On the Use of DELEqC-III in Bilevel Problems with Linear Equality Constraints

Resumo

The bilevel programming problem (BLP) is an optimization problem with another optimization problem in its constraints. This framework finds utility in modeling decentralized scenarios, which arise in real-world applications such as traffic management, transportation, and economic policy. Differential Evolution (DE) techniques have emerged in literature for addressing such complex problems. However, handling linear equality constraints poses a significant challenge for DE and other metaheuristics. To address this issue, we previously introduced DELEqC, enhancing DE with a mechanism to manipulate the linear equality constraints. A specialized variant, BL-DELEqC, was further proposed specifically for tackling general BLPs. Another variant, DELEqC-III, transforms the original constrained optimization problem into a lower-dimensional unconstrained one, offering applicability to BLPs with linear equality constraints. Thus, we explore in this study the efficacy of DELEqC-III in handling BLPs with linear equality constraints. The proposed BL-DELEqC-III is compared to BL-DELEqC on a selection of benchmark BLPs, demonstrating superior results.