Primal–dual type evolutionary multiobjective optimization

• Autorzy: Kaliszewski I. , Miroforidis J
• Języki publikacji: EN

Abstrakty

EN

A new, primal-dual type approach for derivation of Pareto front approximations with evolutionary computations is proposed. At present, evolutionary multiobjective optimization algorithms derive a discrete approximation of the Pareto front (the set of objective maps of efficient solutions) by selecting feasible solutions such that their objective maps are close to the Pareto front. As, except of test problems, Pareto fronts are not known, the accuracy of such approximations is known neither. Here we propose to exploit also elements outside feasible sets with the aim to derive pairs of Pareto front approximations such that for each approximation pair the corresponding Pareto front lies, in a certain sense, in-between. Accuracies of Pareto front approximations by such pairs can be measured and controlled with respect to distance between such approximations. A rudimentary algorithm to derive pairs of Pareto front approximations is pre- sented and the viability of the idea is verified on a limited number of test problems.

Słowa kluczowe

EN

Evolutionary Multiobjective Optimization; lower and upper Pareto front approximation

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2013
• Tom: Vol. 38, No. 4
• Strony: 267--275
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Kaliszewski I.

• Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447Warsaw, Poland

autor

Miroforidis J

Bibliografia

• [1] Coello Coello C. A., Van Veldhuizen D.A., and Lamont G.B. (2002), Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, New York.
• [2] Deb K. (2001), Multi-objective Optimization Using Evolutionary Algorithms. John Wiley and Sons, Chichester.
• [3] Hanne T. (2007), A multiobjective evolutionary algorithm for approximating the efficient set. European Journal of Operational Research, 176, 1723-1734.
• [4] Kaliszewski I., Miroforidis J. (2012), Real and virtual Pareto set upper approximations. In: Multiple Criteria Decision Making ’11, eds. T. Trzaskalik, T. Wachowicz, The University of Economics in Katowice, in print.
• [5] Kaliszewski I., Miroforidis J., Podkopayev D. (2011), Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy - the case of -efficiency. Systems Research Institute Report, RB/1/2011.
• [6] Kaliszewski I., Miroforidis J., Podkopayev D. (2012), Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy. European Journal of Operational Research, 216, 188-199.
• [7] Kita H., Yabumoto Y., Mori N., Nishikawa Y. (1996), Multi-Objective Optimization by Means of the Thermodynamical Genetic Algorithm. In: Parallel Problem Solving from Nature- PPSN IV, Voigt H-M., Ebeling W., Rechenberg I., Schwefel H-P., eds, Lecture Notes in Computer Science, 504-512, Springer-Verlag.
• [8] Kita test problem: http://www.lania.mx/ccoello/EMOO/testfuncs/ , downloaded September 28, 2012.
• [9] Michalewicz Z. (1996), Genetic Algorithms + Data Structures = Evolution Programs. Springer.
• [10] Miroforidis J. (2008), Decision Making Aid for Operational Management of Department Stores with Multi-objective Optimization and Soft Computing. PhD Thesis, Systems Research Institute, Warsaw.
• [11] Talbi E. (2009), Metaheuristics: From Design To Implementation.Wiley.