Sensitivity Analysis of Surrogate-assisted Bilevel Optimisation

Behzad Moradi, Michael Kirley, Mario Andrés Muñoz Acosta

Abstract: Bilevel optimisation problems consist of two interactive optimisation tasks, where an upper-level task must be solved subject to the optimality of a lower-level task. Recently, a range of surrogateassisted bilevel evolutionary algorithms have been proposed, where various approximation models have been used to substitute each of the upper- or lower-level objective functions, and in some cases, the mappings between the levels. These algorithms are highly engineered systems where alternative surrogate models with varying parameters are used, often combined with other mechanisms such as local search and/or knowledge sharing. Consequently, it is difficult to isolate the effect that the surrogate model has on performance. In this paper, we address this issue. Starting from a nested optimisation algorithm - a bilevel Covariance Matrix Adaptation Evolutionary Strategy as a baseline - we systematically introduce surrogate models at the upper-level, lower-level, and both levels simultaneously, as well as for the mapping between the levels. Using a suite of benchmark problems, we scrutinise algorithm performance. The results show the acute sensitivity of performance to the objective function or mapping being modelled within the hierarchical structure. We note that, in most test problems, smaller computation costs are evident when modelling the lower-level objective function.