A Co-Evolutionary Approach for Design Optimization via Ensembles of Surrogates With Application to Vehicle Crashworthiness

In many engineering application, where accurate models require lengthy numerical computations, it is a common design practice to perform design of experiments (DOE) and construct surrogate models that provide computationally-inexpensive approximations. Main challenges to that approach are (i) construction of high-fidelity surrogates and (ii) discovery of high performance designs despite the fidelity limitations. An ensemble of surrogates (EOS) is a collection of different surrogates approximating the same process (typically with some form of weighted averaging to get an overall approximation) and has been demonstrated in the literature to often exhibit better performance than any of the individual surrogates. This paper presents a Multi-Scenario Co-evolutionary Genetic Algorithm (MSCGA) for design optimization via EOS. MSCGA simultaneously evolves multiple populations in a multi-objective sense via the predicted performance by the different surrogates within the ensemble. The outputs of the algorithm are solution sets including several designs that are spread over Pareto-optimal space of best-predictions by the surrogates within EOS, as well as best designs as predicted by individual surrogates and the weighted average of the EOS. Studies using analytical test functions show MSCGA to be more likely to discover better performing designs than an individual surrogate or a weighted ensemble. The primary application for MSCGA presented in this paper is that of vehicle structural crashworthiness since it is a typical design application that requires massive computational resources for accurate modeling. Two studies, which include simplified and detailed vehicle models, MSCGA successfully discovers new high performance designs.