Expensive Optimization via Relation

Expensive optimization problems pose significant challenges to traditional gradient-free optimization due to their costly evaluation overhead. Surrogate model-assisted evolutionary optimization, which substitutes expensive evaluation functions with surrogate models, can effectively overcome these challenges. Designing an efficient surrogate model is the key issue in model-assisted evolutionary optimization. In recent years, establishing surrogate models through the relationships between solutions has become a promising modeling strategy, following regression and classification models. However, there has been a notable lack of systematic organization or comprehensive summary of relation models, which has impeded the structured development of this burgeoning research area. This article seeks to address this gap by viewing relations as a perspective to outline the contextual development of the field, defining a robust framework for researching relation models, and reviewing typical strategies within each framework. Finally, it validates the effectiveness of numerous strategies through experiments. The entire collection of strategies will be open-sourced on GitHub, facilitating greater participation from the research community in this field of study.