Surrogate-based black-box optimisation via domain exploration and smart placement

Abstract

In the era of digital twins, the need for accurately mimicking the reality has given rise to complex, black-box, compute-intensive models that are vital for simulating, analysing, and optimising physicochemical systems. In this work, we propose a novel surrogate-assisted approach for black-box optimisation, which uses efficient domain exploration and smart adaptive sample placement to escape local valleys (traps) and obtain a global minimum efficiently. Our iterative algorithm comprises two stages. The first stage constructs sub-regions based on Delaunay triangulations and selects the best for exploration. The second stage adds a new sample point to the best sub-region via optimisation. The two stages together balance domain exploration versus exploitation. The algorithmic framework is illustrated using the six-hump camel back function. An extensive numerical evaluation using twenty test functions (up to six variables) shows that the proposed algorithm exhibits superior performance against seven well-known commercial global optimisation algorithms including a surrogate-based approach.