基于局部时空的多峰优化算法及其在PID控制中的应用  

Localized Time-Distance-Based Multimodal Optimization Algorithm and Its Application in PID Control

作　　者：赵宏 李珈瑞 刘静 ZHAO Hong;LI Jia-Rui;LIU Jing(Guangzhou Institute of Technology,Xidian University,Guangzhou 510555)

机构地区：[1]西安电子科技大学广州研究院,广州510555

出　　处：《计算机学报》2024年第6期1323-1340,共18页Chinese Journal of Computers

基　　金：国家自然科学基金(62306225);广东省基础与应用基础研究基金(2021A151511073,2022A1515011297,202201011236);广东省高水平创新研究机构项目(2021B0909050008);广州市重点研发计划(202206030003)资助.

摘　　要：多峰优化问题(MultiModal Optimization Problems,MMOPs)需要同时找到问题的多个高精度全局最优解,它需要算法具有较强的全局搜索能力且能很好地平衡种群的多样性和收敛性.当前在处理MMOPs时通常面临以下难点:(1)现有方法通常只考虑到进化过程中种群的当前状态(如常用的贪婪选择策略),容易导致种群陷入局部最优;(2)传统的随机搜索策略在复杂搜索空间内难以快速有效找到全局最优解;(3)当前设计的多峰优化算法往往需要手工设置参数(如变异因子和交叉因子等),而参数的大小将直接影响种群的多样性和收敛性.针对上述难点,本文提出了一种新的基于局部时空的多峰优化(Localized Time-Distance-based Multimodal Optimization,LTDMO)算法,主要包括三个贡献点:首先,提出了结合随机搜索和定向引导的变异(Random and Direction-based Mutation,RDM)策略,利用随机变异增加种群中个体的多样性,并通过划分邻域将整个种群分成不同的可重叠子种群,在局部搜索空间内进行变异操作来更好地定位全局最优解,从而避免个体陷入局部最优.其次,提出了基于时间局部性原理的拥挤选择(Locality-based Crowding Selection,LCS)策略,利用进化过程中的时间局部性记录对当前个体更有潜力的进化方向,并在此方向上生成新的子代,使种群进一步向全局最优解收敛.最后,提出了自适应参数控制(Self-adaptive Parameter Control,SPC)策略,基于个体进化信息自适应调整算法的参数值,降低算法在进化过程中对变异因子和交叉因子的参数敏感性.本文将LTDMO算法在CEC'2013测试集上进行实验,并将结果与其他11种多峰优化算法对比,表明LTDMO算法能有效处理较多的全局最优复杂多峰优化问题,具体地,在F1~F5、F8和F10问题上峰值率和成功率均达到100%;在具有较多局部最优的多峰优化问题(F6和F7)上,LTDMO算法的峰值率达到86%以上,这优于9种其他�MultiModal Optimization Problems(MMOPs)requirefindingmultiplehigh-precision global optima of a problem simultaneously,necessitating algorithms that have strong global search capabilities and can well balance the diversity and convergence of the population.Currently,when dealing with MMOPs,there are typically the following difficulties:(1)Existing methods often only consider the current state of the population during the evolutionary process(such as the commonly used greedy selection strategy),which can easily lead to the population being trapped in local optima;(2)Traditional random search strategies have difficulty quickly and effectively finding global optima within complex search spaces;(3)Current multimodal optimization algorithm designs often require manual parameter setting(such as mutation and crossover factors),where the magnitude of these parameters directly impacts the population's diversity and convergence.To address these challenges,this paper introduces a new Localized Time-Distance-based Multimodal Optimization(LTDMO)algorithm,mainly contributing in three areas:First,a Random and Direction-based Mutation(RDM)strategy combining random search and directed guidance is proposed,using random mutation to increase the diversity of individuals within the population,and by dividing the population into different,possibly overlapping subpopulations for mutation operations in local search spaces,better locating global optima and thus avoiding individuals falling into local optima.Second,a Locality-based Crowding Selection(LCS)strategy is proposed,utilizing the principle of temporal locality in the evolutionary process to record more promising evolutionary directions for the current individual,generating new offspring in this direction to further converge the population towards global optima.Lastly,a Self-adaptive Parameter Control(SPC)strategy is proposed,which adaptively adjusts the algorithm's parameter values based on individual evolutionary information,reducing the algorithm's sensitivity to parameters like

关 键 词：多峰优化问题 邻域变异 时间局部性 自适应调整参数 PID控制 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]