Abstract
It has generally been acknowledged that both proximity to the Pareto front and a certain diversity along the front, should be targeted when using evolutionary multiobjective optimization. Recently, a new partitioning mechanism, the Part and Select Algorithm (PSA), has been introduced. It was shown that this partitioning allows for the selection of a well-diversified set out of an arbitrary given set, while maintaining low computational cost. When embedded into an evolutionary search (NSGA-II), the PSA has significantly enhanced the exploitation of diversity. In this paper, the ability of the PSA to enhance evolutionary multiobjective algorithms (EMOAs) is further investigated. Two research directions are explored here. The first one deals with the integration of the PSA within an EMOA with a novel strategy. Contrary to most EMOAs, that give a higher priority to proximity over diversity, this new strategy promotes the balance between the two. The suggested algorithm allows some dominated solutions to survive, if they contribute to diversity. It is shown that such an approach substantially reduces the risk of the algorithm to fail in finding the Pareto front. The second research direction explores the use of the PSA as an archiving selection mechanism, to improve the averaged Hausdorff distance obtained by existing EMOAs. It is shown that the integration of the PSA into NSGA-II-I and Δ p -EMOA as an archiving mechanism leads to algorithms that are superior to base EMOAS on problems with disconnected Pareto fronts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abbass, H.A.: The self-adaptive Pareto differential evolution algorithm. In: Proceedings of the 2002 Congress on Evolutionary Computation, CEC 2002, vol. 1, pp. 831–836 (May 2002)
Avigad, G., Eisenstadt, E.M., Salomon, S., Guimar, F.G.: Evolution of contours for topology optimization. In: Schütze, O., Coello Coello, C.A., Tantar, A.-A., Tantar, E., Bouvry, P., Del Moral, P., Legrand, P. (eds.) EVOLVE - A Bridge Between Probability, Set Oriented Numerics, and Evolutionary Computation II. AISC, vol. 175, pp. 397–412. Springer, Heidelberg (2012)
Batista, L.S., Campelo, F., Guimarães, F.G., Ramírez, J.A.: Pareto cone ε-dominance: Improving convergence and diversity in multiobjective evolutionary algorithms. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds.) EMO 2011. LNCS, vol. 6576, pp. 76–90. Springer, Heidelberg (2011)
Bosman, P.A.N., Thierens, D.: The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Transactions on Evolutionary Computation 7(2), 174–188 (2003)
Bosman, P.A.N., Thierens, D.: Multi-objective optimization with diversity preserving mixture-based iterated density estimation evolutionary algorithms. International Journal of Approximate Reasoning 31(3), 259–289 (2002)
Coello Coello, C.A., Cortés, N.C.: Solving multiobjective optimization problems using an artificial immune system. Genetic Programming and Evolvable Machines 6(2), 163–190 (2005)
Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary algorithms for solving multi-objective problems, vol. 5. Springer, Heidelberg (2007)
Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Systems 9(2), 115–148 (1995)
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)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the 2002 Congress on Evolutionary Computation, CEC 2002, vol. 1, pp. 825–830 (May 2002)
Deb, K.: Multi objective optimization using evolutionary algorithms. John Wiley and Sons (2001)
Durillo, J.J., Nebro, A.J.: jmetal: A java framework for multi-objective optimization. Advances in Engineering Software 42, 760–771 (2011)
Gerstl, K., Rudolph, G., Schütze, O., Trautmann, H.: Finding evenly spaced fronts for multiobjective control via averaging Hausdorff-measure. In: Int’l. Proc. Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2011, pp. 975–980 (2011)
Heinonen, J.: Lectures on Analysis on Metric Spaces. Springer, New York (2001)
Horn, J., Nafpliotis, N., Goldberg, D.E.: A niched Pareto genetic algorithm for multiobjective optimization. In: Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, vol. 1, pp. 82–87 (June 1994)
Kukkonen, S., Deb, K.: Improved pruning of non-dominated solutions based on crowding distance for bi-objectve optimization problems. In: Proceedings of the 2006 IEEE Congress on Evolutionary Computation, pp. 1179–1186. IEEE Press (2005)
Laumanns, M., Rudolph, G., Schwefel, H.P.: Mutation control and convergence in evolutionary multi-object optimization. HT014601767 (2001)
Laumanns, M., Očenášek, J.: Bayesian optimization algorithms for multi-objective optimization. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 298–307. Springer, Heidelberg (2002)
Li, M., Zheng, J., Xiao, G.: An efficient mufti-objective evolutionary algorithm based on minimum spanning tree. In: IEEE Congress on Evolutionary Computation, CEC 2008, IEEE World Congress on Computational Intelligence, pp. 617–624 (June 2008)
Loridan, P.: ε-solutions in vector minimization problems. Journal of Optimization Theory and Applications 43, 265–276 (1984)
Salomon, S., Avigad, G., Goldvard, A., Schütze, O.: PSA a new scalable space partition based selection algorithm for MOEAs. In: Schütze, O., Coello Coello, C.A., Tantar, A.-A., Tantar, E., Bouvry, P., Del Moral, P., Legrand, P. (eds.) EVOLVE - A Bridge Between Probability, Set Oriented Numerics, and Evolutionary Computation II. AISC, vol. 175, pp. 137–152. Springer, Heidelberg (2012)
Sato, H., Aguirre, H.E., Tanaka, K.: Controlling dominance area of solutions and its impact on the performance of moeas. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 5–20. Springer, Heidelberg (2007)
Schütze, O., Esquivel, X., Lara, A., Coello Coello, C.A.: Using the averaged Hausdorff distance as a performance measure in evolutionary multiobjective optimization. IEEE Transactions on Evolutionary Computation 16(4), 504–522 (2012)
Schütze, O., Laumanns, L., Tantar, E., Coello Coello, C.A., Talbi, E.G.: Computing gap free Pareto front approximations with stochastic search algorithms. Evolutionary Computation 18(1), 65–96 (2010)
Tan, K.C., Chiam, S.C., Mamun, A.A., Goh, C.K.: Balancing exploration and exploitation with adaptive variation for evolutionary multi-objective optimization. European Journal of Operational Research 197(2), 701–713 (2009)
Van Veldhuizen, D.A.: 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
Wineberg, M., Oppacher, F.: The underlying similarity of diversity measures used in evolutionary computation. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 1493–1504. Springer, Heidelberg (2003)
Xiaoning, S., Min, Z., Tao, L.: A multi-objective optimization evolutionary algorithm addressing diversity maintenance. In: International Joint Conference on Computational Sciences and Optimization, CSO 2009, vol. 1, pp. 524–527 (April 2009)
Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation 11(6), 712–731 (2007)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evol. Comput. 8(2), 173–195 (2000)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K.C., et al. (eds.) Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems (EUROGEN 2001), pp. 95–100. International Center for Numerical Methods in Engineering, CIMNE (2002)
Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. PhD thesis, Swiss Federal Institute of Technology Zurich (1999)
Zuiani, F., Vasile, M.: Multi agent collaborative search based on Tchebycheff decomposition. In: Computational Optimization and Applications, pp. 1–20 (March 2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Salomon, S. et al. (2014). PSA Based Multi Objective Evolutionary Algorithms. In: Schuetze, O., et al. EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation III. Studies in Computational Intelligence, vol 500. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-01460-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-01460-9_11
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-01459-3
Online ISBN: 978-3-319-01460-9
eBook Packages: EngineeringEngineering (R0)