Adaptive Model Refinement in Surrogate-based Multiobjective Optimization

Abstract

Surrogate-Based Optimization (SBO), while providing a computationally-efficient alternative to expensive high-fidelity optimization of complex systems, is often plagued by the low reliability of the optimum values obtained thereof. Model refinement techniques are one of the most recognized means to increasing the reliability of the optimum solutions while preserving the computational efficiency of SBO. One such method is the recently developed Adaptive Model Refinement (AMR) technique, which decides when to refine and the desired extent of the refinement, for single-objective optimization using any type of surrogate models (i.e., a model independent approach). In this paper, we make fundamental modifications to the AMR technique to extend its applicability to multiobjective problems, both in the case of problems involving multiple and single high-fidelity source codes or simulations. The AMR technique is designed to work particularly with population-based optimization algorithms. In AMR, the reconstruction of the model is performed by sequentially adding a batch of new samples at any given iteration (of SBO), when a refinement metric is met. This metric is formulated by comparing (1) the uncertainty associated with the outputs of the current model, and (2) the distribution of the latest fitness function improvement over the population of candidate designs. Conservative, non-conservative, and balanced approaches are explored for multiobjective implementation, in terms of the fraction of objectives for which the model refinement metric has been satisfied. In the case of an affirmative decision for model refinement, the history of the fitness function improvement is used to determine the desired fidelity for the upcoming iterations of SBO. The location of the new samples in the input space is determined based on the smallest hypercube enclosing the entire population of candidate designs, the smallest hypercube enclosing the current set of non-dominated designs, and a distance-based criterion that minimizes the correlation between the current sample points and the new points. A multiobjective implementation of GA algorithm is used in conjunction with Kriging surrogate model to apply the new AMR method. The performance of the new multiobjective AMR method is investigated by applying it to a structural wind blade design problem.