Reserch And Application Of Multimodal Optimiza-Tion Algorithm

Many problem s can be transformed into optimization problems in scientific research and practical applications.And some optimization problems are multimodal with multiple global optimal solution points in the solution area at the same time.It has always been hotspots in the research of multimodal optimization problems that how to find all optimal solution points at once effectively.This paper takes multimodal optim ization problems as the main research object,then conducts in-depth analysis and research on multimodal optimization problems based on differential evolution algorithm and niche thinking.Two effective algorithms for solving multimodal optimization problems and an effective algorithm for solving constrained multimodal optimization problems are proposed.The main research work includes the following aspects.(1)Aiming at the shortcomings of the traditional niche differential evolution algorithm in solving the multimodal optimization problem,a differential evolution algorithm based on the Nearest-Better clustering neighborhood mutation is proposed.The algorithm is based on the neighborhood mutation idea and combined with niche technology to solve the multimodal optimization problems.It can realize the adaptive adjustment of the size of the neighborhood,thereby increasing the diversity of the population,improving the ability of the algorithm to explore and maintain multiple optimal solution points.(2)A differential evolution algorithm based on low-density individuals in the neighborhood is proposed.In each generation,at first the algorithm uses the density peak clustering method to obtain the density of each individual,then takes individual which has lower density within the current individual neighborhood as the basis vector of the mutation operator.As the population evolves,the algorithm will automatically transform from the exploration stage to the convergence stage,thereby balancing the exploration and convergence capabilities of the algorithm.This ensures that the algorithm has the advantages of fast convergence and high accuracy.(3)In order to solve the constrained multimodal optimization problem,an improved algorithm is proposed.After improving the two algorithms proposed in this paper,two improved algorithms for solving the constrained multimodal optimization problem are obtained.Numerical simulation results show that the two improved algorithms are feasible and effective in solving constrained multimodal optimization problems.(4)Numerical calculation programs are compiled for the various algorithms proposed in this paper.Numerical simulation calculations are carried out on the test functions,the solution of nonlinear equations in practical applications and the roots of transcendental equations.The results show that the algorithm in this paper is better than other algorithms to a certain extentand,and has strong versatility and high computational efficiency.