Many industrial applications require time-consuming and resource-intensive evaluations of suitable solutions within very limited time frames. Therefore, many surrogate-assisted evaluation algorithms (SAEAs) have been widely used to optimize expensive problems. However, due to the curse of dimensionality and its implications, scaling SAEAs to high-dimensional expensive problems is still challenging. This paper proposes a variable surrogate model-based particle swarm optimization (called VSMPSO) to meet this challenge and extends it to solve 200-dimensional problems. Specifically, a single surrogate model constructed by simple random sampling is taken to explore different promising areas in different iterations. Moreover, a variable model management strategy is used to better utilize the current global model and accelerate the convergence rate of the optimizer. In addition, the strategy can be applied to any SAEA irrespective of the surrogate model used. To control the trade-off between optimization results and optimization time consumption of SAEAs, we consider fitness value and running time as a bi-objective problem. Applying the proposed approach to a benchmark test suite of dimensions ranging from 30 to 200 and comparisons with four state-of-the-art algorithms show that the proposed VSMPSO achieves high-quality solutions and computational efficiency for high-dimensional problems.

许多工业应用需要在非常有限的时间范围内对合适的解决方案进行耗时和资源密集型评估。因此，许多代理辅助评估算法 (SAEA) 已被广泛用于优化昂贵的问题。然而，由于维数灾难及其影响，将 SAEA 扩展到高维代价高昂的问题仍然具有挑战性。本文提出了一种基于变量代理模型的粒子群优化（称为 VSMPSO）来应对这一挑战，并将其扩展到解决 200 维问题。具体来说，采用通过简单随机抽样构建的单一替代模型，在不同的迭代中探索不同的有希望的领域。而且，变量模型管理策略用于更好地利用当前全局模型并加快优化器的收敛速度。此外，该策略可以应用于任何 SAEA，而不管使用的代理模型如何。为了控制 SAEAs 的优化结果和优化时间消耗之间的权衡，我们将适应度值和运行时间视为一个双目标问题。将所提出的方法应用于维度从 30 到 200 的基准测试套件，并与四种最先进的算法进行比较表明，所提出的 VSMPSO 实现了高维问题的高质量解决方案和计算效率。为了控制 SAEAs 的优化结果和优化时间消耗之间的权衡，我们将适应度值和运行时间视为一个双目标问题。将所提出的方法应用于维度从 30 到 200 的基准测试套件，并与四种最先进的算法进行比较表明，所提出的 VSMPSO 实现了高维问题的高质量解决方案和计算效率。为了控制 SAEAs 的优化结果和优化时间消耗之间的权衡，我们将适应度值和运行时间视为一个双目标问题。将所提出的方法应用于维度从 30 到 200 的基准测试套件，并与四种最先进的算法进行比较表明，所提出的 VSMPSO 实现了高维问题的高质量解决方案和计算效率。