Expensive Many-Objective Evolutionary Optimization With a Self-Adaptive Surrogate Model

Surrogate-assisted evolutionary algorithms (SAEAs) have gained increasing attention for addressing expensive many-objective optimization problems (EMaOPs). Generally, the same type of surrogate model is applied to each objective function. However, different objective functions may exhibit distinct characteristics, such as linearity and modality. Therefore, using a uniform type of surrogate model may not be an appropriate choice for assisting evolutionary algorithms in solving expensive many-objective problems. In this paper, we propose to adaptively choose the type of surrogate models for each objective function based on an $R^{2}$ indicator, which measures the accuracy of the model on some randomly chosen solutions that have been evaluated. We introduce a dual-space indicator based on the Euclidean distances in both decision and objective spaces, along with the crowdedness around the solution in a predefined neighborhood. This indicator is then used for selecting an informative solution to be evaluated using the real expensive objective functions. Several experiments are conducted on DTLZ and WFG test suites, as well as two real-world applications, to evaluate the performance of the proposed method. The experimental results show that the proposed algorithm outperforms six state-of-the-art peer approaches, highlighting its effectiveness and superiority in solving expensive many-objective optimization problems.