An Efficient Data-Driven Framework for Detecting Infeasible Solutions in Multiobjective Evolutionary Bilevel Optimization

Abstract

Detecting infeasible solutions is an important challenge in closed-box multiobjective bilevel optimization (MOBO) due to a lower-level (LL) optimization problem used as a constraint (along with equality and inequality constraints) in an upper-level optimization. In this context, a feasible solution is an optimal solution to the LL problem, typically addressed using evolutionary algorithms (EAs) (or other metaheuristics) for complex scenarios. Since metaheuristics do not guarantee optimality, then infeasible solutions are inherently reported. This article introduces a novel data-driven framework to automatically identify infeasible solutions reported by bilevel EAs (BEA) when addressing any MOBO problem. This framework operates without imposing strong assumptions on objectives or constraints, making it versatile and easy to implement. Besides, our approach uses solutions reported by one or multiple BEAs to detect and eliminate possible infeasible solutions. This approach helps to enhance algorithm comparison by eliminating infeasible solutions before applying existing performance indicators. The framework is successfully applied to several MOBO problems, including two real-world instances from specialized literature, solved by four different BEAs. Results suggest that the proposed framework advances the field of bilevel evolutionary optimization, offering a tool for promoting fair algorithmic comparisons and ensuring solution feasibility without requiring a deep understanding of the problem context.