Research On Adaptive Differential Evolution Algorithm Based On Auxiliary Function

Global optimization problems are widely used in common life. It is of great importance to need futher research on these problems. The challenge for global optimization problems is that the problems often have many local optimal solutions. The existing traditional methods show low efficiency in finding the global optimal solution. It is very necessary to study efficient intelligent algorithms. This paper focuses on differential evolution algorithms based on the auxiliary functions.The main work is as follows.1. The diversity of population decreases when differences between individuals decrease in the early stage of evolutionary process, which easily leads to premature convergence to a local optimum. In order to escape from local optima, a new adaptive Differential Evolution algorithm based on filled function is proposed in chapter 3. First, to increase the diversity of the initial population, a new initial method is proposed and it divides population into subpopulations. Second, an improved mutation operation is proposed. A new method to dynamically change scale factor is put forward, which uses the characteristics of the current population, and uses different mutation strategy on different subpopulations to estimate the performance of the algorithm SDEBF.Several experiments are conducted on some classical continuous and differentiable problems, and the results show that our method is efficient in solving these problems.2. A new adaptive differential evolution algorithm based on smoothing function named SDEBS is proposed. First, a smoothing function is used to eliminate local optimal solutions which are worse than the current best individual, with which the search speed is accelerated. Second, a new adaptive uniform crossover operator is designed, which can effectively maintain population diversity. Finally, a new hybrid selection operator is used to overcome the shortcomings of traditional selection operator. It produces individuals with high quality and improves the convergence speed in latter stage of the evolutionary process. To test the new algorithms, some numerical experiments are conducted and the results are compared with those of several existing algorithms. The results show that our new methods are stable and more efficient. In the end of the paper, some deficiencies of these two algorithms are summarized and the future work is outlined.