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Recombination of Similar Parents in SMS-EMOA on Many-Objective 0/1 Knapsack Problems

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7492)

Abstract

In the evolutionary multiobjective optimization (EMO) community, indicator-based evolutionary algorithms (IBEAs) have rapidly increased their popularity in the last few years thanks to their theoretical background and high search ability. Hypervolume has often been used as an indicator to measure the quality of solution sets in IBEAs. It has been reported in the literature that IBEAs work well on a wide range of multiobjective problems including many-objective problems on which traditional Pareto dominance-based EMO algorithms such as NSGA-II and SPEA2 do not always work well. In this paper, we examine the behavior of SMS-EMOA, which is a frequently-used representative IBEA with a hypervolume indicator function, through computational experiments on many-objective 0/1 knapsack problems. We focus on the effect of two mating strategies on the performance of SMS-EMOA: One is to select extreme parents far from other solutions in the objective space, and the other is to recombine similar parents. Experimental results show that the recombination of similar parents improves the performance of SMS-EMOA on many-objective problems whereas the selection of extreme parents is effective only for a two-objective problem. For comparison, we also examine the effect of these mating strategies on the performance of NSGA-II.

Keywords

  • Evolutionary multiobjective optimization
  • evolutionary manyobjective optimization
  • SMS-EMOA
  • mating schemes
  • knapsack problems

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References

  1. Adra, S.F., Fleming, P.J.: Diversity Management in Evolutionary Many-Objective Optimization. IEEE Trans. on Evolutionary Computation 15, 183–195 (2011)

    CrossRef  Google Scholar 

  2. Auger, A., Bader, J., Brockhoff, D., Zitzler, E.: Theory of the Hypervolume Indicator: Optimal μ-Distributions and the Choice of the Reference Point. In: Proc. of FOGA 2009, pp. 87–102 (2009)

    Google Scholar 

  3. Bader, J., Zitzler, E.: HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization. Evolutionary Computation 19, 45–76 (2011)

    CrossRef  Google Scholar 

  4. Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective Selection based on Dominated Hypervolume. European J. of Operational Research 181, 1653–1669 (2007)

    CrossRef  MATH  Google Scholar 

  5. Coello Coello, C.A., Lamont, G.B.: Applications of Multi-Objective Evolutionary Algorithms. World Scientific, Singapore (2004)

    CrossRef  MATH  Google Scholar 

  6. Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)

    MATH  Google Scholar 

  7. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6, 182–197 (2002)

    CrossRef  Google Scholar 

  8. Fonseca, C.M., Fleming, P.J.: On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN IV. LNCS, vol. 1141, pp. 584–593. Springer, Heidelberg (1996)

    CrossRef  Google Scholar 

  9. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  10. Hughes, E.J.: Evolutionary Many-Objective Optimization: Many Once or One Many? In: Proc. of CEC 2005, pp. 222–227 (2005)

    Google Scholar 

  11. Hughes, E.J.: MSOPS-II: A General-Purpose Many-Objective Optimizer. In: Proc. of CEC 2007, pp. 3944–3951 (2007)

    Google Scholar 

  12. Ishibuchi, H., Akedo, N., Ohyanagi, H., Nojima, Y.: Behavior of EMO Algorithms on Many-Objective Optimization Problems with Correlated Objectives. In: Proc. of CEC 2011, pp. 1465–1472 (2011)

    Google Scholar 

  13. Ishibuchi, H., Murata, T.: A Multi-Objective Genetic Local Search Algorithm and Its Application to Flowshop Scheduling. IEEE Trans. on SMC - Part C 28, 392–403 (1998)

    Google Scholar 

  14. Ishibuchi, H., Narukawa, K., Tsukamoto, N., Nojima, Y.: An Empirical Study on Similarity-Based Mating for Evolutionary Multiobjective Combinatorial Optimization. European J. of Operational Research 188, 57–75 (2008)

    CrossRef  MATH  Google Scholar 

  15. Ishibuchi, H., Sakane, Y., Tsukamoto, N., Nojima, Y.: Simultaneous Use of Different Scalarizing Functions in MOEA/D. In: Proc. of GECCO 2010, pp. 519–526 (2010)

    Google Scholar 

  16. Ishibuchi, H., Tsukamoto, N., Hitotsuyanagi, Y., Nojima, Y.: Effectiveness of Scalability Improvement Attempts on the Performance of NSGA-II for Many-Objective Problems. In: Proc. of GECCO 2008, pp. 649–656 (2008)

    Google Scholar 

  17. Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary Many-Objective Optimization: A Short Review. In: Proc. of CEC 2008, pp. 2424–2431 (2008)

    Google Scholar 

  18. Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Diversity Improvement by Non-Geometric Binary Crossover in Evolutionary Multiobjective Optimization. IEEE Trans. on Evolutionary Computation 14, 985–998 (2010)

    CrossRef  Google Scholar 

  19. Jaszkiewicz, A.: On the Computational Efficiency of Multiple Objective Metaheuristics: The Knapsack Problem Case Study. European J. of Operational Research 158, 418–433 (2004)

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Khare, V.R., Yao, X., Deb, K.: Performance Scaling of Multi-objective Evolutionary Algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 376–390. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  21. Knowles, J.D., Corne, D.W.: Approximating the Nondominated Front using the Pareto Archived Evolution Strategy. Evolutionary Computation 8, 149–172 (1999)

    CrossRef  Google Scholar 

  22. Li, H., Zhang, Q.: Multiobjective Optimization Problems with Complicated Pareto Sets, MOEA/D and NSGA-II. IEEE Trans. on Evolutionary Computation 13, 284–302 (2009)

    CrossRef  Google Scholar 

  23. Purshouse, R.C., Fleming, P.J.: On the Evolutionary Optimization of Many Conflicting Objectives. IEEE Trans. on Evolutionary Computation 11, 770–784 (2007)

    CrossRef  Google Scholar 

  24. 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)

    CrossRef  Google Scholar 

  25. Sato, H., Aguirre, H.E., Tanaka, K.: Local Dominance and Local Recombination in MOEAs on 0/1 Multiobjective Knapsack Problems. European J. of Operational Research 181, 1708–1723 (2007)

    CrossRef  MATH  Google Scholar 

  26. Schütze, O., Lara, A., Coello Coello, C.A.: On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem. IEEE Trans. on Evolutionary Computation 15, 444–455 (2011)

    CrossRef  Google Scholar 

  27. Singh, H.K., Isaacs, A., Ray, T.: A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems. IEEE Trans. on Evolutionary Computation 15, 539–556 (2011)

    CrossRef  Google Scholar 

  28. Tan, K.C., Khor, E.F., Lee, T.H.: Multiobjective Evolutionary Algorithms and Applications. Springer, Berlin (2005)

    MATH  Google Scholar 

  29. 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)

    CrossRef  Google Scholar 

  30. While, L., Bradstreet, L., Barone, L.: A Fast Way of Calculating Exact Hypervolumes. IEEE Trans. on Evolutionary Computation 16, 86–95 (2012)

    CrossRef  Google Scholar 

  31. Zhang, Q., Li, H.: MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition. IEEE Trans. on Evolutionary Computation 11, 712–731 (2007)

    CrossRef  Google Scholar 

  32. Zitzler, E., Brockhoff, D., Thiele, L.: The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 862–876. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  33. 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 VIII. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  34. Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. TIK-Report 103, Department of Electrical Engineering, ETH, Zurich (2001)

    Google Scholar 

  35. Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Trans. on Evolutionary Computation 3, 257–271 (1999)

    CrossRef  Google Scholar 

  36. Zitzler, E., Thiele, L., Bader, J.: On Set-Based Multiobjective Optimization. IEEE Trans. on Evolutionary Computation 14, 58–79 (2010)

    CrossRef  Google Scholar 

  37. Zou, X., Chen, Y., Liu, M., Kang, L.: A New Evolutionary Algorithm for Solving Many-Objective Optimization Problems. IEEE Trans. on SMC - Part B 38, 1402–1412 (2008)

    Google Scholar 

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Ishibuchi, H., Akedo, N., Nojima, Y. (2012). Recombination of Similar Parents in SMS-EMOA on Many-Objective 0/1 Knapsack Problems. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds) Parallel Problem Solving from Nature - PPSN XII. PPSN 2012. Lecture Notes in Computer Science, vol 7492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32964-7_14

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  • DOI: https://doi.org/10.1007/978-3-642-32964-7_14

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