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Many-Objective Test Problems to Visually Examine the Behavior of Multiobjective Evolution in a Decision Space

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Parallel Problem Solving from Nature, PPSN XI (PPSN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6239))

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Abstract

Many-objective optimization is a hot issue in the EMO (evolutionary multiobjective optimization) community. Since almost all solutions in the current population are non-dominated with each other in many-objective EMO algorithms, we may need a different fitness evaluation scheme from the case of two and three objectives. One difficulty in the design of many-objective EMO algorithms is that we cannot visually observe the behavior of multiobjective evolution in the objective space with four or more objectives. In this paper, we propose the use of many-objective test problems in a two- or three-dimensional decision space to visually examine the behavior of multiobjective evolution. Such a visual examination helps us to understand the characteristic features of EMO algorithms for many-objective optimization. Good understanding of existing EMO algorithms may facilitates their modification and the development of new EMO algorithms for many-objective optimization.

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References

  1. Abbass, H.A., Alam, S., Bender, A.: MEBRA: Multiobjective Evolutionary-Based Risk Assessment. IEEE Computational Intelligence Magazine 4, 29–36 (2009)

    Article  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: Foundations of Genetic Algorithms: FOGA 2009, pp. 87–102 (2009)

    Google Scholar 

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

    MATH  Google Scholar 

  4. Corne, D., Knowles, J.: Techniques for Highly Multiobjective Optimization: Some Non-Dominated Points are Better Than Others. In: Proc. of 2007 Genetic and Evolutionary Computation Conference, pp. 773–780 (2007)

    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., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: Proc. of 2002 IEEE Congress on Evolutionary Computation, pp. 825–830 (2002)

    Google Scholar 

  8. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Test Problems for Evolutionary Multiobjective Optimization. In: Abraham, A., Jain, L.C., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization: Theoretical Advances and Applications, pp. 105–145. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Fleming, P.J., Purshouse, R.C., Lygoe, R.J.: Many-Objective Optimization: An Engineering Design Perspective. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 14–32. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  12. Ishibuchi, H., Hitotsuyanagi, Y., Nojima, Y.: Scalability of Multiobjective Genetic Local Search to Many-Objective Problems: Knapsack Problem Case Studies. In: Proc. of 2008 IEEE Congress on Evolutionary Computation, pp. 3587–3594 (2008)

    Google Scholar 

  13. Ishibuchi, H., Nojima, Y., Doi, T.: Comparison between Single-Objective and Multi-Objective Genetic Algorithms: Performance Comparison and Performance Measures. In: Proc. of 2006 IEEE Congress on Evolutionary Computation, pp. 3959–3966 (2006)

    Google Scholar 

  14. Ishibuchi, H., Sakane, Y., Tsukamoto, N., Nojima, Y.: Single-Objective and Multi-Objective Formulations of Solution Selection for Hypervolume Maximization. In: Proc. of 2009 Genetic and Evolutionary Computation Conference, pp. 1831–1832 (2009)

    Google Scholar 

  15. 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 

  16. Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary Many-Objective Optimization: A Short Review. In: Proc. of IEEE Congress on Evolutionary Computation, pp. 2424–2431 (2008)

    Google Scholar 

  17. Jeong, S., Hasegawa, S., Shimoyama, K., Obayashi, S.: Development and Investigation of Efficient GA/PSO-HYBRID Algorithm Applicable to Real-World Design Optimization. IEEE Computational Intelligence Magazine 4, 36–44 (2009)

    Article  Google Scholar 

  18. Jin, Y., Sendhoff, B.: A Systems Approach to Evolutionary Multiobjective Structural Optimization and Beyond. IEEE Computational Intelligence Magazine 4, 62–76 (2009)

    Article  Google Scholar 

  19. Khara, 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. Knowles, J.: Closed-loop Evolutionary Multiobjective Optimization. IEEE Computational Intelligence Magazine 4, 77–91 (2009)

    Article  Google Scholar 

  21. Köppen, M., Yoshida, K.: Substitute Distance Assignments in NSGA-II for Handling Many-Objective Optimization Problems. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 727–741. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  22. Rudolph, G., Naujoks, B., Preuss, M.: Capabilities of EMOA to Detect and Preserve Equivalent Pareto Subsets. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 36–50. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  23. 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)

    Chapter  Google Scholar 

  24. Singh, H., Isaacs, A., Ray, T., Smith, W.: A Study on the Performance of Substitute Distance Based Approaches for Evolutionary Many Objective Optimization. In: Li, X., Kirley, M., Zhang, M., Green, D., Ciesielski, V., Abbass, H.A., Michalewicz, Z., Hendtlass, T., Deb, K., Tan, K.C., Branke, J., Shi, Y. (eds.) SEAL 2008. LNCS, vol. 5361, pp. 411–420. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  25. Sülflow, A., Drechsler, N., Drechsler, R.: Robust Multi-Objective Optimization in High Dimensional Spaces. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 715–726. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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

    MATH  Google Scholar 

  27. 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)

    Chapter  Google Scholar 

  28. 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 

  29. Zitzler, E., Deb, K., Thiele, L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8, 125–148 (2000)

    Article  Google Scholar 

  30. 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 

  31. 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 

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

    Article  Google Scholar 

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Author information

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, Yasuhiro Hitotsuyanagi, Noritaka Tsukamoto & Yusuke Nojima

Authors
  1. Hisao Ishibuchi
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  2. Yasuhiro Hitotsuyanagi
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  3. Noritaka Tsukamoto
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  4. Yusuke Nojima
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Editor information

Editors and Affiliations

  1. Faculty of Electrical Engineering, Automatics, Computer Science and Electronics, Department of ComputerScience, AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Robert Schaefer

  2. Departamento de Lenguajes y Ciencias de la Computación, ETSI Informática, Universidad de Málaga, Campus Teatinos, 29071, Málaga, Spain

    Carlos Cotta

  3. Department of Mathematics and Computer Science, University of Bielsko-Biala, Willowa 2, 43-309, Bielsko-Biala, Poland

    Joanna Kołodziej

  4. Fakultät für Informatik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Günter Rudolph

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Ishibuchi, H., Hitotsuyanagi, Y., Tsukamoto, N., Nojima, Y. (2010). 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) Parallel Problem Solving from Nature, PPSN XI. PPSN 2010. Lecture Notes in Computer Science, vol 6239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15871-1_10

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  • DOI: https://doi.org/10.1007/978-3-642-15871-1_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15870-4

  • Online ISBN: 978-3-642-15871-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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