Exploring Long-term Memory in Evolutionary Multi-objective Algorithms: A Case Study with NSGA-III

In the field of many-objective optimization, obtaining a dense solution set is a challenging task, mostly due to having hyper-surface nature of Pareto-front; which cannot be covered by commonly utilized population sizes. This is particularly vital in scenarios where innovization and informed decision-making are crucial. The challenge stems from the constraints imposed by population size limitations in evolutionary algorithms, which impede the efficient exploration of multiple solutions. A contributing factor to this issue is the lack of long-term memory in the well-known evolutionary algorithms to retain these solutions. On the contrary, the effective training of machine learning-assisted optimization or innovization relies on a substantial amount of data, which can be provided by preserving these valuable solutions. Moreover, long-term memory can play a significant role in expensive many-objective optimization, where the repetition of the optimization process is both costly and time-consuming, similar to training deep neural networks. The study focuses on NSGA-III equipped with long-term memory and assessing its performance across 16 benchmark problems, encompassing DTLZ1 to DTLZ7 and WFG1 to WFG9, considering scenarios with 3, 5, and 10 objectives. This paper explores the benefits of incorporating long-term memory in terms of the ultimate optimization outcomes, including the number of non-dominated solutions, knee points, and Inverted Generational Distance (IGD).