Abstract:

The differential evolution algorithm is one of the global numerical optimized algorithms with excellent performance, and it has been widely applied in artificial intelligence, signal processing and so on. However, the current research takes into account the population distribution information of  generation and neglects the distribution information accumulated by the multigeneration cumulative population in the evolution process, thus the distribution information is not fully utilized. Inspired by  covariance matrix adaption evolutionary strategy(CMAES), we propose a new method that can make full use of the accumulated population distribution information in the evolution process. As the CMA tends to premature converge and falls into local optimum, the proposed method improve the mutation operation and cross operation to balance global and local search capability. Firstly, we sort the vectors according to their fitness value, and calculate the probability of individual vector participating in mutation operation based on the probability model improved by cosine function. To improve the global search ability, the proposed method selects the base vectors and the end vectors of difference vectors by their probability value in descending order, and the initial vectors of difference vector are selected in ascending order. Then, we establish the new coordinate system by eigenvectors which are generated from the decomposition of the covariance matrix. Executing crossover operation in the new coordinate system makes the trial vector closer to the global optimum than the traditional way. Experimental results show that, the proposed algorithm outperforms the existing improved algorithms on test function IEEE CEC2014.

Key words: differential evolution algorithm, sorting algorithm, matrix decomposition,
cumulative multigeneration population distribution information