Abstract
This paper presents a population-based heuristic method - a real ant colony optimization (RACO) as a tool for multi-criteria optimization problems. The idea of multi-criteria optimization is discussed and the necessary modifications of RACO are proposed. These modifications made possible to use the method to simultaneously search many Pareto-optimal solutions. The method was numerically tested in problems of benchmark-type and used for solving simple engineering problems. This article presents and discusses all results obtained in tests, and two different approaches to multi-criteria optimization are additionally compared (search then decision and decision then search).
Keywords:
multi-objective optimizationReferences
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[2] R. Barron, B. Barron. Design for Thermal Stressis. Willey & Sons, 2012.
[3] U. Diwekar. Introduction to Applied Optimization. Springer, 2008.
[4] A. Długosz. Multiobjective evolutionary optimization of MEMS structures. CAMES, 17: 41–50, 2010.
[5] E. Elbeltagia, T. Hegazyb, D. Grierso. Comparison among five evolutionary-based optimization algorithms. Advanced Engineering Informatics, 19: 43–53, 2005.
[6] J. Horn. Multicriteria decision making. [In:] Handbook of Evolutionary Computation, T. Back, D.B. Fogel, Z. Michalewicz [Eds.], F1.9, Institute of Physics Publishing, Bristol(UK), 1997.
[7] A. Messac. From dubious construction of objective functions to the application of physical programming, AIAA Journal, 38(1): 155–163, 2000.
[8] H. Nakayama. Multi-objective optimization and its engineering applications. [In:] Practical approaches to multiobjective optimization 04461, J. Branke, K. Deb, K. Miettinen, R.E. Steuer [Eds.], Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany, 2005.
[9] V. Pareto, Manuale di Economia Politica, Societa Editrice Libraria, Milano, Italy, 1906. Translated into English by A.S. Schwier as Manual of Political Economy, Macmillan, New York, 1971.
[10] K. Socha, M. Dorigo. Ant colony optimization for continuous domains, European Journal of Operational Research, 185: 1155–1173, 2008.
[11] O.L. de Weck. Multiobjective optimization: history and promise. Keynote paper. The 3rd China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Kanazawa, Japan, October 30 – November 2, 2004.
[12] Z. Wenping, Z. Yunlong, Ch. Hanning, Z. Beiwei. Solving multiobjective optimization problems using artificial bee colony algorithm. Discrete Dynamics in Nature and Society, article ID 569784: 1–37, 2011.
[13] E. Zitzler. Evolutionary Algorithms for Multiobjective Optimisation: Methods and Applications. PhD thesis, Eidgenössische Technische Hochschule, Zürich, 1999.
[14] E. Zitzler, K. Deb, L. Thiele. Comparison of multiobjective evolutionary algorithms: empirical results. Evolutionary Computation, 8(2): 173–195, 2000.
