Improved Differential Evolution Algorithm Research And Its Application

All the time, constrained optimization problems are the topic which the numerous scholars study unceasingly. At first, scholars have achieved good results by use analytical and numerical methods to solve the optimization problem. However, with the problem to constantly change, lots of constrained optimization problems have the characteristics of non-linear, non-continuous, multi-modal and non-differentiability. It makes traditional optimization methods are hard to solve or failure, so the scholars are dedicated to finding better algorithms for solving constrained optimization problems.Differential evolution algorithm is one of the best in the heuristic algorithm and entered the research scope of many scholars quickly. And a lot of excellent improved algorithms are put forward for solving constrained optimization problems.The three control parameters of differential evolution algorithm are population size NP,crossover probability CR and mutation factor F. The three evolutionary operation of differential evolution algorithm are crossover, variation and selection. Differential evolution algorithm has two shortcomings in the solving process, one is sensitive to the setting of the control parameters and the other one is the choice of evolutionary operation. In order to improve the shortcomings of evolutionary algorithm, this paper proposed two types of improved differential evolution algorithm. It proposed a novel difference evolutionary algorithm based on JADE for constrained optimization(CO-JADE) which combined with ZJADE algorithm and archiving-based adaptive tradeoff model in third chapter. The fourth chapter proposed a novel differential evolution algorithm based on simplex-orthogonal experimental design(SO-DE). SO-DE proposed simplex-orthogonal crossover which combined with simplex crossover and orthogonal experimental design technique and a improved individual comparison criterion which improved archiving-based adaptivetradeoff model. Using benchmark test functions collected for the special session on constrained real-parameter optimization of IEEE CEC2006 to test the performance of CO-JADE and SO-DE. Experimental data show that the CO-JADE algorithm and SO-DE algorithm have excellent performance and robustness.The main achievements and innovations of this paper are as follows:(1) It proposed an improved comparison criterion of individual for the weight relation between the objective function value and the constraint violation degree in the constraint optimization problem. The criterion considered population individuals during the evolution process presented three different situations to using different treatment methods. It mainly considered the range of the objective function value and the constraint violation degree, and transforms the objective function value and the constraint violation degree to a normalized fitness value. Then, select the individual to enter the next generation population according to the normalized fitness value, complete the selection operation of differential evolution algorithm.(2) Simplex crossover has the characteristics of uniform distribution to produce the offspring individuals and invariant mean of the offspring individual. The orthogonal experimental design has the characteristics of uniformly distribution, fewer experiments and neat. It proposed simplex-orthogonal crossover which combining the simplex crossover and the multi-parent orthogonal crossover. The single-orthogonal crossover has the characteristics of uniform distribution of the simplex crossover and also has the representation and high efficiency of the orthogonal experimental design. It makes the simplex-orthogonal crossover has a good search ability.(3) Combined improved adaptive differential evolution algorithm and archiving-based adaptive tradeoff model to solve the constrained optimization problem. Improved adaptive differential evolution algorithm can adaptive selection of different mutation factor F and crossover probability CR according the change of the evolution state. At the same time, it use archiving-based adaptive tradeoff model to deal with the objective function value and the constraint violation degree and select individuals into the next generation. Experiments show that the algorithm has better searching ability, higher accuracy and better robustness.