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Abstrakty
Multiple criteria evolutionary algorithms, being essentially parallel in their character, are a natural instrument of finding a representation of entire Pareto set (set of solutions and outcomes non-dominated in criteria space) for vector optimisation problems. However, it is well known that Pareto sets for problems with more than two criteria might become complicated and their representation very time-consuming. Thus, the application of such algorithms is essentially limited to bi-criteria problems or to vector optimisation problems with more criteria but of simple structure. Even in such cases, there are problems related to various important aspects of vector optimisation, such as the uniformity of representation of Pareto set, stopping tests or the accuracy of representing Pareto set, that are not fully covered by the broad literature on evolutionary algorithms in vector optimisation. These problems and related computational tests and experience are discussed in the paper. In order to apply evolutionary algorithms for decision support, it would be helpful to use them in an interactive mode. However, evolutionary algorithms are in their essence global and of batch type. Nevertheless, it is possible to introduce interactive aspects to evolutionary algorithms by focusing them on a part of Pareto set. The results of experimental tests of such modifications of evolutionary algorithms for vector optimisation are presented in the paper. Another issue related to vector optimisation problems with more than two criteria is the computational difficulty of estimating nadir points of Pareto set. The paper describes the use of diverse variants of evolutionary algorithms to the estimation of nadir points, together with experimental evidence.
Rocznik
Tom
Strony
16--33
Opis fizyczny
Bibliogr 12 poz., tab., rys.
Twórcy
autor
- Damovo Poland Jana Olbrachta st 94 01-102 Warsaw, Poland
autor
- National Institute of Telecommunications Szachowa st 1 04-894 Warsaw, Poland
Bibliografia
- [1] K. Deb, “Non-linear goal programming using multi-objective genetic algorithms”. Tech. Rep. no. CI-60/98, Department of Computer Science, University of Dortmund, 1998.
- [2] D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning. Reading, Mass.: Addison-Wesley, 1989.
- [3] C. M. Fonseca and P. J. Fleming, “An overview of evolutionary algorithms in multiobjective optimization”, Evol. Comput., vol. 3, no. 1, 1995.
- [4] C. M. Fonseca and P. J Fleming, “Genetic algorithms for multi-objective optimization: formulation, discussion and generalization” in Proc. Fifth Int. Conf. Genet. Algor., S. Forrest, Ed., San Mateo, USA, 1993, University of Illinois at Urbana – Champaign, Morgan Kauffman, pp. 416–423.
- [5] J. Horn, Multicriterion Decision Making. Handbook of Evolutionary Computation, IOP & Oxford University Press, 1997.
- [6] J. Horn and N. Nafpliotis, “Multiobjective optimization using the niched Pareto genetic algorithm” in Proc. First IEEE Conf. Evol. Comput., IEEE World Congr. Comput. Intell., vol. 1, 1994.
- [7] P. Korhonen, “Multiple objective programming support”. IR-98-010, International Institute for Applied Systems Analysis, Laxenburg, 1998.
- [8] Z. Kowalczuk, T. Białaszewski, and P. Suchomski, “Genetic polioptimisation in Pareto sense with ranking and niched methods” in Proc. III Nat. Conf. Evol. Algor. Glob. Optim., Warsaw, Poland, 1999.
- [9] M. Ehrgott and D. Tenfelde-Podehl, “Nadir values: computation and use in compromise programming”. Universitat Kaiserslautern Fachbereich Mathematik, 2000.
- [10] D. A. Veldhuizen and G. B. Lamont, “Multiobjective evolutionary algorithm research: a history and analysis”. Tech. Rep. TR-98-03, AirForce Institute of Technology, Wright-Patterson AFB, Ohio, 1998.
- [11] A. P. Wierzbicki, M. Makowski, and J. Wessels, Model-Based Decision Support Methodology with Environmental Applications. Dordrecht – Laxenburg: Kluwer – IIASA, 2000.
- [12] E. Zitzle, “Evolutionary algorithms for multiobjective optimization: methods and applications”. Swiss Federal Institute of Technology (ETH), Zurich, 1999
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPS2-0021-0032