Abstract
This paper presents the Efficient Multi-Objective Particle Swarm Optimizer (EMOPSO), which is an improved version of a multi-objective evolutionary algorithm (MOEA) previously proposed by the authors. Throughout the paper, we provide several details of the design process that led us to EMOPSO. The main issues discussed are: the mechanism to maintain a set of well-distributed nondominated solutions, the turbulence operator that avoids premature convergence, the constraint-handling scheme, and the study of parameters that led us to propose a self-adaptation mechanism. The final algorithm is able to produce reasonably good approximations of the Pareto front of problems with up to 30 decision variables, while performing only 2,000 fitness function evaluations. As far as we know, this is the lowest number of evaluations reported so far for any multi-objective particle swarm optimizer. Our results are compared with respect to the NSGA-II in 12 test functions taken from the specialized literature.
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References
Reyes-Sierra, M., Coello Coello, C.A.: Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art. International Journal of Computational Intelligence Research 2(3), 287–308 (2006)
Toscano Pulido, G.: On the Use of Self-Adaptation and Elitism for Multiobjective Particle Swarm Optimization. PhD thesis, Computer Science Section, Department of Electrical Engineering, CINVESTAV-IPN, Mexico (2005)
Branke, J., Mostaghim, S.: About Selecting the Personal Best in Multi-Objective Particle Swarm Optimization. In: Runarsson, T.P., Beyer, H.-G., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) Parallel Problem Solving from Nature - PPSN IX. LNCS, vol. 4193, pp. 523–532. Springer, Heidelberg (2006)
Toscano Pulido, G., Coello Coello, C.A.: Using Clustering Techniques to Improve the Performance of a Particle Swarm Optimizer. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 225–237. Springer, Heidelberg (2004)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA–II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)
Knowles, J.D., Corne, D.W.: Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy. Evolutionary Computation 8(2), 149–172 (2000)
Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining Convergence and Diversity in Evolutionary Multi-objective Optimization. Evolutionary Computation 10(3), 263–282 (2002)
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)
Zitzler, E., Deb, K., Thiele, L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8(2), 173–195 (2000)
Kursawe, F.: A Variant of Evolution Strategies for Vector Optimization. In: Schwefel, H.-P., Männer, R. (eds.) Parallel Problem Solving from Nature. LNCS, vol. 496, pp. 193–197. Springer, Heidelberg (1991)
Deb, K.: Multi-Objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems. Evolutionary Computation 7(3), 205–230 (1999)
van den Bergh, F.: An Analysis of Particle Swarm Optimization. PhD thesis, Faculty of Natural and Agricultural Science, University of Petoria, Pretoria, South Africa (2002)
Toscano-Pulido, G., Coello Coello, C.A.: A Constraint-Handling Mechanism for Particle Swarm Optimization. In: Proceedings of the Congress on Evolutionary Computation 2004 (CEC’2004), vol. 2, Piscataway, New Jersey, Portland, Oregon, USA, IEEE Service Center (2004) (1396)–1403
Fieldsend, J.E., Singh, S.: A Multi-Objective Algorithm based upon Particle Swarm Optimisation, an Efficient Data Structure and Turbulence. In: Proceedings of the 2002 U.K. Workshop on Computational Intelligence, Birmingham, UK, pp. 37–44 (2002)
Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)
Wolpert, D.H., Macready, W.G.: No Free Lunch Theorems for Optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82 (1997)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)
Deb, K., Pratap, A., Meyarivan, T.: Constrained Test Problems for Multi-objective Evolutionary Optimization. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 284–298. Springer, Heidelberg (2001)
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)
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Toscano-Pulido, G., Coello Coello, C.A., Santana-Quintero, L.V. (2007). EMOPSO: A Multi-Objective Particle Swarm Optimizer with Emphasis on Efficiency. 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_23
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DOI: https://doi.org/10.1007/978-3-540-70928-2_23
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