Abstract
In this chapter, in order to evaluate the performance of the Self-adaptive Multi-objective Optimization Differential Evolution algorithm, a series of mathematical functions are considered. These test cases encompass different levels of difficulties to demonstrate the ability of the new multi-objective optimization algorithm to find the Pareto’s Curve. The results obtained by the proposed methodology demonstrate that the Pareto’s Curve can be found for all test cases. Besides, the number of objective function evaluations is reduced as compared with other evolutionary strategies.
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References
Schaffer, J.D.: Some experiments in machine learning using vector evaluated genetic algorithms. Ph.D Dissertation. Vanderbilt University, Nashville, USA (1984)
Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, Chichester (2001). ISBN 0-471-87339-X
Lobato, F.S.: Multi-objective optimization for engineering system design. Thesis (in Portuguese), Federal University of Uberlândia, Uberlândia (2008)
Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Forrest, S. (ed.) Proceedings of the 5th International Conference on Genetic Algorithms, San Mateo, CA, University of Illinois at Urbana-Champaign, pp. 416–423. Morgan Kauffman, San Mateo (1993)
Kursawe, F.: A variant of evolution strategies for vector optimization. In: Parallel Problem Solving from Nature, pp. 193–197. Springer, Berlin (1990)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algoritms: empirical results. Evol. Comput. J. 8(2), 125–148 (2000)
Binh, T.T., Korn, U.: MOBES: a multiobjective evolution strategy for constrained optimization problems. In: The Third International Congress on Genetic Algorithms, pp. 176–182 (1997)
Srinivas, N., Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithms. Evol. Comput. 2(3), 221–248 (1994)
Osyczka, A., Kundu, S.: A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm. Struct. Optim. 10(2), 94–99 (1995)
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Lobato, F.S., Steffen, V. (2017). Mathematical. In: Multi-Objective Optimization Problems. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-58565-9_5
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DOI: https://doi.org/10.1007/978-3-319-58565-9_5
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