Multilevel optimisation

Abstract

This chapter is a short introduction to multilevel optimisation problems. The simplest multilevel problem is the one that has two levels, where one optimisation problem has as part of its constraints a second optimisation problem, known as bilevel problem. Even this simple version of the problem is from a mathematical point of view, complicated and difficult to solve. Therefore, approaches and examples of bilevel problems, as well as special cases and extensions of this problem that are used widely in literature, are presented. The most common methodologies used to solve multilevel problems are then described, with more extended reference to metaheuristic methods.