Optimistic Variants of Single-Objective Bilevel Optimization for Evolutionary Algorithms

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 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 an 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.

Designing of a Mat-heuristic Algorithm for Solving Bi-level Optimization Problems

“…In [14] classical and evolutionary approaches proposed to solve bi-level programming problems by 2018 are under review and also some uses for bi-level programming problems are raised. Several studies have been done to solve linear and nonlinear bi-level optimization problems using evolutionary methods such as genetic algorithm (GA) and particle swarm optimization (PSO) [15][16][17][18][19][20][21]. The use of evolutionary methods for solving single-level and bi-level programming problems may offer optimal or near-optimal solutions, but using these methods to solve bi-level problems requires, unlike the single-level problems, very large computations and a very long time.…”

“…In the following, several sample problems designed to test bi-level optimization algorithms are considered. These problems are presented in [18], [21], [27]. We solve these problems using the GPBLO algorithm as well as by the model obtained from KKT conditions or by the Complete Enumeration (CE) method.…”

Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond

“…In addition, the existence of multiple optima for the LL problem can result in an inadequate formulation of BLOs and the feasible region of the problem may be nonconvex [33], [34]. Despite the challenges, a lot of research have followed in this field consisting of methods and applications of BLOs, see [35], [28], [36]. Early studies focused on numerical methods, including extreme-point methods [37], branch-and-bound methods [4], [38], descent methods [39], [40], penalty function methods [41], [42], trust-region methods [43], [44], and so on.…”