Research On Differential Evolution Algorithms Based On Population Evolution State And Variable Interaction

Differential evolution algorithm(DE)is a simple and effective heuristic evolutionary algorithm which can be used to solve various global optimization problems.DE is mainly divided into four steps: initialization,mutation,crossover and selection.DE has the advantages of simple model,easy implementation,good robustness and strong scalability.However,in the actual operation of DE,population stagnation or premature convergence often occurs,which makes population evolution very slow or even stagnant.In addition,in the basic DE and some improved DE variants,the interaction between variables is not taken into account.In the process of population evolution,variables are often operated independently,resulting in some related variables not being processed at the same time,thus losing some important information.The performance of DE can be further improved by solving the above problems.Therefore,DE has room for improvement and promotiont.This paper improves the DE from two aspects: selection operation and cross operation.For the two problems mentioned above,two general frameworks based on DE,TBT-DE framework and DE-GExp framework,are proposed correspondingly.The main work is as follows:1.The population in DE often falls into stagnation or premature convergence in the process of evolution,so that it can not converge to the global optimal state.To solve this problem,a tracking mechanism(TM)is proposed to promote population convergence when the population is in a stagnant state,and a backtracking mechanism(BTM)is proposed to re-improve population diversity when the population is in a premature convergence state.More specifically,when the population is stagnated,TM is triggered,making the stagnated individuals close to the excellent individuals in the population,thus promoting population convergence.When the population falls into premature convergence state,BTM is activated,so that the individuals falling into premature convergence can go back to a previous state to restore the diversity of the population.TM and BTM are combined into a general framework TBT-DE,which is embedded in six classical DE and nine most advanced DE variants.The experimental results of 30 CEC2014 test functions show that TM and BTM can effectively overcome stagnation and premature convergence respectively,thus enhancing the performance of the algorithm.The experimental results also confirm the effectiveness of this method.In addition,the experimental results also show that TM combined with BTM as a general framework exhibits better results than they as a general framework respectively.2.When the DE solves the optimization problem,there is a certain interaction between specific variables in most optimization problems.In this paper,we use the interaction between variables to start from two aspects: First,for the inseparable function,the related variables are bundled together for large-scale synchronous change;second,for the separable function,the univariate perturbation method allows only a single variable to inherit the mutant vector at a time.The specific method is: before the population begins to evolve,first consume a part of the function evaluation number to determine whether there is an interaction between the two variables,and group the variables according to the interaction.Then,in the crossover operation of each iteration in the evolution process,the inseparable function is made for the inseparable function to have a greater probability of inheriting the variable value of the target vector or the mutant vector,and for the separable function,the single variable inherits the value of the mutation vector and the other variables inherit the value of the target vector,which improves the performance of the algorithm.As a general framework,DE-GExp can be well embedded in the basic DE and most DE variants to further improve the performance of the algorithm.In order to verify the validity of the framework,this paper embeds the DE-GExp framework into six basic algorithms and two advanced DE variants,and compares the DE with the DE variants added to the DE-GExp framework.Compare performance on the 30 CEC2014 test functions.Experimental results show that the DE-GExp framework can effectively improve the performance of the DE algorithm.