Abstract
In this work, we analyze genetic diversity of Pareto optimal solutions (POS) and study effective crossover operators in evolutionary many-objective optimization. First we examine the diversity of genes in the true POS on many-objective 0/1 knapsack problems with up to 20 items (bits), showing that genes in POS become noticeably diverse as we increase the number of objectives. We also verify the effectiveness of conventional two-point crossover, Local Recombination that selects mating parents based on proximity in objective space, and two-point and uniform crossover operators Controlling the maximum number of Crossed Genes (CCG). We use NSGA-II, SPEA2, IBEA ε + and MSOPS, which adopt different selection methods, and many-objective 0/1 knapsack problems with n = {100,250,500,750,1000} items (bits) and m = {2,4,6,8,10} objectives to verify the search performance of each crossover operator. Simulation results reveal that Local Recombination and CCG operators significantly improve search performance especially for NSGA-II and MSOPS, which have high diversity of genes in the population. Also, results show that CCG operators achieve higher search performance than Local Recombination for m ≥ 4 objectives and that their effectiveness becomes larger as the number of objectives m increases.
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.
References
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)
Hughes, E.J.: Evolutionary Many-Objective Optimisation: Many Once or One Many? In: Proc. IEEE Congress on Evolutionary Computation (CEC 2005), pp. 222–227 (September 2005)
Aguirre, H., Tanaka, K.: Working Principles, Behavior, and Performance of MOEAs on MNK-Landscapes. European Journal of Operational Research 181(3), 1670–1690 (2007)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II, KanGAL report 200001 (2000)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. TIK-Report (103) (2001)
Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: A short review. In: Proc. of 2008 IEEE Congress on Evolutionary Computation (CEC 2008), pp. 2424–2431 (2008)
Wagner, T., Beume, N., Naujoks, B.: Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 742–756. Springer, Heidelberg (2007)
Sato, H., Aguirre, H., Tanaka, K.: Local Dominance and Local Recombination in MOEAs on 0/1 Multiobjective Knapsack Problems. European Jour. on Operational Research 181(3), 1670–1690 (2007)
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., Thiele, L.: Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 292–304. Springer, Heidelberg (1998)
Watanabe, S., Hiroyasu, T., Miki, M.: Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems. In: Proc. Genetic and Evolutionary Computation Conference (GECCO 2002), pp. 458–465 (2002)
Ishibuchi, H., Shibata, Y.: Mating Scheme for Controlling the Diversity-Convergence Balance for Multiobjective Optimization. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 1259–1271. Springer, Heidelberg (2004)
Zhang, Q., Li, H.: MOEA/D: A Multi-objective Evolutionary Algorithm Based on Decomposition. IEEE Trans. on Evolutionary Computation 11(6), 712–731 (2007)
Syswerda, G.: Uniform Crossover in Genetic Algorithms. In: Proc. of the Third International Conference on Genetic Algorithms (ICGA 1989), pp. 2–9 (1989)
Spears, W., De Jong, K.A.: An analysis of multi-point crossover. In: Proc. Foundations of Genetic Algorithms (1990)
Sato, H., Aguirre, H., Tanaka, K.: Pareto Partial Dominance MOEA and Hybrid Archiving Strategy Included CDAS in Many-Objective Optimization. In: Proc. IEEE Congress on Evolutionary Computation (CEC 2010), pp. 3720–3727 (2010)
Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications, PhD thesis, Swiss Federal Institute of Technology, Zurich (1999)
Fonseca, C., Paquete, L., López-Ibáñez, M.: An Improved Dimension-sweep Algorithm for the Hypervolume Indicator. In: Proc. 2006 IEEE Congress on Evolutionary Computation, pp. 1157–1163 (2006)
Sato, M., Aguirre, H., Tanaka, K.: Effects of δ-Similar Elimination and Controlled Elitism in the NSGA-II Multiobjective Evolutionary Algorithm. In: Proc. IEEE Congress on Evolutionary Computation (CEC 2006), pp. 3980–3398 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sato, H., Aguirre, H.E., Tanaka, K. (2011). Genetic Diversity and Effective Crossover in Evolutionary Many-objective Optimization. In: Coello, C.A.C. (eds) Learning and Intelligent Optimization. LION 2011. Lecture Notes in Computer Science, vol 6683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25566-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-25566-3_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25565-6
Online ISBN: 978-3-642-25566-3
eBook Packages: Computer ScienceComputer Science (R0)