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.