Two Stage Surrogate Assisted Framework For Box-Constrained Global Optimisation

Abstract

In this work, we propose a novel black-box optimisation approach, which blends the concepts of “trust-region” and “adaptive sample placement” to obtain the global minimum for limited computational budget while escaping local optima traps, if any. This is translated into mathematical formulation by iteratively constructing sub-regions based on Delaunay triangulation and adding new sample points sequentially to the selected sub-regions via placement optimisation that balances between domain exploration and exploitation. Our numerical evaluation shows that the proposed approach successfully locates the global minima and outperforms four black-box optimisation algorithms from the literature for six test problems. Overall, this work develops a generalised surrogate-assisted framework for black-box optimisation that holds much promise in solving design as well as operational problems.