自适应学习集成优化算法及矩阵特征值求解

Self-Adaptive Learning Based Ensemble Algorithm for Solving Matrix Eigenvalues

为了增强数值优化算法的高效性和鲁棒性,提出一种基于自适应学习的集成算法(self-adaptive-learning-based ensemble algorithm,SALBEA).在SALBEA中,采用贪婪繁殖算子、进化搜索策略学习算子、X进化算子、种群多样性维持算子改进算法进化结构.此外,SALBEA通过引入概率选择模型和自适应学习机制集成了4种有效的进化搜索策略.首先,为了评估所提算法的性能,采用26个测试函数进行算法对比测试,实验结果表明SALBEA比同类算法具有更好的高效性和鲁棒性.最终,将SALBEA用于求解矩阵特征值这一数值计算问题,结果表明该算法求解精度较高,具有较好的应用前景.

In order to enhance the performance of numerical optimization algorithm, a self-adaptive- learnings-based ensemble algorithm （SALBEA） is proposed. In the SALBEA, greedy breeding operator, X-evolution operator, population diversity maintaining operator and evolution strategy learning operator are designed to enhance the evolution structure. Besides, a probability model and a self-adaptive learning mechanism are employed to integrate four effective search strategies. Firstly, in order to evaluate the performance of SALBEA, 26 state-of-the-art test functions are solved by the SALBEA and its competitors, and experimental results indicate that the effectiveness and robustness of the SALBEA outperform its competitors. Then, the SALBEA is employed to solve matrix eigenvalue problem. Experimental results show that the precision of the solutions is very high and SALBEA is a promising algorithm in real-world application.