Various real-world applications can be classified as expensive multimodal optimization problems. When surrogate-assisted evolutionary algorithms (SAEAs) are employed to tackle these problems, they not only face a contradiction between the precision of surrogate models and the cost of individual evaluations but also have the difficulty that surrogate models and problem modalities are hard to match. To address this issue, this article studies a dual-surrogate-assisted cooperative particle swarm optimization algorithm to seek multiple optimal solutions. A dual-population cooperative particle swarm optimizer is first developed to simultaneously explore/exploit multiple modalities. Following that, a modal-guided dual-layer cooperative surrogate model, which contains one upper global surrogate model and a group of lower local surrogate models, is constructed with the purpose of reducing the individual evaluation cost. Moreover, a hybrid strategy based on clustering and peak-valley is proposed to detect new modalities. Compared with five existing SAEAs and seven multimodal evolutionary algorithms, the proposed algorithm can simultaneously obtain multiple highly competitive optimal solutions at a low computational cost according to the experimental results of testing both 11 benchmark instances and the building energy conservation problem.

中文翻译：

---

针对昂贵的多模态问题的双代理辅助协作粒子群优化


各种现实世界的应用可以归类为昂贵的多模态优化问题。当采用代理辅助进化算法（SAEA）来解决这些问题时，不仅面临代理模型精度与个体评估成本之间的矛盾，而且还面临代理模型与问题模态难以匹配的困难。针对这个问题，本文研究了一种双代理辅助的协作粒子群优化算法来寻求多个最优解。首先开发了双群体协作粒子群优化器来同时探索/利用多种模式。随后，构建了一个模态引导的双层合作代理模型，其中包含一个上层全局代理模型和一组下层局部代理模型，以降低个体评估成本。此外，提出了一种基于聚类和峰谷的混合策略来检测新的模态。与现有的5个SAEA和7个多模态进化算法相比，根据11个基准实例和建筑节能问题的实验结果，该算法能够以较低的计算成本同时获得多个极具竞争力的最优解。