Dual-Surrogate-Assisted Cooperative Particle Swarm Optimization for Expensive Multimodal Problems
针对昂贵多模态优化问题中代理模型精度与评估成本矛盾、模型与模态难匹配的困难，提出双代理辅助协同粒子群算法，通过双种群协同探索和模态引导的双层代理模型，以低计算成本同时获得多个高竞争力最优解。
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.