A New Proposal for Multiobjective Optimization Using Particle Swarm Optimization and Rough Sets Theory
This paper presents a new multi-objective evolutionary algorithm which consists of a hybrid between a particle swarm optimization approach and some concepts from rough sets theory. The main idea of the approach is to combine the high convergence rate of the particle swarm optimization algorithm with a local search approach based on rough sets that is able to spread the nondominated solutions found, so that a good distribution along the Pareto front is achieved. Our proposed approach is able to converge in several test functions of 10 to 30 decision variables with only 4,000 fitness function evaluations. This is a very low number of evaluations if compared with today’s standards in the specialized literature. Our proposed approach was validated using nine standard test functions commonly adopted in the specialized literature. Our results were compared with respect to a multi-objective evolutionary algorithm that is representative of the state-of-the-art in the area: the NSGA-II.
KeywordsParticle Swarm Optimization Pareto Front Multiobjective Optimization Nondominated Solution Multiobjective Evolutionary Algorithm
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- 1.Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann Publishers, California (2001)Google Scholar
- 3.Mostaghim, S., Teich, J.: Strategies for Finding Good Local Guides in Multi-objective Particle Swarm Optimization (MOPSO). In: IEEE Swarm Intelligence Symposium Proc., Indianapolis, Indiana, USA, pp. 26–33. IEEE Service Center (2003)Google Scholar
- 7.Hernández-Díaz, A.G., Santana-Quintero, L.V., Coello, C.A.C., Molina, J.: Pareto-adaptive ε-dominance. Technical Report EVOCINV-02-2006, Evolutionary Computation Group at CINVESTAV, Sección de Computación, Departamento de Ingeniería Eléctrica, CINVESTAV-IPN, México (2006)Google Scholar
- 8.Eshelman, L.J., Schaffer, J.D.: Real-coded Genetic Algorithms and Interval-Schemata. In: Whitley, L.D. (ed.) Foundations of Genetic Algorithms, vol. 2, pp. 187–202. Morgan Kaufmann Publishers, San Mateo, California (1993)Google Scholar
- 11.Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Test Problems for Evolutionary Multiobjective Optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization. Theoretical Advances and Applications, pp. 105–145. Springer, USA (2005)CrossRefGoogle Scholar
- 12.Veldhuizen, D.A.V.: Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovations. PhD thesis, Department of Electrical and Computer Engineering. Graduate School of Engineering. Air Force Institute of Technology, Wright-Patterson AFB, Ohio (1999)Google Scholar
- 13.Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)Google Scholar