Expensive constrained multi-objective optimization via adaptive surrogate-assisted dense weight multi-objective evolutionary algorithm

Expensive constrained multi-objective optimization problems (ECMOPs) face challenges in obtaining excellent results for complex PF shapes within limited costly evaluations efficiently and balancing the optimizing on constraints and objectives. Also, one surrogate typically cannot provide the consistent predictive abilities for multiple objectives or constraints with diverse features. This paper designs an adaptive surrogate-assisted dense weight multi-objective evolutionary algorithm (ASDWMOEA), where efficient dense weight-based dual-population evolution and effective surrogate switch mechanism are integrated. Specifically, when there is no feasible solution in the population, the algorithm ignores the constraints of the problem and uses Kriging surrogate model to optimize only for the objective of the problem. When the population enters the feasible domain, the algorithm uses the association information of external weights to implement three mutation operations for generating a large set of high-quality candidate solutions. Each external weight is then refined to produce multiple internal weights, and an elite subset of the candidate solutions is selected to form the internal population corresponding to these internal weights. Subsequently, sequential global and local searches are conducted on the internal population, and the elite individual with the most significant improvement is selected for each internal weight. Hence, the external population is updated based the two metric-based selection strategy, and the algorithm adaptively switches between the employed Kriging and RBF surrogate models based on updates to the external population. Finally, the algorithm is evaluated against seventeen advanced and latest algorithms using five test suites. The results demonstrate that ASDWMOEA exhibits strong performance.