Skip to main content
SpringerLink
Log in

Many-Objective Optimization for Knapsack Problems Using Correlation-Based Weighted Sum Approach

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

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

Included in the following conference series:

Abstract

In this paper, we examine the effectiveness of an EMO (Evolutionary Multi-criterion Optimization) algorithm using a correlation based weighted sum for many objective optimization problems. Recently many EMO algorithms are proposed for various multi-objective problems. However, it is known that the convergence performance to the Pareto-frontier becomes weak in approaches using archives for non-dominated solutions since the size of archives becomes large as the number of objectives becomes large. In this paper, we show the effectiveness of using a correlation information between objectives to construct groups of objectives. Our simulation results show that while an archive-based approach, such as NSGA-II, produces a set of non-dominated solutions with better objective values in each objective, the correlation-based weighted sum approach can produce better compromise solutions that has averagely better objective values in every objective.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Deb, K., Pratap, S., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transaction on Evolutionary Computation 6(2), 182–197 (2002)

    Article  Google Scholar 

  2. Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and strength Pareto approach. IEEE Transaction on Evolutionary Computation 3(4), 257–271 (1999)

    Article  Google Scholar 

  3. 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 

  4. Ishibuchi, H., Nojima, Y., Doi, T.: Comparison between single-objective and multi-objective genetic algorithms: Performance comparison and performance measures. In: Proc. of 2006 Congress on Evolutionary Computation, pp. 3959–3966 (2006)

    Google Scholar 

  5. 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 

  6. Hughes, E.J.: Multiple single objective pareto sampling. In: Proc. of 2003 Congress on Evolutionary Computation, pp. 2678–2684 (2003)

    Google Scholar 

  7. Emmerich, M., Beume, N., Naujoks, B.: An EMO algorithm using the hypervolume measure as selection criterion. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 62–76. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization. In: Proc. of 3rd Int’l. Workshop on Genetic and Evolving Fuzzy Systems, pp. 47–52 (2008)

    Google Scholar 

  9. 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 

  10. Murata, T., Ishibuchi, H., Tanaka, H.: Multi-objective genetic algorithm and its application to flowshop scheduling. Computer and Industrial Engineering Journal 30(4), 957–968 (1996)

    Article  Google Scholar 

  11. Ishibuchi, H., Murata, T.: A multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans. on Systems, Man, and Cybernetics, Part C 28(5), 601–618 (1999)

    Article  Google Scholar 

  12. Murata, T., Ishibuchi, H., Gen, M.: Specification of genetic search directions in cellular multi-objective genetic algorithms. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 82–95. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Hughes, E.J.: MSOP-II: A general-purpose many-objective optimiser. In: Proc. of 2007 Congress on Evolutionary Computation, pp. 3944–3951 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Informatics, Kansai University, 2-1-1, Ryozenji, Takatsuki, Osaka, 569-1073, Japan

    Tadahiko Murata

  2. Policy Grid Computing Laboratory, Institute for Socionetwork Strategies, Kansai University, 3-3-35, Yamate, Suita, Osaka, 564-8680, Japan

    Tadahiko Murata

  3. Graduate School of Informatics, Kansai University, 2-1-1, Ryozenji, Takatsuki, Osaka, 569-1073, Japan

    Akinori Taki

Authors
  1. Tadahiko Murata
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Akinori Taki
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Murata, T., Taki, A. (2009). Many-Objective Optimization for Knapsack Problems Using Correlation-Based Weighted Sum Approach. 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_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-01020-0_37

  • 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)

Publish with us

Policies and ethics

Search

Navigation