Landscape Modification Meets Surrogate Optimization: Towards Developing an Improved Stochastic Response Surface Method

Abstract

In global optimization, surrogate optimization algorithms such as the Stochastic Response Surface (SRS) method are often employed when the objective function is expensive to evaluate or when the gradient information is unavailable. The aim of this paper is to propose and analyze an improved SRS method that instead targets a transformed objective function. The core idea of the transformation rests on introducing a threshold parameter in which the landscape is modified when the algorithm is above this threshold, making the algorithm easier to climb out of a local minimum basin while preserving the set of the stationary points. We prove the asymptotic convergence of the proposed improved SRS method, and provide positive numerical results on some common global optimization benchmark functions which demonstrate the improved convergence of the proposed method. We stress that the proposed method can be implemented with minimal additional computational costs.