Improved Differential Evolution Algorithm And Its Convergence Analysis

Differential evolution algorithm(DE)is a swarm intelligent optimization algorithm,which has become a research hotspot in the area of intelligent algorithms for its strong searching ability and simplicity.However,DE also has such disadvantages as strong sensitivity to control parameters and mutation strategies and poor local search capability.A lot of improved DE algorithms have proposed for these disadvantages,but few researchers can improve it from the perspective of studying the convergence of DE algorithm.Therefore,based on the results of the convergence theory of DE algorithm,this article discusses the construction of an improved DE algorithm that can converge in probability.Below are main works for this article:1.In order to study whether the DE algorithm can converge to the ?-global optimal set of function in probability for the minimum optimization problem,this article gives DE algorithm steps in the discrete space rigorously in theory.Then the population sequence generated by the algorithm is proved to be a time homogeneous Markov chain by using stringent mathematical language.In the course of proof,for the first time,this article clarifies the conditional probability relationships among various steps of the algorithm and one-step transition probability of the population by using specific formulas.Finally,we prove that the DE algorithm cannot guarantee that the population sequence can converge to the ?-global optimal set of the function in probability.2.With respect to the insufficiencies existing in uniform sampling strategy and Gaussian sampling strategy which are frequently used to help DE algorithm convergence,this article proposes a novel diversity mutation search strategy that can assist the convergence of the DE algorithm.Two experiments show that with the strategy,DE has strong optimization performance in low-dimension complex optimization problems,but its convergence capability drops significantly for high-dimension problems.Hence,based on retaining the differential variation strategy of DE algorithm,an improved crossover strategy and mutation scaling factor self-adaptive strategy are used.And before the selection strategy,diversity mutation search strategy is added.According to the above,an improved differential evolution algorithm(DMSDE)based on diversity mutation random search is proposed.Moreover,we prove that the DMSDE algorithm can converge to ?-global optimal set in probability according to the stationary distribution theory of Markov chain.3.Under certain conditions,the proposed DMSDE algorithm is compared with DE algorithm and other four improved DE algorithms by solving the optimal solution of the selected 10 test functions and making the convergence curve of the algorithm on each function.The results show that DMSDE algorithm has higher accuracy and robustness,and faster convergence speed on the whole.Therefore,it can be seen that it is a noteworthy direction to improve DE algorithm by constructing the DE algorithm that can converge in probability.