基于协方差矩阵特征值和特征向量的差分进化算法改进研究

Research on Improvement of Differential Evolution Algorithm Based on Eigenvalues and Eigenvectors of Covariance Matrix

摘要: 差分进化算法是一种具有性能强、简单易用和自适应能力强等优点的全局优化算法，但同时也存在早熟收敛问题和搜索停滞问题，因此本文的研究目的在于研究协方差矩阵的特征值和特征向量对差分进化算法搜索性能的影响，探究特征值和特征向量以何种改进策略能够提高算法搜索性能，这对算法适应更为复杂的优化问题和满足更高的求解质量有非常重要的研究意义。本文使用协方差矩阵的特征值和特征向量改进差分进化算法中初始种群和变异个体的计算规则，通过仿真实验证明，特征值按照本文的改进策略未能提高差分进化算法的搜索性能，而特征向量在一定的种群进化代数内能够正确的引导差分进化算法进行搜索，并有效提高算法搜索性能。

Abstract: The differential evolution algorithm is a global optimization algorithm with strong performance, easy to use and strong adaptability. However, there are also premature convergence problems and search stagnation problems. Therefore, the research of this paper aims to study the influence of the eigenvalues and eigenvectors of the covariance matrix on the search performance of the differential evolution algorithm, and to explore how the improved strategies of eigenvalues and eigenvectors can improve the search performance of the algorithm, which is of great significance for the algorithm to adapt to more complex optimization problems and satisfy higher quality of solution. In this paper, the eigenvalues and eigenvectors of the covariance matrix are used to improve the calculation rules of the initial population and the mutated individual in the differential evolution algorithm. The experimental results show that eigenvalues according to the improved strategy of this paper cannot improve the search performance of the algorithm, and the eigenvectors can correctly guide the differential evolution algorithm in a certain population evolution algebra, and effectively improve the search performance of the algorithm.