Skip to main content
SpringerLink
Log in

A Tutorial on Evolutionary Multiobjective Optimization

  • Conference paper
Metaheuristics for Multiobjective Optimisation

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 535))

Abstract

Multiple, often conflicting objectives arise naturally in most real-world optimization scenarios. As evolutionary algorithms possess several characteristics that are desirable for this type of problem, this class of search strategies has been used for multiobjective optimization for more than a decade. Meanwhile evolutionary multiobjective optimization has become established as a separate subdiscipline combining the fields of evolutionary computation and classical multiple criteria decision making.

This paper gives an overview of evolutionary multiobjective optimization with the focus on methods and theory. On the one hand, basic principles of multiobjective optimization and evolutionary algorithms are presented, and various algorithmic concepts such as fitness assignment, diversity preservation, and elitism are discussed. On the other hand, the tutorial includes some recent theoretical results on the performance of multiobjective evolutionary algorithms and addresses the question of how to simplify the exchange of methods and applications by means of a standardized interface.

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. T. Bäck, U. Hammel, and H.-P. Schwefel. Evolutionary computation: Comments on the history and current state. IEEE Transactions on Evolutionary Computation, 1(1):3–17, 1997.

    Article  Google Scholar 

  2. S. Bleuler, M. Brack, L. Thiele, and E. Zitzler. Multiobjective genetic programming: Reducing bloat by using SPEA2. In Congress on Evolutionary Computation (CEC-2001), pages 536–543, Piscataway, NJ, 2001. IEEE.

    Google Scholar 

  3. S. Bleuler, M. Laumanns, L. Thiele, and E. Zitzler. PISA — a platform and programming language independent interface for search algorithms. In C. M. Fonseca et al., editors, Second International Conference on Evolutionary Multi-Criterion Optimization (EMO 2003), pages 494–508, Berlin, Germany, 2003. Springer.

    Google Scholar 

  4. C. A. Coello Coello, D. A. Van Veldhuizen, and G. B. Lamont. Evolutionary Algorithms for Solving Multiobjective Problems. Kluwer, New York, 2002.

    Google Scholar 

  5. D. W. Corne, J. D. Knowles, and M. J. Oates. The pareto envelope-based selection algorithm for multiobjective optimization. In M. Schoenauer et al., editors, Parallel Problem Solving from Nature (PPSN VI), pages 839–848, Berlin, 2000. Springer.

    Google Scholar 

  6. K. Deb. Multiobjective genetic algorithms: Problem difficulties and construction of test problems. Evolutionary Computation, 7(3):205–230, 1999.

    Article  Google Scholar 

  7. K. Deb. Multiobjective optimization using evolutionary algorithms.Wiley, Chichester, UK, 2001.

    Google Scholar 

  8. K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan. A fast elitist non-dominated sorting genetic algorithm for Multiobjective optimization: NSGA-II. In M. Schoenauer et al., editors, Parallel Problem Solving from Nature (PPSN VI), pages 849–858, Berlin, 2000. Springer.

    Google Scholar 

  9. K. Deb, L. Thiele, M. Laumanns, and E. Zitzler. Scalable Multiobjective optimization test problems. In D. B. Fogel, M. A. El-Sharkawi, X. Yao, G. Greenwood, H. Iba, P. Marrow, and M. Shackleton, editors, Congress on Evolutionary Computation (CEC), pages 825–830, 2002.

    Google Scholar 

  10. 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 

  11. 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  Google Scholar 

  12. T. Erlebach, H. Kellerer, and U. Pferschy. Approximating Multiobjective knapsack problems. In F. K. H. A. Dehne et al., editors, Workshop on Algorithms and Data Structures (WADS 2001), pages 210–221, Berlin, Germany, 2001. Springer.

    Google Scholar 

  13. C. M. Fonseca and P. J. Fleming. Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In S. Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms, pages 416–423, San Mateo, California, 1993. Morgan Kaufmann.

    Google Scholar 

  14. M. P. Fourman. Compaction of symbolic layout using genetic algorithms. In J. J. Grefenstette, editor, Proceedings of an International Conference on Genetic Algorithms and Their Applications, pages 141–153, Pittsburgh, PA, 1985. sponsored by Texas Instruments and U.S. Navy Center for Applied Research in Artificial Intelligence (NCARAI).

    Google Scholar 

  15. D. E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, Massachusetts, 1989.

    Google Scholar 

  16. P. Hajela and C.-Y. Lin. Genetic search strategies in multicriterion optimal design. Structural Optimization, 4:99–107, 1992.

    Article  Google Scholar 

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

    Article  Google Scholar 

  18. T. Hanne. Global multiobjective optimization with evolutionary algorithms: Selection mechanisms and mutation control. In E. Zitzler et al., editors, Evolutionary Multi-criterion Optimization (EMO 2001), Proc., Lecture Notes in Computer Science Vol. 1993, pages 197–212, Berlin, 2001. Springer.

    Google Scholar 

  19. S. Helbig and D. Pateva. On several concepts for E-efficiency. OR Spektrum, 16(3):179–186, 1994.

    Article  Google Scholar 

  20. J. Horn, N. Nafpliotis, and D. E. Goldberg. A niched pareto genetic algorithm for multiobjective optimization. In Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Computation, volume 1, pages 82–87, Piscataway, NJ, 1994. IEEE Press.

    Google Scholar 

  21. H. Ishibuchi and T. Murata. Multiobjective genetic local search algorithm. In Proceedings of 1996 IEEE International Conference on Evolutionary Computation (ICEC′96), pages 119–124, Piscataway, NJ, 1996. IEEE Press.

    Google Scholar 

  22. A. Jaszkiewicz. On the performance of multiple-objective genetic local search on the 0/1 knapsack problem — a comparative experiment.

    Google Scholar 

  23. J.D. Knowles. Local-Search and Hybrid Evolutionary Algorithms for Pareto Optimization. PhD thesis, Department of Computer Science, University of Reading, UK, 2002.

    Google Scholar 

  24. J. D. Knowles and D. W. Corne. The pareto archived evolution strategy: A new baseline algorithm for pareto multiobjective optimization. In Congress on Evolutionary Computation (CEC99), volume 1, pages 98–105, Piscataway, NJ, 1999. IEEE Press.

    Google Scholar 

  25. F. Kursawe. A variant of evolution strategies for vector optimization. In H.-P. Schwefel and R. Männer, editors, Parallel Problem Solving from Nature, pages 193–197, Berlin, 1991. Springer.

    Google Scholar 

  26. M. Lahanas, N. Milickovic, D. Baltas, and N. Zamboglou. Application of multi-objective evolutionary algorithms for dose optimization problems in brachyther-apy. In E. Zitzler, K. Deb, L. Thiele, C. A. C. Coello, and D. Corne, editors, Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization (EMO 2001), volume 1993 of Lecture Notes in Computer Science, pages 574–587, Berlin, 2001. Springer-Verlag.

    Google Scholar 

  27. M. Laumanns, L. Thiele, K. Deb, and E. Zitzler. Combining convergence and diversity in evolutionary Multiobjective optimization. Evolutionary Computation, 10(3):263–282, 2002.

    Article  Google Scholar 

  28. M. Laumanns, L. Thiele, E. Zitzler, and K. Deb. Archiving with guaranteed convergence and diversity in Multiobjective optimization. In W. B. Lang-don, E. Cantú-Paz, K. Mathias, R. Roy, D. Davis, R. Poli, K. Balakrishnan, V. Honavar, G. Rudolph, J. Wegener, L. Bull, M. A. Potter, A. C. Schultz, J. F. Miller, E. Burke, and N. Jonoska, editors, GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, pages 439–447, New York, 9-13 July 2002. Morgan Kaufmann Publishers.

    Google Scholar 

  29. M. Laumanns, L. Thiele, E. Zitzler, E. Welzl, and K. Deb. Running time analysis of Multiobjective evolutionary algorithms on a simple discrete optimization problem. In Parallel Problem Solving From Nature — PPSN VII, 2002.

    Google Scholar 

  30. S. Mostaghim, J. Teich, and A. Tyagi. Comparison of data structures for storing pareto-sets in moeas. In IEEE Proceedings, World Congress on Computational Intelligence (CEC 2002), pages 843–849, Honolulu, USA, May 12-17 2002.

    Google Scholar 

  31. G. T. Parks and I. Miller. Selective breeding in a multiobjective genetic algorithm. In A. E. Eiben et al., editors, Parallel Problem Solving from Nature — PPSN V, pages 250–259, Berlin, 1998. Springer.

    Google Scholar 

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

    Google Scholar 

  33. 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 

  34. G. Rudolph and A. Agapie. Convergence properties of some Multiobjective evolutionary algorithms. In A. Zalzala and R. Eberhart, editors, Congress on Evolutionary Computation (CEC 2000), volume 2, pages 1010–1016, Piscataway, NJ, 2000. IEEE Press.

    Google Scholar 

  35. J. D. Schaffer. Multiple objective optimization with vector evaluated genetic algorithms. In J. J. Grefenstette, editor, Proceedings of an International Conference on Genetic Algorithms and Their Applications, pages 93–100, Pittsburgh, PA, 1985. sponsored by Texas Instruments and U.S. Navy Center for Applied Research in Artificial Intelligence (NCARAI).

    Google Scholar 

  36. J. Scharnow, K. Tinnefeld, and I. Wegener. Fitness landscapes based on sorting and shortest paths problems. In Parallel Problem Solving From Nature — PPSN VII, 2002.

    Google Scholar 

  37. B. W. Silverman. Density estimation for statistics and data analysis.Chapman and Hall, London, 1986.

    Google Scholar 

  38. N. Srinivas and K. Deb. Multiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation, 2(3):221–248, 1994.

    Article  Google Scholar 

  39. 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 

  40. D. A. Van Veldhuizen and G. B. Lamont. On measuring multiobjective evolutionary algorithm performance. In A. Zalzala and R. Eberhart, editors, Congress on Evolutionary Computation (CEC 2000), volume 1, pages 204–211, Piscataway, NJ, 2000. IEEE Press.

    Google Scholar 

  41. 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 

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

    Google Scholar 

  43. E. Zitzler. Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications.Ph.D. thesis, Shaker Verlag, Aachen, Germany, 1999.

    Google Scholar 

  44. E. Zitzler, K. Deb, and L. Thiele. Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation, 8(2):173–195, 2000.

    Article  Google Scholar 

  45. E. Zitzler, K. Deb, L. Thiele, C. A. C. Coello, and D. Corne, editors. Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization (EMO 2001), volume 1993 of Lecture Notes in Computer Science, Berlin, Germany, March 2001. Springer.

    Google Scholar 

  46. E. Zitzler, M. Laumanns, and L. Thiele. SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In K. Giannakoglou, D. Tsahalis, J. Periaux, K. Papailiou, and T. Fogarty, editors, Evolutionary Methods for Design, Optimization, and Control, pages 19-26, Barcelona, Spain, 2002. CIMNE.

    Google Scholar 

  47. E. Zitzler, J. Teich, and S. S. Bhattacharyya. Multidimensional exploration of software implementations for DSP algorithms. Journal of VLSI Signal Processing, 24(l):83–98, February 2000.

    Google Scholar 

  48. E. Zitzler and L. Thiele. 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 

  49. E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, and V. G. da Fonseca. Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation, 7(2):117–132, 2003.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Swiss Federal Institute of Technology (ETH) Zurich, Computer Engineering and Networks Laboratory (TIK), Gloriastrasse 35, CH-8092, Zurich, Switzerland

    Eckart Zitzler, Marco Laumanns & Stefan Bleuler

Authors
  1. Eckart Zitzler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco Laumanns
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stefan Bleuler
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. LAMIH - ROI, University of Valenciennes, UMR CNRS 8530 Campus Le Mont Houy, 59313, Valenciennes Cedex 9, France

    Xavier Gandibleux

  2. LAMIH - SP, University of Valenciennes, UMR CNRS 8530 Campus Le Mont Houy, 59313, Valenciennes Cedex 9, France

    Marc Sevaux

  3. University of Antwerp Faculty of Applied Economics, Prinsstraat 13, 2000, Antwerp, Belgium

    Kenneth Sörensen

  4. Department of Computer Science Polytech’ Tours, University of Tours, 64 avenue Jean Portalis, 37200, Tours, France

    Vincent T’kindt

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zitzler, E., Laumanns, M., Bleuler, S. (2004). A Tutorial on Evolutionary Multiobjective Optimization. In: Gandibleux, X., Sevaux, M., Sörensen, K., T’kindt, V. (eds) Metaheuristics for Multiobjective Optimisation. Lecture Notes in Economics and Mathematical Systems, vol 535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17144-4_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17144-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20637-8

  • Online ISBN: 978-3-642-17144-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation