The Theoretical Researches And Algorithmic Design Of Convergent Differential Evolution Algorithm In Probability

Differential evolution algorithm (DE), proposed in1995, is a new evolutionalgorithm with simple operation, few parameters, and strong robustness. During thenearly past20years, many researches demonstrated that it has become one of themost popular and effective evolution algorithms.Comparing to the application researches, the theoretical researches, especiallythe convergence researches, on DE algorithm made slower progress. Fewconvergence DE algorithms in probability have been proposed. Although thesealgorithms are more effective in theory, the imbalance between exploration abilityand exploitation ability reduce their efficiency in practice. In order to overcomethese shortcomings, this dissertation focuses on researching theoretical theconvergence of DE algorithm and designing convergence DE algorithm. As followsare the idiographic works:(1) Analyze the previous conclusions about the global convergence of the basicDE algorithm. Based on the Markov chain model and random drift model, it isproved that the basic DE algorithm could not guarantee its global convergence inprobability.(2) For the functions with global optimal points near to its solution spaceboundary and a large measure deceptive optimal solution set, it is proved that thebasic DE algorithm could not converge to the global optimum in probability.(3) Prove that the improved DE algorithm could converge in probability if theimproved reproduction operator makes the probability of the individuals in asub-sequence population locating the global optimal solution set be large enough.According to this conclusion, a global convergence DE model is presented. And it isproved that under the DE model, some common evolution operators, such as uniformmutation and Gauss mutation, could assist the DE algorithm to converge inprobability theoretically.(4) A mutation operator, called subspace cluster operator, is designed to assistthe DE algorithm to convergent. The operator selects randomly a quality individual from the DE population as a center of disturbance. The upper bound of thisdisturbance is the difference of two randomly selected bound individuals, and theradius of this disturbance is the product of the upper bound and a random realnumber on [0,1]. The probabilistic and statistical analyses show that under thebalance between exploration ability and exploitation ability, the operator prefers tosearch on the subspace with an excellent individual as its center. Under the aboveDE model, combing the subspace cluster operator and5common DE mutationoperators, some comparative experiments on the CEC2005standard test functionsare performed. And the statistical analyses of the experimental results demonstratethat the subspace cluster operator could improve the DE algorithms with the5common mutation operators.（5） Design a class of convergent DE algorithm for the parameter‘soptimization of a coil compression spring. The class of convergent DE algorithm isbased on the subspace cluster DE algorithm proposed above. Numerical experimentsare implemented to indicate the algorithmic competitiveness.Based on the class of typical functions, this dissertation proves that the basicDE algorithm could not guarantee global convergence in probability. Then asufficient condition is presented to judge the convergence in probability of animproved DE algorithm. And a global convergence DE model satisfying thissufficient condition is designed. In turn, a mutation operator satisfying theconvergence DE model, called a subspace cluster operator, is developed. Under theconvergence DE model, a kind of convergent DE algorithms with high efficiency areobtained by combining the subspace cluster operator and some different DEversions.