Abstract
In this paper we propose an evolutionary algorithm to estimate the minimum (nadir) objective values over the efficient set in multiple objective linear programming problems (MOLP). Nadir values provide valuable information for characterizing the ranges of the objective function values over the efficient set. However, they are very hard to compute in the general case. The proposed algorithm uses a population of weight vectors with particular characteristics, which are then used as parameters in the optimization of weighted-sums of the objective functions. The population evolves through a process of selection, recombination and mutation. The algorithm has been tested on a number of random MOLP problems for which the nadir point is known. A result comparison with an exact method is shown and discussed.
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References
Isermann, H., Steuer, R.E.: Computational Experience Concerning Payoff Tables and Minimum Criterion Values Over the Efficient Set. European Journal of Operational Research 33, 91–97 (1987)
Alves, M.J., Costa, J.P.: An Exact Method for Computing the Nadir Values in Multiple Objective Linear Programming. European Journal of Operational Research (2008) (accepted for publication), Results available at: http://www4.fe.uc.pt/mjalves
Ehrgott, M., Tenfelde-Podehl, D.: Computation of Ideal and Nadir Values and Implications for their use in MCDM Methods. European Journal of Operational Research 151, 119–139 (2003)
Dessouky, M.I., Ghiassi, M., Davis, W.J.: Estimates of the Minimum Nondominated Criterion Values in Multiple-Criteria Decision-Making. Engineering Costs and Production Economics 10, 95–104 (1986)
Korhonen, P., Salo, S., Steuer, R.E.: A Heuristic for Estimating Nadir Criterion Values in Multiple Objective Linear Programming. Operations Research 45, 751–757 (1997)
Deb, K., Chaudhuri, S., Miettinen, K.: Towards Estimating Nadir Objective Vector using Evolutionary Approaches. In: Proceedings of the 8th annual conference on Genetic and evolutionary computation, pp. 643–650. ACM Press, New York (2006)
Yamamoto, Y.: Optimization Over the Efficient Set: Overview. Journal of Global Optimization 22, 285–317 (2002)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 182–197 (2002)
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© 2009 Springer-Verlag Berlin Heidelberg
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Alves, M.J., Costa, J.P. (2009). An Evolutionary Algorithm to Estimate the Nadir Point in MOLP. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, JK., Sevaux, M. (eds) Evolutionary Multi-Criterion Optimization. EMO 2009. Lecture Notes in Computer Science, vol 5467. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01020-0_42
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DOI: https://doi.org/10.1007/978-3-642-01020-0_42
Publisher Name: Springer, Berlin, Heidelberg
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