An Evaluation of Simple Solution Transfer Strategies for Bilevel Multiobjective Optimization

Bilevel optimization problem (BLOP) refers to a class of problems with a hierarchical structure, wherein a lower level optimization problem acts as a constraint for an upper level optimization problem. Evolutionary algorithms (EAs) have been commonly used to solve BLOPs where underlying functions are black-box or do not conform to certain mathematical properties. One of the downsides of using EAs, especially in a nested format, is the significant computational expense (number of function evaluations); and a number of strategies have been proposed to mitigate this. However, most of the existing studies in the domain of evolutionary bilevel optimization are directed towards problems with single-objective at both levels, while very few have explored BLOPs with multiple objectives at one or both levels (BLMOPs). In this study, we investigate the potential benefits of utilizing knowledge transfer by seeding initial population from neighboring solutions for solving BLMOPs. Towards this end, we construct two simple strategies, referred to as full population transfer and selective population transfer, and study their potential to improve the performance over the baseline nested EA for BLMOPs. Experimental results show that the selective transfer strategy has more reliable and competitive performance compared to baseline. Empirical analysis is presented to highlight the relevant factors that lead to the observed performance trends.