Abstract
Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) is one of the dominant algorithmic frameworks for multi-objective optimization in the area of evolutionary computation. The performance of multi-objective algorithms based on MOEA/D framework highly depends on how a diverse set of single objective subproblems are generated. Among all decomposition methods, the Penalty-based Boundary Intersection (PBI) method has received particular research interest in MOEA/D due to its ability for controlling the diversity of population for many-objective optimization. However, optimizing multiple PBI subproblems defined via a set of uniformly-distributed weight vectors may not be able to produce a good approximation of Pareto-optimal front when objectives have different scales. To overcome this weakness, we suggest a new strategy for adjusting weight vectors of PBI-based subproblems in this paper. Our experimental results have shown that the performance of MOEA/D-PBI with adjusted weight vectors is competitive to NSGA-III in diversity when dealing with the scaled version of some benchmark multi-objective test problems.
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References
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)
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
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). https://doi.org/10.1007/978-3-540-30217-9_84
Li, H., Zhang, Q.: Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans. Evol. Comput. 12(2), 284–302 (2009)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Proceedings of Evolutionary Methods Design, Optimisation and Control With Applications to Industrial Problems, pp. 95–100 (2001)
Knowles, J., Corne, D.: The pareto archived evolution strategy: a new baseline algorithm for pareto multiobjective optimisation. In: Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999, vol. 1, January 1999
Li, H., Landa-Silva, D.: An adaptive evolutionary multi-objective approach based on simulated annealing. Evol. Comput. 19(4), 561–595 (2011)
Qi, Y., et al.: MOEA/D with adaptive weight adjustment. Evol. Comput. 22(2), 231–264 (2014)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. Technical report 112, Computer Engineering and Networks Laboratory, ETH Zurich (2001)
Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans. Evol. Comput. 18(4), 577–601 (2014)
Ishibuchi, H., Doi, K., Nojima, Y.: On the effect of normalization in MOEA/D for multi-objective and many-objective optimization. Complex Intell. Syst. 3, 279–294 (2017)
Miettinen, K.: Nonlinear Multiobjective Optimization. Springer, Heidelberg (1998)
Acknowledgment
The authors would like to thank the anonymous reviewers for their insightful comments. This work was supported by National Natural Science Foundation of China (NSFC) grants 61573279, 61175063 and 11131006.
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Li, H., Sun, J., Zhang, Q., Shui, Y. (2019). Adjustment of Weight Vectors of Penalty-Based Boundary Intersection Method in MOEA/D. In: Deb, K., et al. Evolutionary Multi-Criterion Optimization. EMO 2019. Lecture Notes in Computer Science(), vol 11411. Springer, Cham. https://doi.org/10.1007/978-3-030-12598-1_8
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DOI: https://doi.org/10.1007/978-3-030-12598-1_8
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