Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abdou-Sabet, S., Datta, S.: Thermoplastic Vulcanizates. Polymer Blends: Formulation and Performance. Wiley, New York (2000)
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)
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
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)
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
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)
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)
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)
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)
Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. Technical report 214, TIC, ETH Zurich, Switzerland (2006)
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)
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)
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)
Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, London (1999)
Ray, T., Liew, K.M.: A swarm metaphor for multiobjective design optimization. Eng. Optim. 34(2), 141–153 (2002)
Wang, Z., Zhang, Q., Zhou, A., Gong, M., Jiao, L.: Adaptive replacement strategies for MOEA/D. IEEE Trans. Cybern. 46(2), 474–486 (2016)
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)
Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
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)
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
Acknowledgements
This work has been supported by FCT - Fundação para a Ciência e Tecnologia in the scope of the project: PEst-OE/EEI/UI0319/2014.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Denysiuk, R., Gaspar-Cunha, A. (2017). Weighted Stress Function Method for Multiobjective Evolutionary Algorithm Based on Decomposition. In: Trautmann, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2017. Lecture Notes in Computer Science(), vol 10173. Springer, Cham. https://doi.org/10.1007/978-3-319-54157-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-54157-0_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54156-3
Online ISBN: 978-3-319-54157-0
eBook Packages: Computer ScienceComputer Science (R0)