Skip to main content
SpringerLink
Log in

Adaptive ε-Ranking on many-objective problems

  • Special Issue
  • Published:
Evolutionary Intelligence Aims and scope Submit manuscript

Abstract

This work proposes Adaptive ε-Ranking to enhance Pareto based selection, aiming to develop effective many-objective evolutionary optimization algorithms. ε-Ranking fine grains ranking of solutions after they have been ranked by Pareto dominance, using a randomized sampling procedure combined with ε-dominance to favor a good distribution of the samples. In the proposed method, sampled solutions keep their initial rank and solutions located within the virtually expanded ε-dominance regions of the sampled solutions are demoted to an inferior rank. The parameter ε that determines the expanded regions of dominance of the sampled solutions is adapted at each generation so that the number of best-ranked solutions is kept close to a desired number that is expressed as a fraction of the population size. We enhance NSGA-II with the proposed method and analyze its performance on MNK-Landscapes, showing that the adaptive method works effectively and that compared to NSGA-II convergence and diversity of solutions can be improved remarkably on MNK-Landscapes with 3 ≤ M ≤ 10 objectives. Also, we compare the performance of Adaptive ε-Ranking with two representative many-objective evolutionary algorithms on DTLZ continuous functions. Results on DTLZ functions with 3 ≤ M ≤ 10 objectives suggest that the three many-objective approaches emphasize different areas of objective space and could be used as complementary strategies to produce a better approximation of the Pareto front.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester

    MATH  Google Scholar 

  2. Coello C, Van Veldhuizen D, Lamont G (2002) Evolutionary algorithms for solving multi-objective problems. Kluwer, Boston

    MATH  Google Scholar 

  3. Purshouse RC, Fleming PJ (2003, April) Conflict, harmony, and independence: relationships in evolutionary multi-criterion optimization. In: Proceedings of 2nd international conference on evolutionary multi-criterion optimization, vol 2632. LNCS (Springer), pp16–30

  4. Aguirre H, Tanaka K (2004) Insights on properties of multi-objective MNK-landscapes. In: Proceedings of 2004 IEEE congress on evolutionary computation. IEEE Service Center, pp.196–203

  5. Zitzler E, Kunzli S (2004) Indicator based selection in multi-objective search. In: Proceedings of conference on parallel problem solving from nature (PPSN VIII). Springer, pp. 832–842

  6. Aguirre H, Tanaka K (2005) Selection, drift, recombination, and mutation in multi-objective evolutionary algorithms on scalable MNK-landscapes. In: Proceedings of 3rd international conference on evolutionary multi-criterion optimization, vol. 3410. LNCS (Springer), pp 355–369

  7. Hughes EJ (2005, September) evolutionary many-objective optimisation: many once or one many? In: Proceedings of 2005 IEEE congress on evolutionary computation, vol 1. IEEE Service Center, pp 222–227

  8. Aguirre H, Tanaka K (2007, September) Working principles, behavior, and performance of MOEAs on MNK-landscapes. Eur J Oper Res Elsevier 181(3):1670–1690

    Article  MATH  Google Scholar 

  9. Emmerich M, Beume N., Naujoks B (2005) An EMO algorithm using the hypervolume measure as selection criterion. In: Proceedings of 3rd international conference on evolutionary multi-criterion optimization, vol 3410, LNCS (Springer), pp 62–76

  10. Deb K, Saxena K (2006) Searching for pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems. In: Proceedings of 2006 IEEE congress on evolutionary computation (CEC 2006), pp 3353–3360

  11. Deb K, Sundar J (2006) Preference point based multi-objective optimization using evolutionary algorithms. In: Proceedings of 2006 genetic and evolutionary computation conference (GECCO 2006), pp 635–642

  12. Corne D, Knowles J (2007) Techniques for highly multi-objective optimization: some non-dominated points are better than others. In: Proceedings of 2007 genetic and evolutionary computation conference (GECCO 2007), pp 773–780

  13. Kukkonen S, Lampinen J (2007) Ranking-dominance and many objective optimization. In: Proceedings of 2007 IEEE congress on evolutionary computation (CEC 2007), pp 3983–3990

  14. Ishibuchi H, Tsukamoto N, Nojima Y (2007) Iterative approach to indicator-based multi-objective optimization. In: Proceedings of 2007 IEEE congress on evolutionary computation (CEC 2007), pp 3697–3704

  15. Ishibuchi H, Nojima Y (2007) Optimization of scalarizing functions through evolutionary multi-objective optimization. In: Proceedings of 4th international conference on evolutionary multi-criterion optimization (EMO 2007), vol 4403. LNCS (Springer), pp 51–65

  16. Brockhoff D, Zitzler E (2006) Are all objectives necessary? On dimensionality reduction in evolutionary multi-objective optimization. In: Parallel problem solving from nature, PPSN IX, vol 4193. LNCS (Springer), pp 533–542

  17. Sulflow A, Drechsler N, Drechsler R (2007) Robust multi-objective optimization in high dimensional spaces. In: Proceedings of 4th international conference on evolutionary multi-criterion optimization, vol 4403. LNCS (Springer), pp 715–726

  18. Koppen M, Yoshida K (2007) Substitute distance assignments in NSGA-II for handling many-objective optimization problems. In: Proceedings of 4th international conference on evolutionary multi-criterion optimzation, vol 4403. LNCS (Springer), pp 727–741

  19. Wagner T, Beume N, Naujoks B (2007) Pareto-, aggregation, and indicator-based methods in many-objective optimization. In: Proceedings of 4th international conference on evolutionary multi-criterion optimization, vol 4403. LNCS (Springer), pp 742–756

  20. Hughes EJ (2003) Multiple single objective pareto sampling. In: Proceedings of 2003 IEEE congress on evolutionary computation. IEEE Service Center

  21. Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. KanGAL report 200001

  22. Aguirre H, Tanaka K (2008) Robust optimization by ε-Ranking on high dimensional objective spaces. In: Proceedings of 7th international conference on simulated evolution and learning, vol 5361. LNCS (Springer), pp 421–431

  23. Ishibuchi H, Tsukamoto N, Nojima Y (2008) Evolutionary many-objective optimization: a short review. In: Proceedings of IEEE congress on evolutionary computation (CEC 2008). IEEE Press, pp 2424–2431

  24. Yu PL (1974) Cone convexity, cone extreme points, and nondominated solutions in decision problems with multi-objectives. J Optim Theory Appl 14(3):319–377

    Article  MATH  Google Scholar 

  25. Laumanns M, Thiele L, Deb K, Zitzler E (2002) Combining convergence and diversity in evolutionary multi-objective optimization. Evol Comput 10(3):263–282 (Fall)

    Article  Google Scholar 

  26. Kauffman SA (1993) The origins of order: self-organization and selection in evolution. Oxford University Press, New York

    Google Scholar 

  27. Deb K, Thiele L, Laumanns M, Zitzler E (2002) Scalable multi-objective optimization test problems. In: Proceedings of 2002 congress on evolutionary computation. IEEE Service Center, pp 825–830

  28. Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. PhD thesis, Swiss Federal Institute of Technology, Zurich

  29. Knowles J, Corne D (2002) On metrics for comparing non-dominated sets. In: Proceedings of 2002 congress on evolutionary computation. IEEE Press, pp 711–716

  30. Fleischer M (2003) The measure of pareto optima: applications to multi-objective metaheuristics. In: 2nd International conference on evolutionary multi-criterion optimization, Lecture Notes in Computer Science, vol 2632. Springer, pp 519–533

  31. Fonseca C, Paquete L, López-Ibáñez M (2006) An improved dimension-sweep algorithm for the hypervolume indicator. In: Proceedings of 2006 IEEE congress on evolutionary computation, IEEE Service Center, pp 1157–1163

  32. Salomon R (1996) Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions. A survey of some theoretical and practical aspects of genetic algorithms, vol 39, no.3. Byosystems, Elsevier, pp 263–278

  33. Aguirre H, Tanaka K (2003) Genetic algorithms on NK-landscapes: effects of selection, drift, mutation, and recombination. In: Proceedings of 3rd European workshop on evolutionary computation in combinatorial optimization (EvoCOP 2003), vol 2611. LNCS (Springer), pp 131–142

  34. Iorio A.W., Li X (2004) Solving rotated multi-objective optimization problems using differential evolution. In: Proceedings of 17th Australian joint conference on artificial intelligence 2004, vol 3339. LNAI (Springer), pp 861–872

  35. Bleuler S, Laumanns M, Thiele L, Zitzler E (2003) PISA—a platform and programming language independent interface for search algorithms. In: Proceedings of 2nd international conference on evolutionary multi-criterion optimization, vol 2632. LNCS (Springer), pp 494–508

Download references

Acknowledgments

This study was performed through Special Coordination Funds for Promoting Science and Technology of the Ministry of Education, Culture, Sports, Science and Technology, of the Japanese Government.

Author information

Authors and Affiliations

  1. International Young Researcher Empowerment Center, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano, 380-8553, Japan

    Hernán Aguirre

  2. Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano, 380-8553, Japan

    Kiyoshi Tanaka

Authors
  1. Hernán Aguirre
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kiyoshi Tanaka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hernán Aguirre.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aguirre, H., Tanaka, K. Adaptive ε-Ranking on many-objective problems. Evol. Intel. 2, 183–206 (2009). https://doi.org/10.1007/s12065-009-0031-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12065-009-0031-2

Keywords

Search

Navigation