Weighted Stress Function Method for Multiobjective Evolutionary Algorithm Based on Decomposition

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10173)


Multiobjective evolutionary algorithm based on decomposition (MOEA/D) is a well established state-of-the-art framework. Major concerns that must be addressed when applying MOEA/D are the choice of an appropriate scalarizing function and setting the values of main control parameters. This study suggests a weighted stress function method (WSFM) for fitness assignment in MOEA/D. WSFM establishes analogy between the stress-strain behavior of thermoplastic vulcanizates and scalarization of a multiobjective optimization problem. The experimental results suggest that the proposed approach is able to provide a faster convergence and a better performance of final approximation sets with respect to quality indicators when compared with traditional methods. The validity of the proposed approach is also demonstrated on engineering problems.


Quality Indicator Scalarizing Function Pareto Front Multiobjective Optimization Problem Multiobjective Evolutionary Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been supported by FCT - Fundação para a Ciência e Tecnologia in the scope of the project: PEst-OE/EEI/UI0319/2014.


  1. 1.
    Abdou-Sabet, S., Datta, S.: Thermoplastic Vulcanizates. Polymer Blends: Formulation and Performance. Wiley, New York (2000)Google Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    Deb, K., Pratap, A., Moitra, S.: Mechanical component design for multiple ojectives using elitist non-dominated sorting GA. In: Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J.J., Schwefel, H.P. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 859–868. Springer, Heidelberg (2000). doi: 10.1007/3-540-45356-3_84 Google Scholar
  4. 4.
    Denysiuk, R., Costa, L., Espírito Santo, I.: MOEA/VAN: multiobjective evolutionary algorithm based on vector angle neighborhood. In: Proceedings of the Conference on Genetic and Evolutionary Computation, pp. 663–670 (2015)Google Scholar
  5. 5.
    Denysiuk, R., Costa, L., Espírito Santo, I., C. Matos, J.: MOEA/PC: multiobjective evolutionary algorithm based on polar coordinates. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C.C. (eds.) EMO 2015. LNCS, vol. 9018, pp. 141–155. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-15934-8_10 Google Scholar
  6. 6.
    Ferreira, J.C., Fonseca, C.M., Gaspar-Cunha, A.: Methodology to select solutions from the Pareto-optimal set: a comparative study. In: Proceedings of the Conference on Genetic and Evolutionary Computation, pp. 789–796 (2007)Google Scholar
  7. 7.
    Ishibuchi, H., Sakane, Y., Tsukamoto, N., Nojima, Y.: Simultaneous use of different scalarizing functions in MOEA/D. In: Proceedings of the Conference on Genetic and Evolutionary Computation, pp. 519–526 (2010)Google Scholar
  8. 8.
    Jain, H., Deb, K.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part II: handling constraints and extending to an adaptive approach. IEEE Trans. Evol. Comput. 18(4), 577–601 (2002)Google Scholar
  9. 9.
    Jan, M.A., Zhang, Q.: MOEA/D for constrained multiobjective optimization: some preliminary experimental results. In: UK Workshop on Computational Intelligence, pp. 1–6 (2010)Google Scholar
  10. 10.
    Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. Technical report 214, TIC, ETH Zurich, Switzerland (2006)Google Scholar
  11. 11.
    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)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Li, K., Deb, K., Zhang, Q., Kwong, S.: An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans. Evol. Comput. 19(5), 694–716 (2015)CrossRefGoogle Scholar
  13. 13.
    Liu, H.L., Gu, F., Zhang, Q.: Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans. Evol. Comput. 18(3), 450–455 (2014)CrossRefGoogle Scholar
  14. 14.
    Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, London (1999)zbMATHGoogle Scholar
  15. 15.
    Ray, T., Liew, K.M.: A swarm metaphor for multiobjective design optimization. Eng. Optim. 34(2), 141–153 (2002)CrossRefGoogle Scholar
  16. 16.
    Wang, Z., Zhang, Q., Zhou, A., Gong, M., Jiao, L.: Adaptive replacement strategies for MOEA/D. IEEE Trans. Cybern. 46(2), 474–486 (2016)CrossRefGoogle Scholar
  17. 17.
    Wang, L., Zhang, Q., Zhou, A., Gong, M., Jiao, L.: Constrained subproblems in a decomposition-based multiobjective evolutionary algorithm. IEEE Trans. Evol. Comput. 20(3), 475–480 (2016)CrossRefGoogle Scholar
  18. 18.
    Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Zhou, A., Zhang, Q.: Are all the subproblems equally important? Resource allocation in decomposition-based multiobjective evolutionary algorithms. IEEE Trans. Evol. Comput. 20(1), 52–64 (2016)CrossRefGoogle Scholar
  20. 20.
    Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., et al. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-30217-9_84 CrossRefGoogle Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Polymer EngineeringUniversity of MinhoGuimarãesPortugal

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