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Spread Assessment for Evolutionary Multi-Objective Optimization

  • Conference paper
Evolutionary Multi-Criterion Optimization (EMO 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5467))

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Abstract

Convergence, uniformity and spread are three basic issues in comparing the performance of multi-objective evolutionary algorithms. However, most of metrics pay more attention on former two performance indices. In this paper, we introduce a metric for evaluating the spread of non-dominated solutions. Unlike existed metrics only calculating the extreme solutions in objective space, this metric defines boundary concept of non-dominated set. And it evaluates the extent of boundary solutions by projecting them on low-dimensional spaces. Moreover, the centroid of solutions set is introduced to avoid the impact of different convergence result of algorithms. From a comparative study on several test problems, the metric is examined to assess spread of non-dominated solutions set in objective space.

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References

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

    MATH  Google Scholar 

  2. Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, New York (2002)

    Book  MATH  Google Scholar 

  3. Van Veldhuizen, D.A., Lamont, G.B.: Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art. Evolutionary Computation 8(2), 125–147 (2000)

    Article  Google Scholar 

  4. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Fonseca, V.G.: Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)

    Article  Google Scholar 

  5. Okabe, T., Jin, Y., Sendhoff, B.: A Critical Survey of Performance Indices for Multi-Objective Optimization. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), pp. 878–885 (2003)

    Google Scholar 

  6. Knowles, J., Thiele, L., Zitzler, E.: A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers, Technical Report No. 214, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Switzerland (February 2006)

    Google Scholar 

  7. Schott, J.R.: Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. Master’s thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology (1995)

    Google Scholar 

  8. Srinivas, N., Deb, K.: Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation 2(3), 221–248 (1994)

    Article  Google Scholar 

  9. Deb, K., Jain, S.: Running Performance Metrics for Evolutionary Multi-Objective Optimization. In: Proceedings of the 4th Asia-Pacific Conference on Simulated Evolution and Learning (SEAL 2002), pp. 13–20 (2002)

    Google Scholar 

  10. Li, M., Zheng, J., Xiao, G.: Uniformity Assessment for Evolutionary Multi-Objective Optimization. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2008), pp. 625–632 (2008)

    Google Scholar 

  11. Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Computation and Convergence to a Pareto Front. In: Koza, J.R. (ed.) Late Breaking Papers at the Genetic Programming Conference, pp. 221–228 (1998)

    Google Scholar 

  12. Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)

    Article  Google Scholar 

  13. Zhang, Q., Zhou, A., Jin, Y.: RM-MEDA: A Regularity Model-Based Multiobjective Estimation of Distribution Algorithm. IEEE Transactions on Evolutionary Computation 12(1), 41–63 (2008)

    Article  Google Scholar 

  14. Farhang-Mehr, A., Azarm, S.: An Information-Theoretic Entropy Metric for Assessing Multiobjective Optimization Solution Set Quality. Transactions of the ASME, Journal of Mechanical Design 125(4), 655–663 (2003)

    Article  MATH  Google Scholar 

  15. Knowles, J., Corne, D.: Properties of an Adaptive Archiving Algorithm for Storing Nondominated Vectors. IEEE Transactions on Evolutionary Computation 7(2), 100–116 (2003)

    Article  Google Scholar 

  16. Zitzler, E., Deb, K., Thiele, L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8(2), 173–195 (2000)

    Article  Google Scholar 

  17. Wu, J., Azarm, S.: Metrics for Quality Assessment of a Multiobjective Design Optimization Solution Set. Transactions of the ASME, Journal of Mechanical Design 123, 18–25 (2001)

    Article  Google Scholar 

  18. Fleischer, M.: The measure of pareto optima. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 519–533. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  19. While, L., Hingston, P., Barone, L., Huband, S.: A Faster Algorithm for Calculating Hypervolume. IEEE Transactions on Evolutionary Computation 10(1), 29–38 (2006)

    Article  Google Scholar 

  20. 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)

    Chapter  Google Scholar 

  21. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)

    Article  Google Scholar 

  22. Deb, K., Mohan, M., Mishra, S.: Towards a quick computation of well-spread pareto-optimal solutions. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 222–236. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  23. Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm. TIK-Report 103 (2001)

    Google Scholar 

  24. Corne, D., Jerram, N., Knowles, J., Oates, M.: PESA-II: Region-based Selection in Evolutionary Multiobjective Optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2001), pp. 283–290 (2001)

    Google Scholar 

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

    Google Scholar 

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

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Information Engineering, Xiangtan University, 411105, Hunan, China

    Miqing Li & Jinhua Zheng

Authors
  1. Miqing Li
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  2. Jinhua Zheng
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Editor information

Editors and Affiliations

  1. Department of Engineering Science, The University of Auckland, 70 Symonds Street, Room 415, 1001, Auckland, New Zealand

    Matthias Ehrgott

  2. Faculty of Science and Technolgoy, Department of Electronic Engineering and Informatics, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Carlos M. Fonseca

  3. Laboratoire d’ Informatique de Nantes -LINA, UMR CNRS 6241, Université de Nantes, 2, Rue de la Houssinière, BP 92208, 44322, Nantes Cedex 03, France

    Xavier Gandibleux

  4. LERIA, Faculty of Sciences, Université d’Angers, 2 Boulevard Lavoisier, 49045, Angers Cedex 01, France

    Jin-Kao Hao

  5. Université de Bretagne-sud - UEB CNRS, UMR 3192 - Lab-STICC, Centre de Recherche,, BP 92116, 56321, Lorient Cedex, France

    Marc Sevaux

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© 2009 Springer-Verlag Berlin Heidelberg

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Li, M., Zheng, J. (2009). Spread Assessment for Evolutionary Multi-Objective Optimization. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, JK., Sevaux, M. (eds) Evolutionary Multi-Criterion Optimization. EMO 2009. Lecture Notes in Computer Science, vol 5467. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01020-0_20

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  • DOI: https://doi.org/10.1007/978-3-642-01020-0_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01019-4

  • Online ISBN: 978-3-642-01020-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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