摘要:复杂的单目标优化问题是进化计算领域的一个研究热点问题，已有差分进化和协方差进化被认为是处理该问题的较有效方法，其中，差分信息类似于梯度可以有效地指导算法朝着最优解方向搜索，而协方差则是基于统计的方式来生成较优的子代种群.引入了协方差信息对差分算子进行改进，提出了一种基于邻域差分和协方差信息的进化算法（DEA/NC）来处理复杂的单目标优化问题.算法对现有差分算子中通常采用的随机选点或结合当前最优解进行差分的方式进行了分析：当随机选择的差分个体间的差异较大时，差分信息不能作为一种局部的梯度信息来指导算法的搜索；而结合最优解的差分信息又会使得种群朝着当前最优解的方向搜索，导致种群快速地陷入局部最优.基于此，采用了邻域差分的方式来提高差分算子的有效性，同时避免种群的多样性丢失.另外，引入了协方差来度量个体变量间的相关度，并利用相关度来优化差分算子.最后，算法对cec2014中的单目标优化问题进行了测试，并将实验结果与已有较好的差分进化算法进行了比较，实验结果表明了该算法的有效性.



Abstract:Complex single-objective optimization problem is a hot topic in the field of evolutionary computation. Differential evolution and covariance evolution are considered to be two of the most effective algorithms for this problem, as the difference information similar to the gradient can effectively guide the algorithm towards the optimal solution direction, and the covariance is based on statistics to generate an offspring population. In this paper, the covariance information is introduced to improve the difference operator, then an evolutionary algorithm based on neighborhood difference and covariance information (DEA/NC) is proposed to deal with complex single-objective optimization problem. The two commonly used difference operators generated by random selection individuals and combined by the current optimal solution are analyzed. With the first approach, the difference information cannot be used as a local gradient information to guide the search of the algorithm when the Euclidean distance between randomly selected individuals is large. Meanwhile, the second approach will make the population search in the direction of the current optimal solution, which will lead the population to quickly fall into local optimum. In this paper, a neighborhood difference method is proposed to improve the effectiveness of the differential operator while avoiding the diversity of population loss. In addition, a covariance is introduced to measure the correlation between individual variables, and the correlation is used to optimize the difference operator. Finally, the algorithm tests the single-objective optimization problem in cec2014, and compares the results with the existing differential evolution algorithms. The experimental results show the effectiveness of the proposed algorithm.



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