Abstract
The bi-objective ring star problem aims to locate a cycle through a subset of nodes of a graph while optimizing two types of cost. The first criterion is to minimize a ring cost, related to the length of the cycle, whereas the second one is to minimize an assignment cost, from non-visited nodes to visited ones. In spite of its natural multi-objective formulation, this problem has never been investigated in such a way. In this paper, three metaheuristics are designed to approximate the whole set of efficient solutions for the problem under consideration. Computational experiments are performed on well-known benchmark test instances, and the proposed methods are rigorously compared to each other using different performance metrics.
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References
Basseur, M., Burke, E.K.: Indicator-based multi-objective local search. In: CEC 2007, Singapore, pp. 3100–3107 (2007)
Bean, J.: Genetic algorithms and random keys for sequencing and optimization. ORSA Journal on Computing 6(2), 154–160 (1994)
Bleuler, S., Laumanns, M., Thiele, L., Zitzler, E.: PISA — a platform and programming language independent interface for search algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 494–508. Springer, Heidelberg (2003)
Burke, E.K., Kendall, G. (eds.): Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques. Springer, Heidelberg (2005)
Current, J.R., Schilling, D.A.: The median tour and maximal covering tour problems: Formulations and heuristics. European Journal of Operational Research 73, 114–126 (1994)
Deb, K.: Multi-objective optimization. In: [4], ch. 10, pp. 273–316 (2005)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Doerner, K., Focke, A., Gutjahr, W.J.: Multicriteria tour planning for mobile healthcare facilities in a developing country. European Journal of Operational Research 179(3), 1078–1096 (2007)
Glover, F.W., Kochenberger, G.A. (eds.): Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 57. Kluwer Academic Publishers, Boston, USA (2003)
Hansen, M.P., Jaszkiewicz, A.: Evaluating the quality of approximations of the non-dominated set. Technical Report IMM-REP-1998-7, Institute of Mathematical Modeling, Technical University of Denmark (1998)
Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. Technical report, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Switzerland (revised version) (2006)
Labbé, M., Laporte, G., Rodríguez Martín, I., Salazar González, J.J.: The ring star problem: Polyhedral analysis and exact algorithm. Networks 43, 177–189 (2004)
Liefooghe, A., Basseur, M., Jourdan, L., Talbi, E.-G.: ParadisEO-MOEO: A framework for evolutionary multi-objective optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 386–400. Springer, Heidelberg (2007)
Miettinen, K.: Nonlinear Multiobjective Optimization, vol. 12. Kluwer Academic Publishers, Boston, USA (1999)
Reinelt, G.: TSPLIB – A traveling salesman problem library. ORSA Journal on Computing 3(4), 376–384 (1991)
Renaud, J., Boctor, F.F., Laporte, G.: Efficient heuristics for median cycle problems. Journal of the Operational Research Society 55(2), 179–186 (2004)
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)
Zitzler, E., Thiele, L., Laumanns, M., Foneseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
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Liefooghe, A., Jourdan, L., Basseur, M., Talbi, EG., Burke, E.K. (2008). Metaheuristics for the Bi-objective Ring Star 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_18
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DOI: https://doi.org/10.1007/978-3-540-78604-7_18
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