基于矩阵运算的改进单纯形寻优方法

为解决单纯形法优化容易陷入局部极值的问题,通过随机设置若干初始点,利用矩阵进行多点并行搜索方法,可搜索到全部极大(极小)值点,达到全局最优化目的. 与常规的重复设置单初始点循环搜索的方法相比,该方法明显减小了初始值设置对单纯形法寻优的影响,提高了搜索速度并获得全局最优值,优化效率大幅提高. 仿真结果表明:该改进的寻优方法不仅可应用于函数极值搜索,而且应用在控制系统PID参数寻优中,能获得满意的调节效果.

Improved Optimization for Simplex Method Based on Matrix Calculation

To solve the problem of liability of falling into regional extreme values in simplex search,by setting a number of starting points at random,a method of multipoint parallel search is proposed based on matrix.It can find all the maxima(minima) values in the main and thereby the goal of global(optimization) is achieved.Compared with the traditional method of circular search with a single starting point,the modified method,which is far more effective,obviously reduces the effects caused by(setting) starting points.Thus the searching time will be shortened and the global optimization results can be reached.Analyzing the results of simulation,it was found that the modified method can not(only) be adopted to search the optimizing values of function,but can also be applied to optimize the PID(parameters) of control systems,and the adjusted results on the basis of optimal PID parameters are(satisfactory.)