Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Coello Coello, C.A.: Evolutionary Multi-Objective Optimization: A Historical View of the Field. IEEE Computational Intelligence Magazine 1(1), 28–36 (2006)
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)
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)
Srinivas, N., Deb, K.: Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation 2(3), 221–248 (1994)
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)
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)
Knowles, J.D., Corne, D.W.: Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy. Evolutionary Computation 8(2), 149–172 (2000)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6(2), 182–197 (2002)
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)
Zhang, Q.F., Zhou, A.M., Jin, Y.: RM-MEDA: A Regularity Model-Based Multiobjective Estimation of Distribution Algorithm. IEEE Trans. on Evolutionary Computation 11(1), 41–63 (2007)
Gong, M.G., Jiao, L.C., Du, H.F., Bo, L.F.: Multiobjective Immune Algorithm with Nondominated Neighbor-Based Selection. Evolutionary Computation 16(2), 225–255 (2008)
Aguirre, A.H., Rionda, S.B., Coello Coello, C.A., Lizrraga, G.L., Montes, E.M.: Handling Constraints Using Multiobjective Optimization Concepts. Int’l Journal for Numerical Methods in Engineering 59(15), 1989–2017 (2004)
Surry, P.D., Radcliffe, N.J.: The COMOGA Method: Constrained Optimization by Multi-Objective Genetic Algorithms. Control and Cybernetics 26(3), 391–412 (1997)
Wang, Y., Cai, Z.X., Guo, G.Q., Zhou, Y.R.: Multiobjective Optimization and Hybrid Evolutionary Algorithm to Solve Constrained Optimization Problems. IEEE Trans. on System, Man And Cybernetics 37(3), 560–575 (2007)
Deb, K., Jain, S.: Running Performance Metrics for Evolutionary Multi-Objective Optimization, Technical Report. Kanpur: Indian Institute of Technology Kanpur. NO. 2002004 (2002)
Schott, J.R.: Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. Masters Thesis, Massachusetts Institute of Technology, Cambridge, MA (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jiang, H., Zhang, S., Ren, Z. (2010). Solving Multiobjective Optimization Problem by Constraint Optimization. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds) Parallel Problem Solving from Nature, PPSN XI. PPSN 2010. Lecture Notes in Computer Science, vol 6238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15844-5_64
Download citation
DOI: https://doi.org/10.1007/978-3-642-15844-5_64
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15843-8
Online ISBN: 978-3-642-15844-5
eBook Packages: Computer ScienceComputer Science (R0)