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

This paper advances a model management technique that is implemented in population-based optimization algorithms to provide high fidelity optimum designs at reasonable computational expense. This technique adaptively selects different computational models (both physics-based and surrogate models) of varying levels of fidelity during optimization. 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 fitness function. The model output uncertainty is represented using Log-normal distributions, and the function improvement (across the population) is expressed as KDE-based 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 could become too conservative, leading to premature model-switching and thus higher computing expense. The proposed variable fidelity optimization is applied to two practical design optimization problems through PSO: (i) Airfoil design, and (ii) Cantilever Composite Beam design. The application case studies indicate that the proposed model switching technique can provide a significantly superior balance between accuracy of the optimum and computational efficiency, compared to purely low fidelity or purely high fidelity optimizations.