Solving Multiobjective Optimization Problem by Constraint Optimization
Multiobjective optimization problems (MOPs) have attracted intensive efforts from AI community and many multiobjective evolutionary algorithms (MOEAs) were proposed to tackle MOPs. In addition, a few researchers exploited MOEAs to solve constraint optimization problems (COPs). In this paper, we investigate how to tackle a MOP by iteratively solving a series of COPs and propose the algorithm named multiobjective evolutionary algorithm based on constraint optimization (MEACO). In contrast to existing MOEAs, MEACO requires no complex selection mechanism or elitism strategy in solving MOPs. Given a MOP, MEACO firstly constructs a new COP by transforming all but one of objective functions into constraints. Then, the optimal solution of this COP is computed by a subroutine evolutionary algorithm so as to determine some Pareto-optimal solutions. After that, a new COP with dramatically reduced search space can be constructed using existing Pareto-optimal solutions. This new generated COP will be further solved to find more Pareto-optimal solutions. This process is repeated until the stopping criterion is met. Experimental results on 9 well-known MOP test problems show that our new algorithm outperforms existing MOEAs in terms of convergence and spacing metrics.
KeywordsMultiobjective Optimization Constraint Optimization Evolutionary Algorithm
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- 2.Schaffer, J.D.: Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. In: Proc. of the 1st Int’l Conf. on Genetic Algorithms, pp. 93–100. L. Erlbaum Associates, Inc., Hillsdale (1985)Google Scholar
- 3.Fonseca, C.M., Fleming, P.J.: Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization. In: Proc. of the 5th Int’l Conf. on Genetic Algorithms, pp. 416–423. Morgan Kauffman, San Mateo (1993)Google Scholar
- 5.Horn, J., Nafpliotis, N., Goldberg, D.E.: A Niched Pareto Genetic Algorithm for Multiobjective Optimization. In: Proc. of the 1st IEEE Conference on Evolutionary Computation, pp. 82–87. IEEE, Piscataway (1994)Google Scholar
- 6.Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. In: Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, pp. 95–100. Springer, Berlin (2001)Google Scholar
- 9.Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J.: PESA-II: Region-Based Selection in Evolutionary Multiobjective Optimization. In: Proc. of the Genetic and Evolutionary Computation Conf., pp. 283–290. Morgan Kaufmann Publishers, San Francisco (2001)Google Scholar
- 15.Deb, K., Jain, S.: Running Performance Metrics for Evolutionary Multi-Objective Optimization, Technical Report. Kanpur: Indian Institute of Technology Kanpur. NO. 2002004 (2002)Google Scholar
- 16.Schott, J.R.: Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. Masters Thesis, Massachusetts Institute of Technology, Cambridge, MA (1995)Google Scholar