Improving Resource Allocation in MOEA/D with Decision-Space Diversity Metrics

  • Yuri LavinasEmail author
  • Claus Aranha
  • Marcelo Ladeira
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11934)


One of the main algorithms for solving Multi-Objective Optimization Problems is the Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA/D). It is characterized by decomposing the multiple objectives into a large number of single-objective subproblems, and then solving these subproblems in parallel. Usually, these subproblems are considered equivalent, but there are works that indicate that some subproblems can be more difficult than others, and that spending more computational resources in these subproblems can improve the performance of MOEA/D. One open question about this strategy of “Resource Allocation” is: what should be the criteria for allocating more computational effort on one problem or another? In this work we investigate this question. We study four different ways to prioritize subproblems: Randomly, Relative Improvement, Diversity in Decision Space (proposed in this work), and inverted Diversity in Decision Space (also proposed in this work). We compare the performance of MOEA/D using these four different “priority functions” on the DTLZ and UF benchmarks. We evaluate the resulting IGD, proportion of non-dominated solutions, and visually analyse the resulting resource allocation and Pareto Front. The result of our experiments is that the priority function using diversity in decision space improved the MOEA/D, achieving better IGD values and higher proportion of non-dominated solutions.


Multi-Objective Optimization Resource Allocation Priority Functions 


  1. 1.
    Bezerra, L.C.T., López-Ibáñez, M., Stützle, T.: Comparing decomposition-based and automatically component-wise designed multi-objective evolutionary algorithms. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C.C. (eds.) EMO 2015. LNCS, vol. 9018, pp. 396–410. Springer, Cham (2015). Scholar
  2. 2.
    Cai, X., Li, Y., Fan, Z., Zhang, Q.: An external archive guided multiobjective evolutionary algorithm based on decomposition for combinatorial optimization. IEEE Trans. Evol. Comput. 19(4), 508–523 (2015)CrossRefGoogle Scholar
  3. 3.
    Campelo, F., Aranha, C.: MOEADr: Component-wise MOEA/D implementation, R package version 1.2.0 (2018).
  4. 4.
    Chankong, V., Haimes, Y.: Multiobjective Decision Making: Theory and Methodology. North Holland, New York (1983)zbMATHGoogle Scholar
  5. 5.
    Chiang, T.C., Lai, Y.P.: MOEA/D-AMS: improving MOEA/D by an adaptive mating selection mechanism. In: 2011 IEEE Congress on Evolutionary Computation (CEC), pp. 1473–1480. IEEE (2011)Google Scholar
  6. 6.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization, pp. 105–145. Springer, London (2005). CrossRefzbMATHGoogle Scholar
  7. 7.
    Kang, Q., Song, X., Zhou, M., Li, L.: A collaborative resource allocation strategy for decomposition-based multiobjective evolutionary algorithms. IEEE Trans. Syst. Man Cybern. Syst. (2018)Google Scholar
  8. 8.
    Kohira, T., Kemmotsu, H., Akira, O., Tatsukawa, T.: Proposal of benchmark problem based on real-world car structure design optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 183–184. ACM (2018)Google Scholar
  9. 9.
    Lavinas, Y., Aranha, C., Sakurai, T.: Using diversity as a priority function for resource allocation on MOEA/D. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion. ACM (2019)Google Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Nasir, M., Mondal, A.K., Sengupta, S., Das, S., Abraham, A.: An improved multiobjective evolutionary algorithm based on decomposition with fuzzy dominance. In: 2011 IEEE Congress on Evolutionary Computation (CEC), pp. 765–772. IEEE (2011)Google Scholar
  12. 12.
    Trivedi, A., Srinivasan, D., Sanyal, K., Ghosh, A.: A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans. Evol. Comput. 21(3), 440–462 (2017)Google Scholar
  13. 13.
    Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRefGoogle Scholar
  14. 14.
    Zhang, Q., Liu, W., Li, H.: The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances. In: 2009 IEEE Congress on Evolutionary Computation, CEC 2009, pp. 203–208. IEEE (2009)Google Scholar
  15. 15.
    Zhang, Q., Zhou, A., Zhao, S., Suganthan, P.N., Liu, W., Tiwari, S.: Multiobjective optimization test instances for the CEC 2009 special session and competition. University of Essex, Colchester, UK and Nanyang Technological University, Singapore, special session on performance assessment of multi-objective optimization algorithms, Technical report 264 (2008)Google Scholar
  16. 16.
    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
  17. 17.
    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). Scholar

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Authors and Affiliations

  1. 1.University of TsukubaTsukubaJapan
  2. 2.University of BrasiliaBrasíliaBrazil

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