PSAF: a probabilistic surrogate-assisted framework for single-objective optimization

In the last two decades, significant effort has been made to solve computationally expensive optimization problems using surrogate models. Regardless of whether surrogates are the primary drivers of an algorithm or improve the convergence of an existing method, most proposed concepts are rather specific and not very generalizable. Some important considerations are selecting a baseline optimization algorithm, a suitable surrogate methodology, and the surrogate's involvement in the overall algorithm design. This paper proposes a probabilistic surrogate-assisted framework (PSAF), demonstrating its applicability to a broad category of single-objective optimization methods. The framework injects knowledge from a surrogate into an existing algorithm through a tournament-based procedure and continuing the optimization run on the surrogate's predictions. The surrogate's involvement is determined by updating a replacement probability based on the accuracy from past iterations. A study of four well-known population-based optimization algorithms with and without the proposed probabilistic surrogate assistance indicates its usefulness in achieving a better convergence. The proposed framework enables the incorporation of surrogates into an existing optimization algorithm and, thus, paves the way for new surrogate-assisted algorithms dealing with challenges in less frequently addressed computationally expensive functions, such as different variable types, large dimensional problems, multiple objectives, and constraints.