A Brief Review of Bilevel Optimization Techniques and Their Applications

Bilevel optimization is an area of applied mathematics that deals with hierarchical decision-making processes, where a decision at one level affects the other levels’ optimization problem. The process is complex, and several approaches like the branch-and-bound (B&B) algorithm, genetic algorithm (GA), truncated Newton algorithm, and Levenberg method have been applied in the literature for the solution of bilevel optimization problems. Bilevel optimization problems can occur in certainty and uncertainty conditions. There can be single-objective or multi-objective bilevel optimization problems. The application areas of bilevel optimization include topological optimization, transport planning, set design, power resource management, battery storage management, supply chain management, and irrigation channel scheduling. Several classical methods, such as Karush–Kuhn–Tucker (KKT) conditions, and iterative, evolutionary techniques, such as GA, particle swarm optimization, and simulated annealing approaches, have been used to solve these problems. This chapter explains various techniques of bilevel optimization and its applications.