Bi-Level Model Management Strategy for Solving Expensive Multi-Objective Optimization Problems

Model management strategy is the main component of surrogate-assisted evolutionary algorithms for solving expensive multi-objective optimization problems(EMOPs). In such problems, evaluating the true fitness function requires significant computational resources, which necessitates effective determination of which individuals should be selected for evaluation. However, existing model management strategies often struggle to effectively balance exploration and exploitation when selecting individuals. To mitigate this issue, a bi-level model management strategy is proposed. The selection procedure not only considers exploring the objective space by balancing predicted values and uncertainty in the lower-level but also considers convergence and diversity in the upper-level selection. Specifically, we first divide the objective space into some sub-spaces through a set of direction vectors. Then, we select the first rank individuals via adopting the non-dominated sorting to balance the predicted objective values and the uncertainty in each subspace. The intersection individuals of the selected candidates can be denoted as the lower-level solutions. In the upper-level selection, we combine the modified inverted generational distance (IGD
$^+$
) and shift-based density estimation (SDE) indicators to select the most promising individuals from the lower-level to update the model. Experimental results on benchmark instances show that the proposed algorithm is competitive compared with some representative algorithms.