一类受随机扰动的动态优化问题的环境检测与响应  

Environmental Detection and Response to a Kind of Dynamic Optimization Problem Subjected to Random Disturbance

作　　者：聂嘉乐 余旌胡[1] Jiale Nie;Jinghu Yu(School of Science,Wuhan University of Technology,Wuhan 430070)

机构地区：[1]武汉理工大学理学院,武汉430070

出　　处：《数学物理学报（A辑）》2022年第5期1560-1574,共15页Acta Mathematica Scientia

摘　　要：动态优化问题在实际生产或生活中广泛存在,其中环境检测与响应方法是解决此类问题的核心.在许多实际问题中,由于随机因素的干扰,优化问题的真实最优解会在一定程度上发生随机偏移,该文考虑最优解随机偏移服从正态分布的随机动态优化问题.首先,该文改进了现有基于正交试验设计思想的区间收缩方法,进而提出了动态优化问题的环境检测与响应策略,在一定程度上避免了已有方法的盲目性与随机性.其次,给出了扰动前后环境检测无变化所对应随机扰动的标准差上限.最后利用粒子群算法进行测试,实验结果表明:该文提出的环境检测与响应方法不仅能够有效处理最优解受随机扰动的随机动态优化问题,而且也能提高利用粒子群算法处理其它动态优化问题的能力.改进的环境检测与响应方法可以应用到粒子群算法外的其它演化算法上.Dynamic optimization problems are widespread in actual production or life,and environmental detection and response methods are the core of solving such problems.In many practical problems,due to the interference of random factors,the true optimal solution of the optimization problem will be randomly offset to a certain extent.This paper considers the stochastic dynamic optimization problem in which the random offset of the optimal solution obeys the normal distribution.First of all,this paper improves the existing interval shrinkage method based on the idea of orthogonal experimental design,and then proposes an environmental detection and response strategy for dynamic optimization problems,which avoids the blindness and randomness of the existing methods to a certain extent.Secondly,the upper limit of the standard deviation of the random perturbation corresponding to no change in the environmental detection before and after the perturbation is given.Finally,the particle swarm optimization algorithm is used for testing.And the experimental results show that the environmental detection and response method proposed in this paper can not only effectively deal with the stochastic dynamic optimization problem in which the optimal solution is disturbed by random,but also improve the ability of using particle swarm optimization to deal with other dynamic optimization problems.The improved environment detection and response method can be applied to other evolutionary algorithms besides particle swarm optimization.

关 键 词：动态优化 环境检测与响应 随机扰动 正交试验设计 

分 类 号：O213.9[理学—概率论与数理统计]