Optimistic variants of single-objective bilevel optimization for evolutionary algorithms

TL;DR

This paper introduces optimistic variants of bilevel optimization algorithms using evolutionary methods, demonstrating improved convergence and competitive performance on benchmark problems.

Contribution

It proposes an extreme optimistic approach for bilevel optimization, enhancing existing methods with a new convergence variant and demonstrating superior results.

Findings

Optimistic variants outperform pessimistic approaches.

The extreme optimistic approach shows different convergence behavior.

The proposed method achieves competitive results on benchmark problems.

Abstract

Single-objective bilevel optimization is a specialized form of constraint optimization problems where one of the constraints is an optimization problem itself. These problems are typically non-convex and strongly NP-Hard. Recently, there has been an increased interest from the evolutionary computation community to model bilevel problems due to its applicability in the real-world applications for decision-making problems. In this work, a partial nested evolutionary approach with a local heuristic search has been proposed to solve the benchmark problems and have outstanding results. This approach relies on the concept of intermarriage-crossover in search of feasible regions by exploiting information from the constraints. A new variant has also been proposed to the commonly used convergence approaches, i.e., optimistic and pessimistic. It is called extreme optimistic approach. The experimental results demonstrate the algorithm converges differently to known optimum solutions with the optimistic variants. Optimistic approach also outperforms pessimistic approach. Comparative statistical analysis of our approach with other recently published partial to complete evolutionary approaches demonstrates very competitive results.