New Approach to Adjusting the Objective Function Gaussian Surrogate Model in the Problem of Design Solution Parametric Optimization

Abstract

The paper considers methods for solving the problem of design solution parametric optimization based on constructing the Gaussian surrogate model of this problem objective function. The problem is set of finding optimal values of the surrogate model free parameters (hyper-parameters), it is called the problem of its adjustment. The adjustment problem is built over the top of the surrogate model synthesis problem and has a higher computational complexity. The approach to adjusting a surrogate model is proposed, which is able to make the adjustment procedure acceptable in terms of the computational costs. This approach includes the setup and operation stages. The adjustment stage contains the following main steps: formation of a set of test objective functions; generation of a set of learning samples for each of them; determination of their characteristic features values for the generated samples; determination of the hyper-parameters optimal values for all considered test functions and learning samples; formation of a set of pairs, characteristic features of the sample--hyper-parameters optimal values; building on this basis a predictive model forecasting the hyper-parameters optimal values according to the learning sample characteristic features. For the initial problem at the operation stage, a learning sample was generated, its characteristic features were determined, and the hyper-parameters optimal values of the surrogate model were predicted. Based on the specified learning sample, the objective function surrogate model was synthesized. Using the surrogate model, the original optimization problem was solved, where the hyper-parameters predictive values were applied as the optimal values. The approach is able to provide an increase of up to 30 % in efficiency of the basic optimization algorithm