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International Conference on Evolutionary Multi-Criterion Optimization

EMO 2013: Evolutionary Multi-Criterion Optimization pp 459–474Cite as

Relation between Neighborhood Size and MOEA/D Performance on Many-Objective Problems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7811))

Abstract

MOEA/D is a simple but powerful scalarizing function-based EMO algorithm. Its high search ability has been demonstrated for a wide variety of multiobjective problems. MOEA/D can be viewed as a cellular algorithm. Each cell has a different weight vector and a single solution. A certain number of the nearest cells are defined for each cell as its neighbors based on the Euclidean distance between weight vectors. A new solution is generated for each cell from current solutions in its neighboring cells. The generated solution is compared with the current solutions in the neighboring cells for solution replacement. In this paper, we examine the relation between the neighborhood size and the performance of MOEA/D. In order to examine the effect of local mating and local replacement separately, we use a variant of MOEA/D with two different neighborhoods: One is for local mating and the other is for local replacement. The performance of MOEA/D with various combinations of two neighborhoods is examined using the hypervolume in the objective space and a diversity measure in the decision space for many-objective problems. Experimental results show that MOEA/D with a large replacement neighborhood has high search ability in the objective space. However, it is also shown that small replacement and mating neighborhoods are beneficial for diversity maintenance in the decision space. It is also shown that the appropriate specification of two neighborhoods strongly depends on the problem.

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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)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    MATH  Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. Deb, K., Tiwari, S.: Omni-Optimizer: A Generic Evolutionary Algorithm for Single and Multi-Objective Optimization. European Journal of Operational Research 185, 1062–1087 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hughes, E.J.: Evolutionary Many-Objective Optimisation: Many Once or One Many? In: Proc. of 2005 IEEE Congress on Evolutionary Computation, pp. 222–227 (2005)

    Google Scholar 

  9. Ishibuchi, H., Akedo, N., Nojima, Y.: A Many-Objective Test Problem for Visually Examining Diversity Maintenance Behavior in a Decision Space. In: Proc. of 2011 Genetic and Evolutionary Computation Conference, pp. 649–656 (2011)

    Google Scholar 

  10. Ishibuchi, H., Akedo, N., Nojima, Y.: 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.) PPSN XII, Part II. LNCS, vol. 7492, pp. 132–142. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. Ishibuchi, H., Hitotsuyanagi, Y., Ohyanagi, H., Nojima, Y.: Effects of the Existence of Highly Correlated Objectives on the Behavior of MOEA/D. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds.) EMO 2011. LNCS, vol. 6576, pp. 166–181. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Ishibuchi, H., Hitotsuyanagi, Y., Tsukamoto, N., Nojima, Y.: Many-Objective Test Problems to Visually Examine the Behavior of Multiobjective Evolution in a Decision Space. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI, Part II. LNCS, vol. 6239, pp. 91–100. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. Ishibuchi, H., Sakane, Y., Tsukamoto, N., Nojima, Y.: Evolutionary Many-Objective Optimization by NSGA-II and MOEA/D with Large Populations. In: Proc. of 2009 IEEE International Conference on Systems, Man, and Cybernetics, pp. 1820–1825 (2009)

    Google Scholar 

  14. Ishibuchi, H., Sakane, Y., Tsukamoto, N., Nojima, Y.: Adaptation of Scalarizing Functions in MOEA/D: An Adaptive Scalarizing Function-Based Multiobjective Evolutionary Algorithm. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 438–452. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  15. Ishibuchi, H., Sakane, Y., Tsukamoto, N., Nojima, Y.: Simultaneous Use of Different Scalarizing Functions in MOEA/D. In: Proc. of Genetic and Evolutionary Computation Conference, 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 2008 Genetic and Evolutionary Computation Conference, pp. 649–656 (2008)

    Google Scholar 

  17. Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary Many-Objective Optimization: A Short Review. In: Proc. of 2008 IEEE Congress on Evolutionary Computation, 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)

    Article  Google Scholar 

  19. Khare, V., 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)

    Chapter  Google Scholar 

  20. Kowatari, N., Oyama, A., Aguirre, H., Tanaka, K.: Analysis on Population Size and Neighborhood Recombination on Many-Objective Optimization. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN XII, Part II. LNCS, vol. 7492, pp. 22–31. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  21. 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)

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. 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)

    Article  MATH  Google Scholar 

  24. Schütze, O., Lara, A., Coello, C.A.C.: 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)

    Article  Google Scholar 

  25. Solow, A.R., Polasky, S.: Measuring Biological Diversity. Environmental and Ecological Statistics 1, 95–103 (1994)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  27. Ulrich, T., Bader, J., Thiele, L.: Integrating Decision Space Diversity into Hypervolume-Based Multiobjective Search. In: Proc. of 2010 Genetic and Evolutionary Computation Conference, pp. 455–462 (2010)

    Google Scholar 

  28. Ulrich, T., Bader, J., Thiele, L.: Defining and Optimizing Indicator-Based Diversity Measures in Multiobjective Search. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI, Part I. LNCS, vol. 6238, pp. 707–717. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  29. Ulrich, T., Thiele, L.: Maximizing Population Diversity in Single-Objective Optimization. In: Proc. of 2011 Genetic and Evolutionary Computation Conference, pp. 641–648 (2011)

    Google Scholar 

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

    Article  Google Scholar 

  31. Zhang, Q., Liu, W., Li, H.: The Performance of a New Version of MOEA/D on CEC09 Unconstrained MOP Test Instances. In: Proc. of 2009 Congress on Evolutionary Computation, pp. 203–208 (2009)

    Google Scholar 

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

    Google Scholar 

  33. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Trans. on Evolutionary Computation 7, 117–132 (2003)

    Article  Google Scholar 

  34. 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)

    Article  Google Scholar 

  35. 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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Authors and Affiliations

  1. Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka, 599-8531, Japan

    Hisao Ishibuchi, Naoya Akedo & Yusuke Nojima

Authors
  1. Hisao Ishibuchi
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  2. Naoya Akedo
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  3. Yusuke Nojima
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Editor information

Editors and Affiliations

  1. Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, S1 3JD, Sheffield, UK

    Robin C. Purshouse

  2. Department of Automatic Control Systems and Engineering, University of Sheffield, Mappin Street, S1 3JD, Sheffield, UK

    Peter J. Fleming

  3. Department of Informatics Engineering, University of Coimbra, Pólo II, Pinhal de Marrocos, 3030-290, Coimbra, Portugal

    Carlos M. Fonseca

  4. Department of Economics and Business, University of Catania, Corso Italia 55, 95129, Catania, Italy

    Salvatore Greco

  5. Unilever Research & Development Port Sunlight, Quarry Road East, CH63 3JW, Merseyside, UK

    Jane Shaw

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Ishibuchi, H., Akedo, N., Nojima, Y. (2013). Relation between Neighborhood Size and MOEA/D Performance on Many-Objective Problems. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds) Evolutionary Multi-Criterion Optimization. EMO 2013. Lecture Notes in Computer Science, vol 7811. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37140-0_35

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  • DOI: https://doi.org/10.1007/978-3-642-37140-0_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37139-4

  • Online ISBN: 978-3-642-37140-0

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