Evolving Continuous Pareto Regions

  • D. Dumitrescu
  • Crina Groşan
  • Mihai Oltean
Part of the Advanced Information and Knowledge Processing book series (AI&KP)

Summary

In this chapter we propose a new evolutionary elitist approach combining a non-standard solution representation and an evolutionary optimization technique. The proposed method permits detection of continuous decision regions. In our approach an individual (a solution) is either a closed interval or a point. The individuals in the final population give a realistic representation of the Pareto-optimal set. Each solution in this population corresponds to a decision region of the Pareto-optimal set. The proposed technique is an elitist one. It uses a unique population. The current population contains non-dominated solutions already computed.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Corne, DW and Knowles, JD., The Pareto-Envelope Based Selection Algorithm for Multiobjective Optimization. In Proceedings of the Sixth International Conference on Parallel Problem Solving from Nature, Springer-Verlag, pp. 839–848, Berlin, 2000Google Scholar
  2. 2.
    Deb, K, (1999) Multiobjective Evolutionary Algorithms: Problem Difficulties and Construction of Test Problems. Evolutionary Computation 1999; 7: 205–230.PubMedGoogle Scholar
  3. 3.
    Deb, K, Agrawal, S, Pratap, A and Meyarivan, T, A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA II. In Schoenauer, M, et al. (eds), Parallel Problem Solving From Nature-PPSN VI, Springer-Verlag, pp. 849–858, Berlin, 2000.Google Scholar
  4. 4.
    Dumitrescu, D, Grosan, C and Oltean M, An Evolutionary Algorithm for Detecting Continuous Pareto Regions. Studia Babes-Bolyai University, Ser. Informatica, 2000; 45: 51–68.Google Scholar
  5. 5.
    Goldberg, DE, Evolutionary Algorithms in Search, Optimization and Machine Learning. Reading, Addison Wesley, 1989.Google Scholar
  6. 6.
    Grosan, C, A New Evolutionary Technique for Detecting Pareto Continuos Regions, Proceedings of Genetic and Evolutionary Computation Conference (GECCO-2003), Workshop Program, Barry, A (ed), pp. 304–307, 2003.Google Scholar
  7. 7.
    Horn, J and Nafpliotis, N, Multiobjective Optimization Using Niched Pareto Evolutionary Algorithms. IlliGAL Report 93005, Illinois Evolutionary Algorithms Laboratory, University of Illinois, Urbana Champaign, 1993.Google Scholar
  8. 8.
    Horn, J, Nafpliotis, N and Goldberg, DE, A Niche Pareto Evolutionary Algorithm for Multiobjective Optimization. In Proc. 1st IEEE Conf. Evolutionary Computation, Piscataway, 1: pp. 82–87, 1994.Google Scholar
  9. 9.
    Knowles, JD and Corne, DW, Approximating the Nondominated Front Using the Pareto Archived Evolution Strategies. Evolutionary Computation 2000; 8(2):149–172.CrossRefPubMedGoogle Scholar
  10. 10.
    Knowles, JD and Corne, DW, The Pareto Archived Evolution Strategy: A New Baseline Algorithm for Pareto Multiobjective Optimization. In Congress on Evolutionary Computation (CEC 99), Piscataway, NJ, 1: pp. 98–105, 1999.Google Scholar
  11. 11.
    Schaffer, JD, Multiple Objective Optimization with Vector Evaluated Evolutionary Algorithms. Evolutionary Algorithms and Their Applications, In Grefenstette, JJ, (ed.), pp. 93–100, Hillsdale, NJ, Erlbaum, 1985.Google Scholar
  12. 12.
    Srinivas, N and Deb, K, Multiobjective Function Optimization Using Nondominated Sorting Evolutionary Algorithms. Evolutionary Computing 1994; 2: 221–248.Google Scholar
  13. 13.
    Zitzler, E, Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. Doctoral Dissertation, Swiss Federal Institute of Technology Zurich, 1999.Google Scholar
  14. 14.
    Zitzler, E, Laumanns, M and Thiele, L, SPEA 2: Improving the Strength Pareto Evolutionary Algorithm, TIK Report 103, Computer Engineering and Networks Laboratory (TIK), Department of Electrical Engineering, Swiss Federal Institute of Technology (ETH) Zurich, 2001.Google Scholar
  15. 15.
    Coello, CAC, A Comprehensive Survey of Evolutionary-based Multiobjective Optimization Techniques. Knowledge and Information Systems, 1999; 1(3): 269–308.Google Scholar
  16. 16.
    Veldhuizen, DAV, Multiobjective Evolutionary Algorithms: Classification, Analyses and New Innovations. Ph.D Thesis, Graduated School of Engineering of the Air Force Institute of Technology, Air University, 1999.Google Scholar
  17. 17.
    Veldhuizen, DAV and Lamont, GB, Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-art. Evolutionary Computation, 2000; 8: 125–147.CrossRefPubMedGoogle Scholar
  18. 18.
    Dumitrescu, D, Genetic Chromodynamics. Studia, Babes-Bolyai University, Ser. Informatica, 2000; 45: 39–50.Google Scholar

Copyright information

© Springer-Verlag London Limited 2005

Authors and Affiliations

  • D. Dumitrescu
  • Crina Groşan
  • Mihai Oltean

There are no affiliations available

Personalised recommendations