Abstract
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.
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
Notes
- 1.
or maximization
- 2.
References
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). https://doi.org/10.1007/978-3-319-15934-8_27
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)
Campelo, F., Aranha, C.: MOEADr: Component-wise MOEA/D implementation, R package version 1.2.0 (2018). https://cran.R-project.org/package=MOEADr
Chankong, V., Haimes, Y.: Multiobjective Decision Making: Theory and Methodology. North Holland, New York (1983)
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)
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). https://doi.org/10.1007/1-84628-137-7_6
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)
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)
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)
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)
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)
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)
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
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)
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)
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). https://doi.org/10.1007/978-3-540-30217-9_84
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Lavinas, Y., Aranha, C., Ladeira, M. (2019). Improving Resource Allocation in MOEA/D with Decision-Space Diversity Metrics. In: Martín-Vide, C., Pond, G., Vega-Rodríguez, M. (eds) Theory and Practice of Natural Computing. TPNC 2019. Lecture Notes in Computer Science(), vol 11934. Springer, Cham. https://doi.org/10.1007/978-3-030-34500-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-34500-6_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-34499-3
Online ISBN: 978-3-030-34500-6
eBook Packages: Computer ScienceComputer Science (R0)