基于多代种群进化信息改进的差分进化算法研究

An improved differential evolution algorithm based on multi-generation population evolution information

差分进化算法是进化算法中一种性能较为优良的全局数值优化算法,已在人工智能、信号处理等方面取得广泛应用,但当前研究往往仅考虑进化过程中某一代种群的分布信息,而忽略进化过程中多代种群累积的分布信息,造成信息利用不充分。借助自适应协方差矩阵进化策略的思想,充分利用进化过程中累积的种群分布信息,同时,由于自适应协方差矩阵存在收敛早熟、易陷入局部最优的缺点,先后对变异和交叉操作进行相应改进,以平衡算法的全局搜索能力和局部搜索能力。首先,根据种群中个体适应度值进行排序,由余弦函数改进的概率模型计算个体参与变异操作的概率,基向量和差分向量中末端向量根据概率值降序选择,差分向量中起始向量升序选择,从而提高种群的搜索范围;然后,对协方差矩阵进行特征分解,并在由特征向量构建的坐标系中执行交叉操作,该种方式生成的实验向量更接近全局最优解。针对上述改进操作,采用IEEE CEC2014作为评估函数,实验结果表明,相比现有的差分进化改进算法,本改进算法的实验性能提升更为明显。

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 gen eration and neglects the distribution information accumulated by the multi generation cumulative popula tion in the evolution process, thus the distribution information is not fully utilized. Inspired by covari ance 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 opera tion 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 probabili ty 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.