A Surrogate Assisted Approach for Single-Objective Bilevel Optimization

Bilevel optimization refers to a hierarchical problem in which optimization needs to be performed at two nested levels, namely the upper level and the lower level. The aim is to identify the optimum of the upper level problem, subject to optimality of the corresponding lower level problem. Several problems from the domain of engineering, logistics, economics, and transportation have inherent nested structure which requires them to be modeled as bilevel optimization problems. Bilevel optimization usually requires inordinate amount of function evaluations since a lower level search needs to be conducted for evaluating each upper level solution. The evaluations are especially high when the problems are not suited for exact techniques and evolutionary techniques are employed instead. Reducing this computational effort has been one of the key pursuits in this domain recently. However, the use of surrogate modeling to achieve this goal has so far been scarcely studied. In this paper, we present a surrogate assisted optimization approach toward addressing this research gap. The approach uses surrogates of multiple types in order to provide flexibility of approximating different types of functions more accurately. The algorithm is further strengthened through the use of selective re-evaluation of promising solutions and periodic nested local search. The performance of the proposed algorithm is presented on twenty five standard benchmark problems. The results are compared with a number of other established evolutionary and hybrid algorithms to demonstrate the efficacy of the proposed approach in obtaining competitive results using relatively fewer function evaluations.