Study On Strategy Of Differential Evolution Algorithm Based On Fitness Landscape

As a difficult problem to be solved in engineering application,optimization problem has always been the focus of experts and scholars.With the development of society and the deepening of theoretical study,the optimization problems that people need to solve are becoming more and more complex,and these problems have the characteristics of nonlinearity,discontinuity and non-differentiability.The complexity of the problem is increasing,and traditional mathematical optimization methods are difficult to solve these problems.Differential evolution(DE)algorithm is an evolutionary algorithm based on the idea of individual difference recombination.As a well-known heuristic algorithm in the field of optimization,DE is suitable for solving optimization problems in continuous domain.Because of the simple structure and strong convergence ability,DE is often preferred in solving optimization problems.However,the traditional DE has some shortcomings,such as: 1)The traditional DE has different kinds of mutation operator,which have different effects on individuals,and it is difficult to select the suitable one according to the characteristics of optimization problems.2)The traditional DE does not have adaptive parameter mechanism,so it often needs experience and experiments to find the best scaling factor and crossover probability for different problems.When the fitness function of the problem is complex,the evaluation will consume a lot of computing resources.Aiming at the difficulty of selecting mutation operator and the tedious process of finding good parameters in DE,the following study works have been done in the paper:Firstly,study on strategy of mutation operator and algorithm parameter based on fitness landscape.Different combinations have been constructed by enumerating different mutation operators,scaling factors and crossover probabilities.Each combination is considered as a strategy of standard DE,and the performance of each strategy is obtained by running DE on some classical benchmark functions.The local fitness distance correlation and entropy ruggedness of these benchmarks are extracted as the fitness landscape characteristics of benchmarks,and the performance differences of different strategies in different landscape are analyzed.Machine learning methods are used to establish the relationship between fitness landscape and good performance strategy,then a strategy selector is obtained.The advantage of using strategy selector to select strategy is getting suitable mutation operator and parameters by sampling a small number of points and calculating the fitness landscape of problem.The experimental results show that for most test functions,the average performance of standard DE using strategy selector for mutation operator and parameter initialization is better than that of single mutation operator.Secondly,study on mutation strategy selection in a running DE based on fitness landscape.An improved DE named Mixed Mutation Fitness Landscape Differential Evolution(MMFLDE)is proposed.This algorithm updates the mutation operator and scaling factor according to the autocorrelation ruggedness and gradient measurement of local fitness landscape,and enhances the optimization ability of the algorithm.In order to achieve this goal,this paper uses Deep Q Network(DQN)algorithm to construct a decision controller,which includes the following tasks: 1)According to the characteristics of different benchmark functions,improves the gradient measurement method,and the state space is designed based on autocorrelation ruggedness and improved gradient measurement.2)Designing the action space according to the mutation strategy of MMFLDE.3)According to the concept of evolvability,a dynamic fitness landscape measurement named Evolutionary Efficiency of Population(EEP)is proposed as the reward function of decision controller.Compared with other differential evolution algorithms and improved algorithms,MMFLDE has good performance on some problems.Thirdly,the relationship between fitness landscape and mutation strategy is analyzed.By studying the changes of local fitness landscape and mutation strategy during the running of MMFLDE,the relationship between the update of mutation strategy and the change of local fitness landscape of population are described in a graph,which further illustrates that the mutation strategy tuning of MMFLDE is related to fitness landscape.