D-MEANDS-MD: an Improved Evolutionary Algorithm with Memory and Diversity Strategies Applied to a Discrete, Dynamic, and Many-Objective Optimization Problem.

Abstract Several real-world optimization problems are dynamic and involve a number of objectives. Different researches using evolutionary algorithms focus on these characteristics, but few works investigate problems that are both dynamic and many-objective. Although widely investigated in formulations with multiple objectives, the evolutionary approaches are still challenged by the dynamic multiobjective optimization problems defining a relevant research topic. Some models have been proposed specifically to attack them as the well-known DNSGA-II and MS-MOEA algorithms, which have been extensively investigated on formulations with two or three objectives. Recently, the D-MEANDS algorithm was proposed for dynamic many-objective problems (DMaOPs). In a previous work, D-MEANDS was confronted to DNSGA-II and MS-MOEA solving dynamic many-objective scenarios of the knapsack problem: up to six objectives with five changes or four objectives with ten changes. In this work, we evaluate the behavior of such algorithms in instances up to eight objectives and twenty environmental changes. These enabled us to better understand D-MEANDS weak points which led us to the proposition of D-MEANDS-MD. The proposal offers a better balance between memory and diversity. We also included a more recent MOEA in this comparison: the DDIS-MOEA/D-DE. From the results obtained using 27 instances of the dynamic multiobjective knapsack problem, D-MEANDS-MD showed promise for solving discrete DMaOPs compared with the others.