Multi-stage Self-adapting Differential Evolution Algorithm And Its Application

Differential evolution (DE) algorithm has demonstrated a reliable, accurate, robust and fast evolutionary algorithm and successful applied in many real-world areas. However, DE has shown some weaknesses, especially DE in solving complex functions with high dimensions has shown some weaknesses, such as low convergence speed, premature convergence and low precision. With an eye to improve the performance of DE, it is necessary to depend upon appropriately choosing control parameters. In view of this problem dependency, a novel self-adapting differential evolution algorithm with piecewise operators is proposed. Operators are respectively self-adapted based on Cauchy or normal distribution random number, and dynamically generate these control parameters in this algorithm. The evolution process is divided into two stages, different configuration parameters are used to generate amplification factors and crossover probability by respective operators (or to choose suitable crossover probability) at each stage. At the same time, to enhance the convergent speed, a new mutation strategy is introduced to guide searching direction. Benchmark problems are used to verify this algorithm and the result of simulation indicated that has improved significantly both in convergence speed and precision of optimization.In this study, differential evolutionary computing and its application are focused on. Some novel self-adaptive algorithms are proposed based on multi-stage and traditional differential evolution. To repair deficiencies, such as problem dependency, low precision in solving complex functions with high dimensions and easily trapped into a local optimum, segmental wave and piecewise crossover algorithms are proposed. In order to improve the practicality of the algorithm, a solution to deal with the constrained optimization problems is also provided.The proposed algorithms finally apply in the fields such as transportation problems, quadratic programs, blocking flow shop scheduling and clustering problems. More details are given as follow:(1) In solving a specific problem crucially depends on appropriately choosing control parameters, a novel two-stage differential evolution strategy is proposed.(2) In solving complex functions with high dimensions has shown low precision, a new self-adapting differential evolution algorithm with segmental crossover is proposed. So crossover probability is sensitive to the optimization problem, self-adaptive control factors are obtained to improve the algorithm in high dimensional accuracy of the optimization problem.(3) At the same time, to enhance the local convergent speed, the optimal function fitness value of randomly selected vectors provides information of progress direction as the base mutation strategy in these new algorithms.(4) There are the majority constrained problems in specific applications fields, a constraint handling mechanism is provided to be compatible with the new algorithms.(5) This paper presents a novel two-stages discrete differential evolution applied to solve the blocking flow shop scheduling problems. (6) The new DE can be used to find the optimization effectively, so a novel clustering algorithm by using of multi-stage differential evolution algorithm is employed to improve the accuracy and quality of clustering.Finally, a summary of the thesis is made, and the deficiency of the study and the further development are narrated respectively.