The Study On Performances Of Differential Evolution Algorithm Based On Dynamic Fitness Landscapes And Its Applications In Clustering

Evolutionary algorithms(EAs)are heuristic search algorithms which can simulate the process of biological evolution.They comprise genetic algorithms,genetic programming,evolution strategies,evolution programming and differential evolution,which have advantages of wide universalities,simple structures and parallel processing capabilities.Evolutionary algorithms are not restricted by characteristics of problems.Therefore,they can be used to solve multiple and nonlinear complex optimization problems and can be applied in different fields,such as biomedical science,engineering design,data mining,economic management,agricultural management,etc.Although Evolutionary algorithms obtain better results in simulation experiments and practical applicatio ns,they contain a lot of complex and random behaviors and are hard to be comprehensively analyzed due to lack of rigorous theoretical bases.In this study,the improvements of the gene expression programming algorithm and the differential evolution algorithm are researched and we firstly use effective analysis strategies of dynamic fitness landscapes to analyze the theoretical study of the improved differential evolution algorithm.The main work is summarized below:First of all,in order to prevent from p lunging into local optimum while K-means clustering algorithm selects initial clustering central points,we improve a gene expression programming algorithm.The improved algorithm presents a new chromosome expression formula which is constituted by a homeo tic gene and an automatically defined function.Besides,it proposes a novel inserting rule called NCR-ADF to keep population diversity.Based on our experimental results,initial central points exist a number of uncertain factors because of random selection.It will have a major influence on the results of clustering.By contrast,initial central points selected from trained data make the algorithm avoid plunging into local optimum,which can improve the stability of the traditional K-means algorithm.Then,the differential evolution algorithm has three important parameters including population size,the scaling factor and the crossover probability.In this paper,we present a self-adapting scaling factor and a combined crossover probability.The self-adapting scaling factor can control search step lengths of the algorithm and affect the optimal solution search and the population diversity.The combined crossover probability can influence the convergence speed and balance the global/local search ability of the differential evolution algorithm.Here,to choose more appropriate clustering central points for K-means clustering algorithm,we adopt the improved differential evolution algorithm.As a result,the accuracy of clustering has been significantly improved.Finally,the dynamic fitness landscape is firstly applied in analyzing the performance of the improved differential evolution(GDE)algorithm.Four analysis strategies including fitness distance correlation,ruggedness,dynamic severity and gradient measure,are introduced to collect and solve the relational values between fitness values and solutions.In this paper,in the process of calculating the optimal solutions of twelve selected representative test functions through GDE algorithm,some data would be produced,and then is collected and solved by the dynamic fitness landscape.Next,the two-dimensional chart is used to demonstrate the trend changes of experimental data.We analyze the trend changes of experimental data and illustrate reasonably the performance according to each analytical measure which can reflect different characteristics of the algorithm.At the same time,this study can enrich theoretical foundations of the differential evolution algorithm.