A surrogate-assisted metaheuristic for bilevel optimization

Abstract

A Bilevel Optimization Problem (BOP) is related to two optimization problems in a hierarchical structure. A BOP is solved when an optimum of the upper level problem is found, subject to the optimal response of the respective lower level problem. This paper presents a metaheuristic method assisted by a kernel interpolation numerical technique to approximate optimal solutions of a BOP. Two surrogate methods approximate upper and lower level objective functions on solutions obtained by a population-based algorithm adapted to save upper level objective function evaluations. Some theoretical properties about kernel interpolation are used to study global convergence in some particular BOPs. The empirical results of this approach are analyzed when representative test functions for bilevel optimization are solved. The overall performance provided by the proposal is competitive.