摘要
现实生活中的很多黑盒优化问题可归为高计算代价的多模态优化问题(Multimodal optimization problem,MMOP),即昂贵多模态优化问题(Expensive MMOP,EMMOP).在处理该类问题时,决策者希望以尽量少的计算代价(即尽量少的真实函数评价次数)找到多个高质量的最优解.然而,已有代理辅助的进化优化算法(Surrogate-assisted evolutionary algorithm,SAEA)很少考虑问题的多模态属性,运行一次仅可获得问题的一个最优解.鉴于此,研究一种异构集成代理辅助的区间多模态粒子群优化(Interval multimodal particle swarm optimization algorithm assisted by heterogeneous ensemble surrogate,IMPSO-HES)算法.首先,借助异构集成的思想构建一个由多个基础代理模型组成的模型池;随后,依据待评价粒子与已发现模态之间的匹配关系,从模型池中自主选择部分基础代理模型进行集成,并使用集成后的代理模型预测该粒子的适应值.进一步,为节约代理模型管理的代价,设计一种增量式的代理模型管理策略;为减少代理模型预测误差对算法性能的影响,首次将区间排序关系引入到进化过程中.将所提算法与当前流行的5种代理辅助进化优化算法和7种最先进的多模态优化算法进行对比,在20个测试函数和1个建筑节能实际问题上的实验结果表明,所提算法可以在较少计算代价下获得问题的多个高竞争最优解.
Many real-world black-box optimization problems can be classified as multimodal optimization problems(MMOPs)with high computational cost,that is,expensive multimodal optimization problems(EMMOPs).When dealing with such problems,decision-makers hope to find multiple high-quality solutions with less computational cost(i.e.,the least number of real function evaluations).However,existing surrogate-assisted evolutionary algorithms(SAEAs)seldom consider the multimodal properties of problem,and they can only obtain one optimal solution of the problem at a time.In view of this,this paper studies an interval multimodal particle swarm optimization(PSO)algorithm assisted by heterogeneous ensemble surrogate(IMPSO-HES).Firstly,a model pool composed of multiple basic surrogate models is constructed with the idea of heterogeneous ensemble.Then,according to the matching relationship between the particle to be evaluated and the discovered modalities,some basic surrogate models will be selected from the model pool for integration,and the integrated surrogate model is utilized to predict the fitness value of the particle.Furthermore,in order to save the cost of model management,an incremental surrogate model management strategy is designed.In order to reduce the influence of prediction error of surrogate model on the algorithm's performance,the interval ordering relation is introduced into the evolutionary process for the first time.The proposed algorithm is compared with five SAEAs and seven state-of-the-art multimodal algorithms,experimental results on 20 benchmark functions and the building energy conservation problem show that the proposed algorithm can obtain multiple highly-competitive optimal solutions at a low computational cost.
作者
季新芳
张勇
巩敦卫
郭一楠
孙晓燕
JI Xin-Fang;ZHANG Yong;GONG Dun-Wei;GUO Yi-Nan;SUN Xiao-Yan(School of Information and Control Engineering,China University of Mining and Technology,Xuzhou 221116;School of Mechanical Electronic and Information Engineering,China University of Mining and Technology(Beijing),Beijing 100083)
出处
《自动化学报》
EI
CAS
CSCD
北大核心
2024年第9期1831-1853,共23页
Acta Automatica Sinica
基金
国家自然科学基金(62273348,62133015)
北方民族大学青年人才培育项目(2024QNPY04)资助。
关键词
粒子群优化
多模态优化
高昂计算代价
代理辅助
Particle swarm optimization(PSO)
multimodal optimization
expensive computational cost
surrogateassisted
