一种采用改进交叉熵的多目标优化问题求解方法  

A Solution to Multi-Objective Optimization Problem with Improved Cross Entropy Optimization

作　　者：赵舵[1] 唐启超 余志斌[1] ZHAO Duo;TANG Qichao;YU Zhibin(School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China)

机构地区：[1]西南交通大学电气工程学院,成都610031

出　　处：《西安交通大学学报》2019年第3期66-74,共9页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(U1730105);国家科技支撑计划资助项目(2015BAG14B01-05);四川省科技厅资助项目(17ZDYF1517)

摘　　要：针对传统交叉熵算法不能解决多目标优化问题,采用单目标交叉熵优化算法提出了改进多目标交叉熵优化(Multi-Objective Cross Entropy Optimization,MOCEO)算法。首先,采用个体选择机制来保留进化过程中的优良个体,通过精英保留策略提取优良个体分布信息以不断修正算法正态分布概率模型参数;其次,引入进化方向在正态分布群体采样过程中,引导所产生新个体在解空间中的分布使得种群朝着性能提高的方向进化;最后,为了避免陷入局部最优点在参数平滑操作过程中,定义了调节系数随机调整正态分布概率模型参数。ZDT和DTLZ系列多目标问题的测试结果表明,与经典多目标优化算法NSGA-II、SPEA2、MOEAD、PAES相比,MOCEO在超体积和反转世代距离性能指标以及进化速度等方面较好,是一种收敛速度快、寻优能力强、鲁棒性高的算法。为验证MOCEO在工程实际中的效果,将其应用于某型高速列车悬挂系统横向平稳控制系统的参数优化中,仿真结果表明:相比于NSGA-II算法,使用MOCEO优化调整控制系统参数后,车体横向平稳性指标提高4.16%,横向加速度峰值减小10.34%,横向振动加速度在1～2 Hz人体敏感频率范围内有一定改善,列车具有更好的横向平稳性能。Due to the traditional cross entropy algorithm is unable to solve multiobjective optimization problem, an improved multi-objective cross entropy optimization (MOCEO) algorithm is proposed based on the single target cross entropy optimization algorithm. The individual selection mechanism is adopted to retain the elite individuals in the evolution process, and the distribution information is extracted via the elite retention strategy to constantly correct the parameters of the normal distribution probability model of the algorithm. Then the evolution direction in the traditional normal distribution population is introduced. During the sampling process, the new individuals are guided to the spatial distribution of the solution so that the population evolves towards the improvement of performance. To avoid the algorithm falling into local optimum, the adjustment coefficient is defined in the process of the traditional parameter smoothing operation. Adjusting the parameters of the normal distribution probability model, premature convergence of the algorithm is effectively avoided. This paper implements the MOCEO and compares it in terms of the hyper volume, the inverted generational distance performance indications and the evolutionary speed with the NSGA-II, SPEA2, MOEAD, PAES algorithms using the ZDT and DTLZ test functions. The results indicate that MOCEO is superior to the other algorithms with fast convergence, strong searching ability and high robustness. An optimization for parameters of horizontal stability control system of a high-speed train suspension system verifies the effect of MOCEO. Compared with the NSGA-II algorithm, the lateral stability index of the train body is increased by 4.16% and the peak value of lateral acceleration is reduced by 10.34% by adjusting the MOCEO optimization parameters of the control system. The lateral vibration acceleration of the vehicle body is improved in the frequency range of 1-2 Hz, to which human body is sensitive, and the train achieves better lateral stability.

关 键 词：多目标优化 进化算法 交叉熵优化算法 横向平稳性 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]