Abstract
To find solutions as close to the Pareto front as possible, and to make them as diverse as possible in the obtained non-dominated front is a challenging task for any multiobjective optimization algorithm.ε-dominance is a concept which can make genetic algorithm obtain a good distribution of Pareto-optimal solutions and has low computational time complexity,and the orthogonal design method can generate an initial population of points that are scattered uniformly over the feasible solution space.In this paper, combining ε-dominance and orthogonal design method, we propose a novel Differential Evolution (DE) algorithm for multiobjective optimization .Experiments on a number of two- and three-objective test problems of diverse complexities show that our approach is able to obtain a good distribution with a small computational time in all cases. Compared with several other state-of-the-art evolutionary algorithms, it achieves not only comparable results in terms of convergence and diversity metrics, but also a considerable reduction of the computational effort.
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References
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA”CII. IEEE Transactions on Evolutionary Computation 6, 182–197 (2002)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (2001)
Schaffer, J.D.: Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. Ph. D. thesis, Vanderbilt University. Unpublished (1984)
Hajela, P., Lin, C.Y.: Genetic search strategies in multicriterion optimal design. Structural Optimization 4, 99–107 (1992)
Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In: Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 416–423 (1993)
Horn, J., Nafpliotis, N.: Multiobjective optimization using the niched pareto genetic algorithm. IlliGAL Report 93005, Illinois Genetic Algorithms Laboratory, University of Illinois, Urbana, Champaign (1993)
Knowles, J.D., Corne, D.W.: Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy. Evolutionary Computation 8(2), 149–172 (2000)
Storn, R., Price, K.: Differential evolution–A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11, 341–359 (1997)
Storn, R., Price, K.: Home Page of Differential Evolution (2003), Available online at, http://www.ICSI.Berkeley.edu/~storn/code.html
Lampinen, J.: A bibliography of differential evolution algorithm. Available online at, http://www2.lut.fi/~jlampine/debiblio.htm
Abbass, H.A., Sarker, R., Newton, C.: PDE: A pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of the Congress on Evolutionary Computation 2001 (CEC2001), vol. 2, Piscataway, New Jersey, IEEE Service Center, pp. 971–978 (2001)
Abbass, H.A.: The self-adaptive pareto differential evolution algorithm. In: Congress on Evolutionary Computation (CEC2002), vol. 1, New Jersey, IEEE Service Center, pp. 831–836 (2002)
Madavan, N.K.: Multiobjective optimization using a pareto differential evolution approach. In: Congress on Evolutionary Computation (CEC2002), vol. 2, Piscataway, New Jersey, IEEE Service Center, pp. 1145–1150 (2002)
Xue, F., Sanderson, A.C., Graves, R.J.: Pareto-based multi-objective differential evolution. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC2003), vol. 2, Canberra, Australia, pp. 862–869. IEEE Press, Los Alamitos (2003)
Robič, T., Filipič, B.: DEMO: Differential Evolution for Multiobjective Optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 520–533. Springer, Heidelberg (2005)
Fang, K.T., Ma, C.X.: Orthogonal and Uniform Design ((in Chinese)). Science Press, Beijing (2001)
Leung, Y.W., Wang, Y.: An Orthogonal Genetic Algorithm with Quantization for Global Numerical Optimization. IEEE Transactions on Evolutionary Computation 5(1), 41–53 (2001)
Zeng, S., Kang, L., Ding, L.: An Orthogonal Multiobjective Evolutionary Algorithm for Multi-objective Optimization Problems with Constraints. Evolutionary Computation 12(1), 77–98 (2004)
Zeng, S., Yao, S., Liu, L., Liu, Y.: An Efficient Multi-objective Evolutionary Algorithm: OMOEA-II. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 108–119. Springer, Heidelberg (2005)
Deb, K., Mohan, M., Mishra, S.: Towards a quick computation of well-spread Pareto-optimal solutions. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 222–236. Springer, Heidelberg (2003)
Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary Computation 10(3), 263–282 (2002)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8, 173–195 (2000)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: Congress on Evolutionary Computation (CEC2002), pp. 825–830 (2002)
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Cai, Z., Gong, W., Huang, Y. (2007). A Novel Differential Evolution Algorithm Based on ε-Domination and Orthogonal Design Method for Multiobjective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_24
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DOI: https://doi.org/10.1007/978-3-540-70928-2_24
Publisher Name: Springer, Berlin, Heidelberg
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