.M., Lorena, L.A.N.: Hybrid evolutionary algorithms and clustering search. In: Grosan, C., Abraham, A., Ishibuchi, H. (eds.) Hybrid Evolutionary Systems - Studies in Computational Intelligence. SCI Series, pp. 81–102. Springer, Heidelberg (2007)
Gomes, L.M., Diniz, V.B., Martinhon, C.A.: An hybrid grasp+vnd metaheuristic fo the prize collecting traveling salesman problem. In: XXXII Brazilian Symposium of Operational Research (SBPO), pp. 1657–1665 (2000)
Glover, F.: Tabu search and adaptive memory programing: Advances, applications and challenges. In: Interfaces in Computer Science and Operations Research, pp. 1–75 (1996)
Croes, G.: A method for solving travelling salesman problems. Operations Research 6, 791–812 (1958)
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Chaves, A.A., Lorena, L.A.N. (2008). Hybrid Metaheuristic for the Prize Collecting Travelling Salesman Problem. In: van Hemert, J., Cotta, C. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2008. Lecture Notes in Computer Science, vol 4972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78604-7_11
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DOI: https://doi.org/10.1007/978-3-540-78604-7_11
Publisher Name: Springer, Berlin, Heidelberg
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