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Modelling the Population Distribution in Multi-objective Optimization by Generative Topographic Mapping

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Parallel Problem Solving from Nature - PPSN IX (PPSN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4193))

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Abstract

Under mild conditions, the Pareto set of a continuous multi-objective optimization problem exhibits certain regularity. We have recently advocated taking into consideration such regularity in designing multi-objective evolutionary algorithms. Following our previous work on using Local Principal Component Analysis for capturing the regularity, this paper presents a new approach for acquiring and using the regularity of the Pareto set in evolutionary algorithms. The approach is based on the Generative Topographic Mapping and can be regarded as an Estimation of Distribution Algorithm. It builds models of the distribution of promising solutions based on regularity patterns extracted from the previous search, and samples new solutions from the models thus built. The proposed algorithm has been compared with two other state-of-the-art algorithms, NSGA-II and SPEA2 on a set of test problems.

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References

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

    MATH  Google Scholar 

  2. Ghosh, A., Dehuri, S.: Evolutionary algorithms for multi-criterion optimization: A survey. International Journal of Computing & Information Sciences 2(1), 38–57 (2004)

    Google Scholar 

  3. Zitzler, E., Laumanns, M., Bleuler, S.: A tutorial on evolutionary multiobjective optimization. In: Workshop on Multiple Objective Metaheuristics (MOMH 2002), Berlin, Germany. Lecture Notes in Economics and Mathematical Systems, vol. 535, pp. 3–37. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  4. Larrañaga, P., Lozano, J.A. (eds.): Estimation of distribution algorithms: a new tool for evolutionary computation. Kluwer Academic Publishers, Norwell (2001)

    Google Scholar 

  5. Zhang, Q.: On stability of fixed points of limit models of univariate marginal distribution algorithm and factorized distribution algorithm. IEEE Transactions on Evolutionary Computation 8(1), 80–93 (2004)

    Article  Google Scholar 

  6. Zhang, Q., Mühlenbein, H.: On the convergence of a class of estimation of distribution algorithms. IEEE Transactions on Evolutionary Computation 8(2), 127–136 (2004)

    Article  Google Scholar 

  7. Bosman, P.A.N., Thierens, D.: The naive MIDEA: A baseline multi-objective EA. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 428–442. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Sastry, K., Pelikan, M., Goldberg, D.E.: Decomposable problems, niching, and scalability of multiobjective estimation of distribution algorithms. IlliGAL Report 2005004, Illinois Genetic Algorithms Laboratory (2005)

    Google Scholar 

  9. Okabe, T., Jin, Y., Sendhoff, B., Olhofer, M.: Voronoi-based estimation of distribution algorithm for multi-objective optimization. In: Proceedings of the Congress on Evolutionary Computation (CEC 2004), Portland, Oregon, USA, June 2004, pp. 1594–1601. IEEE Press, Los Alamitos (2004)

    Google Scholar 

  10. Schütze, O., Mostaghim, S., Dellnitz, M., Teich, J.: Covering Pareto sets by multilevel evolutionary subdivision techniques. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 118–132. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Jin, Y., Sendhoff, B.: Connectedness, regularity and the success of local search in evolutionary multi-objective optimization. In: Proceedings of the Congress on Evolutionary Computation (CEC 2003), Canberra, Australia, December 2003, pp. 1910–1917. IEEE Press, Los Alamitos (2003)

    Google Scholar 

  12. Okabe, T., Jin, Y., Olhofer, M., Sendhoff, B.: On test functions for evolutionary multi-objective optimization. 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. 792–802. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Zhou, A., Zhang, Q., Jin, Y., Tsang, E., Okabe, T.: A model-based evolutionary algorithm for bi-objective optimization. In: Proceedings of the Congress on Evolutionary Computation (CEC 2005), Edinburgh, U.K, September 2005, pp. 2568–2575. IEEE Press, Los Alamitos (2005)

    Google Scholar 

  14. Zhou, A., Jin, Y., Zhang, Q., Okabe, T., Tsang, E.: Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion. In: Proceedings of the Congress on Evolutionary Computation (CEC 2006) (to be published, 2006)

    Google Scholar 

  15. Zhang, Q., Zhou, A., Jin, Y.: Modelling the regularity in estimation of distribution algorithm for continuous multi-objective evolutionary optimization with variable linkages (to be submitted, 2006)

    Google Scholar 

  16. Kambhatla, N., Leen, T.K.: Dimension reduction by local principal component analysis. Neural Computation 9(7), 1493–1516 (1997)

    Article  Google Scholar 

  17. Deb, K.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)

    Article  Google Scholar 

  18. Büche, D., Milano, M., Koumoutsakos, P.: Self-organizing maps for multi-objective optimization. In: Proceedings of Genetic and Evolutionary Computation Conference (GECCO 2002), New York, July 2002, pp. 152–155. Morgan Kaufmann Publishers, San Francisco (2002)

    Google Scholar 

  19. Bishop, C.M., Svensén, M., Williams, C.K.I.: GTM:the generative topographic mapping. Neural Computation 10(1), 215–234 (1998)

    Article  Google Scholar 

  20. Okabe, T.: Evolutionary Multi-Objective Optimization: On the Distribution of Offspring in Parameter and Fitness Space. PhD thesis, Honda Research Institute Europe GmbH (2004)

    Google Scholar 

  21. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. Technical Report 112, Computer Engineering and Networks Laboratory (TIK),Swiss Federal Institute of Technology (ETH) (2001)

    Google Scholar 

  22. Jin, Y. (ed.): Knowledge Incorporation in Evolutionary Computation. Studies in Fuzziness and Soft Computing, vol. 167. Springer, Berlin, Heidelberg (2004)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Essex, Colchester, CO4 3SQ, UK

    Aimin Zhou, Qingfu Zhang & Edward Tsang

  2. Honda Research Institute Europe, Carl-Legien-Str. 30, 63073, Offenbach, Germany

    Yaochu Jin & Bernhard Sendhoff

Authors
  1. Aimin Zhou
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  2. Qingfu Zhang
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  3. Yaochu Jin
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  4. Bernhard Sendhoff
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  5. Edward Tsang
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Editor information

Editors and Affiliations

  1. Science Institute, University of Iceland, P.O. Box, Iceland

    Thomas Philip Runarsson

  2. Vorarlberg University of Applied Sciences, Hochschulstr. 1, A-6850, Dornbirn, Austria

    Hans-Georg Beyer

  3. Automated Scheduling, Optimisation and Planning Group, School of Computer Science & IT, University of Nottingham, NG8 1BB, Nottingham, UK

    Edmund Burke

  4. Depto. Arquitectura y Tecnologa de Computadores, ETS Ingeiera Informtica, C/Daniel Saucedo Aranda, s/n, 18071, Granada, Spain

    Juan J. Merelo-Guervós

  5. Colorado State University, 80523, Fort Collins, CO, USA

    L. Darrell Whitley

  6. University of Birmingham, Birmingham, UK

    Xin Yao

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© 2006 Springer-Verlag Berlin Heidelberg

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Zhou, A., Zhang, Q., Jin, Y., Sendhoff, B., Tsang, E. (2006). Modelling the Population Distribution in Multi-objective Optimization by Generative Topographic Mapping. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_45

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  • DOI: https://doi.org/10.1007/11844297_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38990-3

  • Online ISBN: 978-3-540-38991-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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