Differential Evolution assisted by a surrogate model for bilevel programming problems

Bilevel programming is used to model decentralized problems involving two levels of decision makers that are hierarchically related. Those problems, which arise in many practical applications, are recognized to be challenging. This paper reports a Differential Evolution (DE) method assisted by a surrogate model to solve bilevel programming problems (BLPs). The method proposed is an extension of a previous one, BlDE, developed by the authors, where two DE methods are used to generate and evolve the upper and the lower level variables. Here, the use of a similarity-based surrogate model, and a different stopping criteria, are proposed in order to reduce the number of function evaluations on both levels of the problem. The numerical results show a significant reduction in the number of function evaluations in the lower level of the problem, as well as some improvement in the upper level.