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

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.