A Historical Surrogate Model Ensemble Assisted Bayesian Evolutionary Optimization Algorithm for Solving Expensive Many-Objective Problems

Surrogate-assisted evolutionary optimization has become a promising approach for solving expensive multi-objective optimization problems. However, as the dimension of the objective space increases, it becomes difficult to obtain a sufficient number of samples to train a high-precision surrogate model. Despite the lack of training samples, there is a significant amount of sample prediction information provided by the surrogate model. Therefore, this paper proposes a historical surrogate model ensemble-assisted Bayesian evolutionary optimization algorithm (HMBEO) to address high-dimensional many-objective optimization problems. This method fully utilizes the historical information captured by the surrogate model. Specifically, it uses promising individuals selected by historical surrogate models as parents to guide the evolution of the population. The selection of the next generation of parents considers both the convergence of the objective space and the diversity of the decision space. Additionally, an improved infill sampling strategy is introduced to select samples for original expensive evaluation. This strategy uses the maximum distance criterion to select potential individuals and supplements sample points in sparse areas to ensure good diversity of objectives. The performance of the proposed algorithm is evaluated on a set of expensive many-objective benchmark problems. Experimental results demonstrate that it outperforms four state-of-the-art surrogate-assisted evolutionary algorithms.