The Research And Applications Of Differential Evolution Algorithm

This paper firstly introduced the important impact of intelligent optimization algorithms for modern optimization technique. And then, the necessary of the research and development of intelligent optimization technique for modern optimization technique and real engineer application is expatiated. Lastly, the characteristics of intelligent optimization algorithms are induced, and the application areaes of intelligent optimization algorithms are introduced briefly.The differential evolution algorithm (DE) is introduced in detail, and the pseudocode of DE is given. Aiming to the characteristics of mixed-integer nonlinear programming (MINP), a rounding operation was added to the mutation operator, and a modified differential evolution (MDE) algorithm fitted to the MINP is proposed. At the same time, the method of time-varying crossover probability factor was adopted to improve the global searching ability and convergence speed of MDE. The experiments researching were done by four classic testing functions. The experiment results show that the MDE has fast convergence speed, high precision and good robustness for solving MINP.Using non-stationary multi-stage assignment penalty function to deal with the constrained conditions, a modified differential evolution (MDE) for nonlinear constrained optimization is proposed. In order to improve global convergence and convergence speed of the algorithm, two different mutation scheme of DE were combined, and simulation anneal tactics was adapted, which ensure the algorithm has good global exploring ability at the beginning stage and good local exploring ability at the last stage. Several classic Benchmarks functions were tested, the experiment results show that the MDE has powerful global exploring ability, good robustness, high precision, and fast convergence speed. So it is an effective way for nonlinear constrained optimization problems.In order to preserve the diversity of Pareto optimality of multi-objective optimization problems (MOP), a differential evolution algorithm for MOP adopting elitist archive and sorting tactic based on objective function value is presented. The selection methods to the objective function in the sorting tactic were analyzed and compared. And the same time, a threshold determining way was proposed to decide whether a elitist solve found in the evolutionary process added to the Pareto set or not. The experiments were done using several classic test functions, and the comparisons were done with NSGA-Ⅱ. The experiment results show that, the proposed approach can convergence to the Pareto front and preserve the diversity of Pareto optimality efficiently, the obtained optimality has wider bound. A new adaptive second mutation differential evolution algorithm (ASMDE) based on the variance of the population's fitness is presented. In order to improve the population's diversity and the ability of breaking away from the local optimum, according to the value of the variance of the population's fitness during the running time, a new mutation operator is adapted to mutate both the best individual and partial other individuals. Several classic Benchmarks functions are tested, the results show that the new algorithm can avoid the premature convergence and improve the global convergence ability greatly. The proposed ASMDE was applied to optimize parameters of PID controller with incomplete derivation. To overcome the disadvantages of the integral performance criteria in the frequency domain such as IAE, ISE, and ITSE, a new performance criterion in the time domain was proposed. Three typical control systems were chosen to test and evaluate the adaptation and robustness of the proposed DE-PID controller. The simulation results show that the proposed approach had superior features, including easy implementation, stable convergence characteristic and good computational efficiency. Compared with the ZN, GA, and ASA, the proposed design method was indeed more efficient and robust in improving the step response of a control system.To improve the global searching ability and convergence speed of DE, a pseudo parallel differential evolution algorithm with dual subpopulations (DSPPDE) is proposed. Combining with the properties of good local searching ability and fast convergence speed of DE/best/2/bin mutation scheme and the properties of good global searching ability and robustness of DE/rand/1/bin mutation scheme, the algorithm applied the ideal of isolated evolution and information exchanging in parallel DE algorithm by serial program structure. To diversify the initial individuals in the search space and improve the robustness of convergence to the global optimum, an initialization tactic based on the mean entropy is proposed. The tests of several classic Benchmarks function and the parameters estimation result of a nonlinear system model show that the proposed algorithm can improve the convergence speed and the global searching ability greatly.Control parameters of original DE are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE for different optimization problems. According to relative position of the two different individual vectors selected to generate a difference vector in the searching place, a self-adapting strategy for the amplification factor F of the difference vector is proposed. In term of the convergence status of target vector, a self-adapting crossover probability constant CR strategy is proposed. Therefore, good target vectors have lower CR while worse target vectors have large CR. And the same time, the mutation operation was modified to improve the convergence speed. The performance of these proposed approaches are studied with the use of some benchmark problems and applied to trajectory planning of a three-joint redundant manipulator. The experiment results show that the proposed approaches can improve robustness and convergence speed greatly.