Adaptive switching of variable-fidelity models in population-based optimization

Abstract

This article presents a novel model management technique to be implemented in population-based heuristic optimization. This technique adaptively selects different computational models (both physics-based models and surrogate models) to be used during optimization, with the overall objective to result in optimal designs with high fidelity function estimates at a reasonable computational expense. For example, in optimizing an aircraft wing to obtain maximum lift-to-drag ratio, one can use low fidelity models such as given by the vortex lattice method, or a high fidelity finite volume model, or a surrogate model that substitutes the high-fidelity model. The information from these models with different levels of fidelity is integrated into the heuristic optimization process using the new adaptive model switching (AMS) technique. The model switching technique replaces the current model with the next higher fidelity model, when a stochastic switching criterion is met at a given iteration during the optimization process. The switching criterion is based on whether the uncertainty associated with the current model output dominates the latest improvement of the relative fitness function, where both the model output uncertainty and the function improvement (across the population) are expressed as probability distributions. For practical implementation, a measure of critical probability is used to regulate the degree of error that will be allowed, i.e., the fraction of instances where the improvement will be allowed to be lower than the model error, without having to change the model. In the absence of this critical probability, model management might become too conservative, leading to premature model-switching and thus higher computing expense. The proposed AMS-based optimization is applied to two design problems through Particle Swarm Optimization, which are: (i) Airfoil design, and (ii) Cantilever composite beam design. The application case studies of AMS illustrated: (i) the computational advantage of this method over purely high fidelity model-based optimization, and (ii) the accuracy advantage of this method over purely low fidelity model-based optimization.