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Generalized Multiobjective Evolutionary Algorithm Guided by Descent Directions

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.

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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 

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Correspondence to Roman Denysiuk.

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

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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

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

Keywords

  • Multiobjective optimization
  • Multiobjective evolutionary algorithms
  • Performance assessment