Study On The Algorithm For Solving Multi-modal Function Optimization Problem Based On Gradient Dynamic System

Solving optimization problems in practical applications, often encounter a plurality of global optimum and local optimum function optimization problems, such problems may be referred to multimodal function optimization problem. In the transportation, construction, manufacturing and many other fields, the problem can to be processed and transformed these problems into multi-modal function. This problem has a strong practical value, so it has been the focus of optimization and engineering.Before solving multimodal function optimization algorithm for the problem are mainly based on Niche Genetic Algorithm and the traditional numerical method, but the method in solving a number of local peak point has great limitations, is very easy to fall into local optimal solution. Multiple initial points are selected randomly in the feasible region. A local optimal solution can be obtained by integrating the associated gradient systemThis paper describes in detail the gradient dynamical system model. A algorithm based gradient dynamical system is proposed to solve multimodal fuction optimization problems. This algorithm in this paper removes the iterative mechanism and randomly selects multiple initial points in the feasible region. Then the corresponding gradient dynamic system is integrated to obtain the equilibrium point of the system and the equilibrium point is a global or local optimal solution. The algorithm in this paper can effectively calculate the multiple global and local optimal solutions. At the same time, it can avoid premature phenomenon.This algorithm can easily find multiple solutions of multi-modal optimization problems, including both the global optimal solution and local solution, and don't need to know any information about the peaks. In this paper, a number of standard multi-modal optimization test problem is studied, and the results of the test and the niche genetic algorithm are compared, the superiority of the algorithm is proved.