Skip to main content
SpringerLink
Log in

Generalized Multiobjective Evolutionary Algorithm Guided by Descent Directions

  • Published:
Journal of Mathematical Modelling and Algorithms in Operations Research

Abstract

This paper proposes a generalized descent directions-guided multiobjective algorithm (DDMOA2). DDMOA2 uses the scalarizing fitness assignment in its parent and environmental selection procedures. The population consists of leader and non-leader individuals. Each individual in the population is represented by a tuple containing its genotype as well as the set of strategy parameters. The main novelty and the primary strength of our algorithm is its reproduction operator, which combines the traditional local search and stochastic search techniques. To improve efficiency, when the number of objective is increased, descent directions are found only for two randomly chosen objectives. Furthermore, in order to increase the search pressure in high-dimensional objective space, we impose an additional condition for the acceptance of descent directions found for leaders during local search. The performance of the proposed approach is compared with those produced by representative state-of-the-art multiobjective evolutionary algorithms on a set of problems with up to 8 objectives. The experimental results reveal that our algorithm is able to produce highly competitive results with well-established multiobjective optimizers on all tested problems. Moreover, due to its hybrid reproduction operator, DDMOA2 demonstrates superior performance on multimodal problems.

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

Similar content being viewed by others

References

  1. Beyer, H.-G., Schwefel, H.-P.: Evolution strategies: a comprehensive introduction. Nat. Comput. 1(1), 3–52 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bleuler, S., Laumanns, M., Thiele, L., Zitzler, E.: PISA: a platform and programming language independent interface for search algorithms. In: Proceedings of the Conference on Evolutionary Multi-Criterion Optimization, pp. 494–508. EMO’03 (2003)

  3. Bosman, P.A.N., Thierens, D.: The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Trans. Evol. Comput. 7(2), 174–188 (2003)

    Article  Google Scholar 

  4. Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems. Genetic and Evolutionary Computation, 2 edn. Springer (2007)

  5. Costa, L., Espírito Santo, I., Denysiuk, R., Fernandes, E.M.G.P.: Hybridization of a genetic algorithm with a pattern search augmented Lagrangian method. In: Proceedings of the Conference on Conference on Engineering Optimization, p. 1195. EngOpt’10 (2010)

  6. Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley-Interscience Series in Systems and Optimization. Wiley (2001)

  7. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  8. Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. Technical Report 112, Swiss Federal Institute of Technology, Zurich, Switzerland (2001)

  9. Denysiuk, R., Costa, L., Espírito Santo, I.: DDMOA: Descent directions based multiobjective algorithm. In: Proceedings of the Conference on Computational and Mathematical Methods in Science and Engineering, pp. 460–471. CMMSE’12 (2012)

  10. Denysiuk, R., Costa, L., Espírito Santo, I.: DDMOA2: Improved descent directions-based multiobjective algorithm. In: Proceedings of the Conference on Computational and Mathematical Methods in Science and Engineering. pp. 513–524. CMMSE’13 (2013)

  11. Denysiuk, R., Costa, L., Espírito Santo, I.: A new hybrid evolutionary multiobjective algorithm guided by descent directions. J. Math. Model. Algoritm. Oper. Res. 12(3), 233–251 (2013)

    Article  MATH  Google Scholar 

  12. Durillo, J.J., Nebro, A.J.: jMetal: a Java framework for multi-objective optimization. Adv. Eng. Softw. 42(10), 760–771 (2011)

    Article  Google Scholar 

  13. García, S., Molina, D., Lozano, M., Herrera, F.: A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J. Heuristics 15(6), 617–644 (2009)

    Article  MATH  Google Scholar 

  14. Hughes, E.J.: MSOPS-II: A general-purpose many-objective optimiser. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 3944–3951. CEC’07 (2007)

  15. Ishibuchi, H., Doi, T., Nojima, Y.: Incorporation of scalarizing fitness functions into evolutionary multiobjective optimization algorithms. In: In Proceedings of the Conference on Parallel Problem Solving from Nature, pp. 493–502. PPSN’06 (2006)

  16. Khare, V.R., Yao, X., Deb, K.: Performance scaling of multi-objective evolutionary algorithms. In: Proceedings of the Conference on Evolutionary Multi-Criterion Optimization, pp. 376–390. EMO’03 (2003)

  17. Knowles, J., Corne, D.: Memetic algorithms for multiobjective optimization: issues, methods and prospects. Recent Adv. Memet. Algoritm. Stud. Fuzziness Soft Comput. 166, 313-352 (2005)

    Article  Google Scholar 

  18. Li, H., Zhang, Q.: Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans. Evol. Comput. 13(2), 284–302 (2009)

    Article  Google Scholar 

  19. Loh, W.L.: On Latin hypercube sampling. Ann. Stat. 33(6), 2058–2080 (1996)

    Article  MathSciNet  Google Scholar 

  20. Miettinen, K.: Nonlinear multiobjective optimization. International Series in Operations Research and Management Science, vol. 12. Kluwer Academic Publishers (1999)

  21. Purshouse, R.C., Fleming, P.J.: Evolutionary many-objective optimisation: an exploratory analysis. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC’03, pp. 2066–2073 (2003)

  22. Shukla, P.K., Deb, K.: On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods. Eur. J. Oper. Res. 181(3), 1630–1652 (2007)

    Article  MATH  Google Scholar 

  23. Torczon, V.: On the convergence of pattern search algorithms. SIAM J. Optim. 7, 1–25 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  24. Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Proceedings of the Conference on Parallel Problem Solving from Nature, PPSN’04, pp. 832–842 (2004)

  25. Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms - A case comparative case study. In: Proceedings of the Conference on Parallel Problem Solving from Nature, PPSN’98, pp. 292–304 (1998)

  26. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Algoritmi R&D Center, University of Minho, Braga, Portugal

    Roman Denysiuk

  2. Department of Production and Systems Engineering, University of Minho, Braga, Portugal

    Lino Costa & Isabel Espírito Santo

Authors
  1. Roman Denysiuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lino Costa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Isabel Espírito Santo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roman Denysiuk.

Additional information

Proceedings of the 13th International Conference on Computational and MathematicalMethods in Science and Engineering, CMMSE’13, held in Almeria, Spain 24-27 June, 2013.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Denysiuk, R., Costa, L. & Santo, I.E. Generalized Multiobjective Evolutionary Algorithm Guided by Descent Directions. J Math Model Algor 13, 387–403 (2014). https://doi.org/10.1007/s10852-014-9255-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10852-014-9255-y

Keywords

Search

Navigation