Radial projection-based adaptive sampling strategies for surrogate-assisted many-objective optimization

Intelligent manufacturing and industrial control systems frequently encounter expensive many-objective optimization problems (EMaOPs). Surrogate-assisted evolutionary algorithms (SAEAs) build predictive models to substitute the expensive fitness evaluation, enabling them to solve optimization more efficiently. In SAEAs, to enhance the exploration of optimization and the generalization of the surrogate model, the diversity of infill offspring and training database should be well-maintained, which is challenging in high-dimensional spaces or problems with disconnected Pareto front. This paper suggests a radial projection-based surrogate-assisted framework for solving EMaOPs. The radial projection can map the high-dimensional objective space into a 2-dimensional radial space. Based on this, a dynamic quadratic division method is proposed to enhance the diversity of solutions. Furthermore, an adaptive infill sampling criterion is introduced based on the distribution of selected convergent solutions, and a training database updating strategy is designed under the premise of maintaining its diversity and the model training efficiency. The presented framework exhibits a notable level of flexibility and adaptability as it can be effortlessly combined with other multi-objective optimization algorithms. Several experimental results on a set of expensive multi/many-objective test problems have demonstrated the superiority of the framework.