Investigating Neighborhood Solution Transfer Schemes for Bilevel Optimization

Abstract

Bilevel optimization refers to a challenging class of problems where a lower level (LL) optimization task acts as a constraint for an upper level (UL) optimization task. When a bilevel problem is solved using a nested evolutionary algorithm (EA), a large number of function evaluations are consumed since an LL optimization needs to be conducted to evaluate every candidate UL solution. Knowledge transfer of optimal LL solutions between neighboring UL solutions is a plausible approach to improve the search efficiency. Even though some of the past studies have utilized this strategy intuitively, the specific impact of the transferred solution(s) has not been clearly differentiated since it forms only a small component of a much more elaborate search framework. In this study, we intend to examine closely the effectiveness of direct solution transfer. To do so, the transferred solution (LL optimum of the nearest UL solution) is considered as the mainstay of the LL search, acting as the starting point for a direct local LL search. We first observe the performance of this approach on existing benchmarks. Based on the understanding gained from the experiments, we design modified problems where such a direct transfer is likely to face significant challenges. We then propose an improved approach that uses solution transfer more selectively by considering correlations between neighboring landscapes for a more effective transfer. Numerical experiments are conducted to demonstrate the challenges faced by the direct transfer on the modified problems, as well as the competitive performance of the correlation-based approach. We hope that the insights gained from the study will be beneficial for future development of efficient transfer-based approaches for bilevel optimization.