Research On Evolution Model Analysis And Algorithm Improvement For Differential Evolution Algorithm

Differential evolution algorithm (DE) is a heuristic search algorithm based on the principle of biological evolution, which is also an outstanding representative of various intelligent algorithms. Over the past 10 years, the DE algorithm has developed rapidly and been widely used. Compared with other intelligent algorithms, the DE algorithm has the advantages of simple implementation, fast convergence speed and strong robustness. Therefore, the DE algorithm has been favored by many researchers. At present, the DE algorithm is extensively used to solve various kinds of complex optimization problems, and many practical applications such as engineering design, industrial production, management scheduling and so on.DE still has many unsolved problems at the present. First, the theoretical study of DE is still relatively weak. Compared with some similar algorithms such as genetic algorithm (GA) or evolutionary strategy (ES), the theoretical analysis of DE is not sufficient, and its complex optimizing code has not been cracked. Second, the new application is endless, and each problem has its own characteristics. In order to get better results and performance, we often need to do some work to DE in solving these problems. At present, improving DE based on the existing parameters and operators, or introducing some external optimization mechanisms or algorithms, have become a significant method by many scholars. The main research contents of this dissertation are as follows:(1) Researching on the evolution process of DE algorithm and its searching mechanism. The basic numerical characteristics of DE population and evolution operations are analyzed, also, the function of various DE operations and the influence of the control parameters on the evolution performance are analyzed. In the study of the numerical characteristics of the evolutionary population of adjacent generations, it is found that the differential operation has the intrinsic ability to expand search area. Moreover, crossover rate parameter not only affects the composition of the trial vector, but also can adjust the convergence rate of the algorithm. In addition, a simple evolutionary computation model is constructed based on the numerical features of the mutation and crossover operators. The research also shows that the operations and control parameters of DE algorithm are not isolated, and their influence on the various optimization features of DE algorithm is intertwined with each other.(2) Using opposition-based DE algorithm to solve the parameter identification problems. Due to the inverse problem of parameter identification for hyperbolic partial differential equation is very ill-posed. Thus, a new regularization method which is combined with Tikhonov regularization and total variation regularization is introduced to form a new fitness function of DE. In addition, the generalized opposition-based learning mechanism and smoothing operator are also integrated into DE algorithm to improve its performance and convergence rate.(3) Proposing two adaptive algorithm performance enchancement mechanisms. The first is an adaptive opposition-based learning mechanism, which uses the successful rate of opposition operations in a certain period to adjust dynamically the parameter of opposition probability, and then controlls the opposition operations in subsequent evolution, so as to improve the performance of DE. The second one is a dynamic population mechanism, which introduces a boundary function of population size according to the experimental experience, and the actual population size can be dynamically adjusted according to the evolutionary effect. If the best individual of evolution is updated quickly, the individuals will be reduced to speed up the convergence rate; whereas, the population diversity will be enhanced by increasing some individuals.(4) Introducing a rotation-based learning mechanism. The new mechanism can search any point in the rotation space by specifying different rotation angles, which can effectively improve the search ability compared to the opposition-based learning. The simulation shows that the rotation-based learning mechanism is a kind of nonlinear search method, and different rotation angles have different search features. By adjusting the rotation angle, the mechanism has various application modes.(5) Proposing a rotation-based DE algorithm. An application mode of the rotation-based learning mechanism is embeded into DE algorithm to enhance its searching ability. Moreover, an adaptive mechanism is used to simplify the parameter control and improve the robustness of the new algorithm. The analysis shows that the new algorithm can achieve better performance without increasing the computational time complexity of DE algorithm. According to the sufficient condition of convergence in probability of DE algorithm, it is proved that the new rotation-based DE algorithm is also convergent in probability.In short, the evolution principle of DE algorithm is researched in this dissertation, and some corresponding improvement measures are put forward to enhance the performance of DE, which include the adaptive opposition-based learning mechanism, the dynamic population mechanism and the rotation-based learning mechanism. Through the combination of these mechanisms and the DE algorithm, some new algorithms are proposed to solve some optimization problems and the effectiveness of the proposed mechanisms and algorithms are verified by some numerical experiments.