Abstract
Most of the well known methods for solving multi-objective combinatorial optimization problems deal with only two objectives. In this paper, we develop a metaheuristic method for solving multi-objective assignment problems with three or more objectives. This method is based on the dominance cost variant of the multi-objective simulated annealing (DCMOSA) and hybridizes neighborhood search techniques which consist of either a local search or a multi-objective branch and bound search (here the multi-objective branch and bound search is used as a local move to a fragment of a solution).
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Adiche, C., Aïder, M.: New variants of the simulated annealing for solving bi-objective assignment problem. RSTI-RIA 22(2), 237–255 (2008)
Bhatia, H.L., Malhotra, R., Puri, M.C.: Bi-criteria assignment problem. Oper. Res. 19(2), 84–96 (1982)
Czyz̀ak, P., Jaskiewicz, A.: Pareto simulated annealing—a metaheuristic technique for multiple objective combinatorial optimization. J. Multi-Criteria Decis. Anal. 7, 34–47 (1998)
Guo, Y., Lim, A., Rodrigues, B., Zhu, Y.: Heuristics for bidding problem. Comput. Oper. Res. 33, 2179–2188 (2006)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Knowles J., Thiele L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. TIK Report 214, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, February 2006
Przybylski A., Gandibleux, X., Ehrgott, M.: Two phase algorithm for the bi-objective assignment problem. Eur. J. Oper. Res. 185(2), 509–533 (2008)
Serafini, P.: Some considerations about computational complexity for multi objective combinatorial problems. In: Jahn, J., Krabs, W. (eds.) Recent advances and historical development of vector optimization vol. 294 of Lecture Notes in Economics, pp. 51–61. Springer, Berlin (1987)
Smith, K.I., Everson, R.M., Fieldsend, J. E.: Dominance mesures for multi objective simulated annealing. In: Proceedings of Congress on Evolutionary Computation, CEC04, pp. 23–30 (2004)
Suman, B.: Study of self-stopping PDMOSA and performance measure in multiobjective optimization. Comput. Chem. Eng. 29, 1131–1147 (2005)
Suppapitnarm, A., Seffen, K.A., Parks, G.T., Clarkson, P.J.: Simulated annealing: an alternative approach to true multiobjective optimisation. Eng. Optim. 3, 59–85 (2000)
Tuyttens, D., Teghem, J., Fortemps, P., Van Nieuwenhuyse, K.: Performance of the MOSA method for the bicriteria assignment problem. J Heuristics 6(3), 295–310 (2000)
Ulungu, E.L., Teghem, J., Fortemps, P.: Heuristics for multi-objective combinatorial optimisation problem by simulated annealing. In: Wei, Q., Gu Chen, J., Wang, S. (eds.) MCDM : Theory and applications, pp. 228–238. SCI-TECH Information services (1995)
Ulungu, E.L., Fortemps, P., Tuyttens, D.: MOSA method : a tool for solving multiobjective combinatorial decision problems. Int. J. Multi-Criteria Decis. Anal. 8, 221–236 (1999)
Ulungu, E.L., Teghem, J.: The two phases method : an efficient procedure to solve bi-objective combinatorial optimization problems. Found Comput Decis Sci 20(2), 149–165 (1994)
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Adiche, C., Aïder, M. A Hybrid Method for Solving the Multi-objective Assignment Problem. J Math Model Algor 9, 149–164 (2010). https://doi.org/10.1007/s10852-010-9123-3
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DOI: https://doi.org/10.1007/s10852-010-9123-3
Keywords
- Combinatorial optimization
- Multi-objective simulated annealing
- Assignment problem
- Multi-objective branch and bound method