A Variance-Control Strategy for Expensive Optimization Problems

초록

Expensive optimization problems widely arise nowadays in engineering design, simulation-based modeling, and scientific computing, where objective function evaluations are computationally costly and only a limited number of samples can be obtained. Data-driven evolutionary algorithms (DDEAs) offer a promising approach for tackling EOPs by using surrogate models to approximate candidate fitness and reduce costly evaluations. However, in some circumstances, existing surrogate ensemble approaches primarily focus on model selection strategies while overlooking the impact of surrogate model variance on optimization stability. High-capacity surrogate models may produce spurious local optima in unexplored regions while low-capacity surrogate models are likely too simple to accurately fit some complicated or high-dimensional functions, which can mislead the evolutionary search process. In this paper, we investigate the role of surrogate variance in offline surrogate-assisted evolutionary optimization with limited data. Through theoretical analysis, we show that excessive model capacity leads to unstable predictions and degraded optimization performance. Therefore, to address this issue, we propose a variance-controlled surrogate model ensemble strategy that employs mixed-capacity surrogate models. Experimental results on five benchmark functions with varying dimensionalities demonstrate that the proposed approach consistently improves optimization performance under fixed data budgets. The findings highlight the importance of variance control in expensive optimization. © 2026 IEEE.

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