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 algorithms to evolve solutions to multi-objective optimization problems. Although many evolutionary algorithms are equipped with mechanisms to achieve both targets, most give priority to proximity over diversity. This priority is embedded within the algorithms through the selection of solutions to the elite population based on the concept of dominance. Although the current study does not change this embedded preference, it does utilize an improved diversity preservation mechanism that is based on a recently introduced partitioning algorithm for function selection. It is shown that this partitioning allows for the selection of a well-diversified set out of an arbitrary given set. Further, when embedded into an evolutionary search, this procedure significantly enhances the exploitation of diversity. The procedure is demonstrated on commonly used test cases for up to five objectives. The potential for further improving evolutionary algorithms through the use of the partitioning algorithm is highlighted.
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
Ahn, C.W., Ramakrishna, R.S.: A diversity preserving selection in multiobjective evolutionary algorithms. Applied Intelligence 32(3), 231–248 (2010), doi:10.1007/s10489-008-0140-0
Avigad, G., Goldvard, A., Salomon, S.: Time-response-based evolutionary optimization. Tech. Rep. br352012, Ort Braude Academic College (2012), http://brd.braude.ac.il/gideon
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)
Coello Coello, C.A., van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Springer (2007)
Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Inc., New York (2001)
Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9, 115–148 (1995)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimisation: NSGA-II. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000), http://dl.acm.org/citation.cfm?id=645825.668937
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. Report 2 001 001, Kanpur Genetic Algorithms Lab (KanGAL), Indian Inst. Technol., Kanpur, India (2001)
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)
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, pp. 82–87. IEEE Press (1994)
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 multi-objective evolutionary algorithm based on minimum spanning tree. In: Evolutionary Computation, CEC 2008 (IEEE World Congress on Computational Intelligence), pp. 617–624 (2008), doi:10.1109/CEC.2008.4630860
Wineberg, M., Oppacher, F.: The Underlying Similarity of Diversity Measures Used in Evolutionary Computation. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 1493–1504. Springer, Heidelberg (2003)
Schütze, O., Esquivel, X., Lara, A., Coello Coello, C.A.: Using the averaged Hausdorff distance as a performance measure in evolutionary multi-objective optimization. IEEE Transactions on Evolutionary Computation 1 (to appear, 2012), doi:10.1109/TEVC.2011.2161872
Shen, X., Zhang, M., Li, T.: 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 (2009), doi:10.1109/CSO.2009.28
Sierra, M.R., Coello, C.A.C.: Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and ε-Dominance. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 505–519. Springer, Heidelberg (2005)
Solow, A., Polasky, S.: Measuring biological diversity. Environmental and Ecological Statistics 1, 95–103 (1994), http://dx.doi.org/10.1007/BF02426650 , doi:10.1007/BF02426650
van Veldhuizen, D.A.: Multiobjective evolutionary algorithms: Classifications, analyses and new innovations. Ph.D. thesis, Department of Electrical and Computer Engineering. Graduate School of Engineering. Air Force Institute of Technology, Wright-Patterson AFB, Ohio, USA (1999)
Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation 11(6), 712–731 (2007), doi:10.1109/TEVC.2007.892759
Zitzler, E.: Evolutionary algorithms for multiobjective optimization: Methods and applications. Ph.D. thesis, ETH, Zurich, Switzerland (1999)
Zitzler, E., Künzli, S.: Indicator-Based Selection in Multiobjective Search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K.C., Tsahalis, D.T., Périaux, J., Papailiou, K.D., Fogarty, T. (eds.) Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems. International Center for Numerical Methods in Engineering, Athens, Greece, pp. 95–100 (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Salomon, S., Avigad, G., Goldvard, A., Schütze, O. (2013). PSA – A New Scalable Space Partition Based Selection Algorithm for MOEAs. In: Schütze, O., et al. EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II. Advances in Intelligent Systems and Computing, vol 175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31519-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-31519-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31518-3
Online ISBN: 978-3-642-31519-0
eBook Packages: EngineeringEngineering (R0)