Pseudo-feasible solutions in evolutionary bilevel optimization: Test problems and performance assessment

• Published in: Applied mathematics and computation Vol. 412; p. 126577
• Main Authors: Mejía-de-Dios, Jesús-Adolfo, Mezura-Montes, Efrén, Toledo-Hernández, Porfirio
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2022
• Subjects: Bilevel optimization; Evolutionary algorithms; Performance comparison; Bilevel optimization; Performance comparison; Evolutionary algorithms
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2021.126577

•Theoretical study on the existence of pseudo-feasible solutions in bilevel optimization.•Test problems are proposed to assess, via an empirical study, the performance of state-of-the-art evolutionary algorithms.•Conditions to identify pseudo-feasible solutions and also exemplify its usage.•Studying pseudo-feasible solutions provides more information about bilevel optimization problems.•More robust proposals (test problems, algorithms, bilevel mathematical models, etc.) can be designed in the future. This work presents a study about a special class of infeasible solutions called here as pseudo-feasible solutions in bilevel optimization. This work is focused on determining how such solutions can affect the performance of an evolutionary algorithm. After its formal definition, and based on theoretical results, two conditions to detect and deal with them are proposed. Moreover, a novel and scalable set of test problems with characterized pseudo-feasible solutions is introduced. Furthermore, an algorithm designed to solve bilevel optimization problems (BOP) is adapted with the above mentioned conditions and tested in already known test problems and also in the new testbed so as to analyze its performance when compared with state-of-the-art evolutionary approaches for BOPs. The obtained results suggest that the presence of pseudo-feasible solutions can be considered as a source of difficulty in this type of optimization problems, since their presence may lead to incorrect comparisons among algorithms.