Research On Optimization Of Complex High-dimensional And Low-dimensional Functions

With the development of computer,the progress of industrial science and technology,the scale and complexity of optimization problems also increase rapidly,which puts forward higher requirements for various optimization methods.As one of the methods to solve optimization problems,meta heuristic algorithm has been widely used because of its simple parameters,independent of the specific function form of optimization problems and strong global search ability.With the increase of the dimension of optimization problem,the space of optimization problem increases exponentially,and the complexity increases rapidly.Many optimization algorithms will suffer from ”dimension curse”,and its performance decreases rapidly with the increase of dimension.In order to solve the complex highdimensional optimization problems,this thesis improves the exploitation and exploration ability of whale optimization algorithm and improves the optimization performance.When the optimization problem has the characteristics of asymmetry,overlap,ill condition and offset,it is difficult to find the optimal solution.In this thesis,a discrete region limited difference evolution algorithm(DRDE)is proposed to improve the exploration and exploitation performance of the algorithm,and is used to solve complex low-dimensional optimization problems.The main work of this thesis is as follows:(1)This thesis introduces the meta heuristic algorithm,and focuses on the basic principles of whale optimization algorithm and differential evolution algorithm.This thesis introduces the current research status of meta heuristic algorithm,complex high-dimensional and lowdimensional optimization problems.The classification of complex high-dimensional and low-dimensional optimization functions is introduced.(2)Considering that whale algorithm has some problems such as prematurity,low precision,search stagnation and slow convergence rate when dealing with complex high-dimensional function optimization problems,this thesis proposes an improved whale optimization algorithm(MIWOA)is proposed.Firstly,MIWOA divides the population into better and worse groups according to the fitness.The better population is used to improve the exploitation performance,and the poor population is used to improve the exploration performance,so as to make full use of the individual characteristics to improve the exploration and exploitation performance of the algorithm.Secondly,MIWOA improves the ability of exploration and convergence by using weighted center learning strategy,and introduces the quadratic interpolation algorithm to further improve the exploitation performance of the algorithm.Finally,the control parameters are used to balance the exploitation and exploration process.The simulation results show that MIWOA is superior to other comparison algorithms in solving complex and high-dimensional optimization problems in terms of precision,convergence speed and execution time.(3)In order to solve the complex low-dimensional optimization problems,a discrete region limited difference evolution algorithm(DRDE)is proposed.Firstly,DRDE algorithm introduces discrete region search strategy and region restriction strategy to search the most promising solution region,narrow the search range and reduce the complexity of global search.On this basis,the Lévy flight process and whale exploitation process are introduced to further improve the exploitation performance and convergence speed of the algorithm.In addition,the algorithm also introduces the control parameters of the balance exploration and exploitation process.The DRDE algorithm is compared with the latest correlation algorithm on CEC'2013 low-dimensional test function.The experimental results show that the DRDE algorithm has a great improvement in accuracy and convergence speed.