Efficient Global Optimization for Solving Computationally Expensive Bilevel Optimization Problems

A number of real-life optimization problems operate in hierarchical model, where a "leader" entity is trying to optimize its objective(s), while in response a "follower" entity is also optimizing its own objective(s). Such problems are referred to as bilevel optimization problems. Given their nested nature, they have additional challenges compared to the traditional single-level optimization problems. Recent studies in the domain make it evident that the number of function evaluations needed to solve such problems using evolutionary algorithms is excessive. Development of efficient techniques that could reduce this computational effort is therefore of significant interest. In our previous work, we proposed and studied the use of multiple surrogate assisted optimization (SAO) to reduce the required evaluations of the lower level problem. In this work, we extend the idea further through the use of efficient global optimization (EGO) in solving bilevel problems. We refer to the approach as BLEGO (bilevel EGO). Unlike the standard SAO techniques, EGO samples new infill locations based on expected improvement in the objective value. Two different versions of BLEGO are studied - one where EGO is used only at the lower level, and another where EGO is used at both levels. Numerical experiments are conducted on SMD benchmark problem suite and the results are compared with the previously developed surrogate assisted bilevel algorithm (SABLA) to demonstrate its efficacy.