Skip to main content
SpringerLink
Log in

Running Time Analysis of Multi-objective Evolutionary Algorithms on a Simple Discrete Optimization Problem

  • Conference paper
  • First Online:
Parallel Problem Solving from Nature — PPSN VII (PPSN 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2439))

Included in the following conference series:

Abstract

For the first time, a running time analysis of populationbased multi-objective evolutionary algorithms for a discrete optimization problem is given. To this end, we define a simple pseudo-Boolean bi-objective problem (Lotz: leading ones– trailing zeroes) and investigate time required to find the entire set of Pareto-optimal solutions. It is shown that different multi-objective generalizations of a (1+1) evolutionary algorithm (EA) as well as a simple population-based evolutionary multi-objective optimizer (SEMO) need on average at least Θ(n 3) steps to optimize this function. We propose the fair evolutionary multi- objective optimizer (FEMO) and prove that this algorithm performs a black box optimization in Θ(n 2 log n) function evaluations where n is the number of binary decision variables.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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. K. Deb. Multi-objective optimization using evolutionary algorithms. Wiley, Chichester, UK, 2001.

    Google Scholar 

  2. S. Droste, T. Jansen, and I. Wegener. A rigorous complexity analysis of the (1+1) evolutionary algorithm for separable functions with Boolean inputs. Evolutionary Computation, 6(2):185–196, 1998.

    Article  Google Scholar 

  3. S. Droste, T. Jansen, and I. Wegener. On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science, 276(1–2):51–81, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  4. T. Hanne. On the convergence of multiobjective evolutionary algorithms. European Journal Of Operational Research, 117(3):553–564, 1999.

    Article  MATH  Google Scholar 

  5. T. Hanne. Global multiobjective optimization with evolutionary algorithms: Selection mechanisms and mutation control. In Evolutionary Multi-Criterion Optimization (EMO 2001), Proc., LNCS 1993, pages 197–212, Berlin, 2001. Springer.

    Google Scholar 

  6. J. D. Knowles and D. W. Corne. Approximating the non-dominated front using the Pareto Archived Evolution Strategy. Evolutionary Computation, 8(2):149–172, 2000.

    Article  Google Scholar 

  7. M. Laumanns, L. Thiele, K. Deb, and E. Zitzler. Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary Computation, 10(3), 2002.

    Google Scholar 

  8. G. Rudolph. Convergence Properties of Evolutionary Algorithms. Verlag Dr. Kovač, Hamburg, 1997.

    Google Scholar 

  9. G. Rudolph. Evolutionary search for minimal elements in partially ordered sets. In Evolutionary Programming VII-Proc. Seventh Annual Conf. on Evolutionary Programming (EP-98), San Diego CA, 1998. The MIT Press, Cambridge MA.

    Google Scholar 

  10. G. Rudolph. On a multi-objective evolutionary algorithm and its convergence to the pareto set. In IEEE Int'l Conf. on Evolutionary Computation (ICEC’98), pages 511–516, Piscataway, 1998. IEEE Press.

    Google Scholar 

  11. G. Rudolph. Evolutionary Search under Partially Ordered Fitness Sets. In Proceedings of the International NAISO Congress on Information Science Innovations (ISI 2001), pages 818–822. ICSC Academic Press: Millet/Sliedrecht, 2001.

    Google Scholar 

  12. G. Rudolph and A. Agapie. Convergence properties of some multi-objective evolutionary algorithms. In Congress on Evolutionary Computation (CEC 2000), volume 2, pages 1010–1016, Piscataway, NJ, 2000. IEEE Press.

    Google Scholar 

  13. J. Scharnow, K. Tinnefeld, and I. Wegener. Fitness landscapes based on sorting and shortest paths problems. This volume.

    Google Scholar 

  14. D. A. Van Veldhuizen. Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovations. PhD thesis, Graduate School of Engineering of the Air Force Institute of Technology, Air University, June 1999.

    Google Scholar 

  15. I. Wegener. Methods for the analysis of evolutionary algorithms on pseudo-boolean functions. Technical Report CI-99/00, SFB 531, Universität Dortmund, 2000.

    Google Scholar 

  16. I. Wegener. Theoretical aspects of evolutionary algorithms. In ICALP 2001, volume 2076 of LNCS, pages 64–78. Springer-Verlag, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Engineering and Networks Laboratory, ETH Zürich, CH-8092, Zürich

    Marco Laumanns, Lothar Thiele & Eckart Zitzler

  2. Institute of Theoretical Computer Science, ETH Zürich, CH-8092, Zürich

    Emo Welzl

  3. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, PIN 208 016, Kanpur, India

    Kalyanmoy Deb

Authors
  1. Marco Laumanns
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lothar Thiele
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eckart Zitzler
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Emo Welzl
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kalyanmoy Deb
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Escuela Técnica Superior de Ingeniería Informática, 18071, Granada, Spain

    Juan Julián Merelo Guervós

  2. Department of Informatics, Technological Educational Institute of Thessaloniki, 54101, Thessaloniki, Greece

    Panagiotis Adamidis

  3. Department of Informatics XI, University of Dortmund, 44221, Dortmund, Germany

    Hans-Georg Beyer  & Hans-Paul Schwefel  & 

  4. Department of Signal Theory and Communications, Universidad Carlos III, Madrid, Spain

    José-Luis Fernández-Villacañas

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Laumanns, M., Thiele, L., Zitzler, E., Welzl, E., Deb, K. (2002). Running Time Analysis of Multi-objective Evolutionary Algorithms on a Simple Discrete Optimization Problem. In: Guervós, J.J.M., Adamidis, P., Beyer, HG., Schwefel, HP., Fernández-Villacañas, JL. (eds) Parallel Problem Solving from Nature — PPSN VII. PPSN 2002. Lecture Notes in Computer Science, vol 2439. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45712-7_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-45712-7_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44139-7

  • Online ISBN: 978-3-540-45712-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation