Abstract: In order to solve the problem of premature convergence caused by the decrease of population diversity in the optimization process of Krill Herd (KH) algorithm, an improved krill herd algorithm based on Generalized Opposition-Based Learning was proposed, namely GOBL-KH. Firstly, step size factors were determined by cosine decreasing strategy to balance the exploration and exploitation ability of the algorithm. Then, a generalized opposition-based learning strategy was added to search each krill, which enhanced the ability of the krill to explore the neighborhood space around it. The proposed algorithm was tested on fifteen benchmark functions and compared with the original KH algorithm, KH with Linear Decreasing step (KHLD) and KH with Cosiner Decreasing step (KHCD). The experimental results show that the proposed algorithm can effectively avoid premature and has higher accuracy. In order to demonstrate the effectiveness of the proposed algorithm, it was combined with K-means algorithm to solve the data clustering problem, namely HK-KH. In this fusion algorithm, after each iteration, the worst individual was replaced by the optimal individual or a new individual after the K-means iteration. Five datasets of UCI were used to test HK-KH algorithm and the results were compared with the K-means, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), KH, KH Clustering Algorithm (KHCA), Improved KH (IKH) algorithm for clustering problems. The experimental results show that HK-KH algorithm is suitable to solve the data clustering problem and has strong global convergence and high stability.

Key words: Krill Herd (KH) algorithm, cosine decreasing strategy, generalized opposition-based learning, data clustering, K-means clustering algorithm

摘要： 针对磷虾群（KH）算法在寻优过程中因种群多样性降低而过早收敛的问题，提出基于广义反向学习的磷虾群算法GOBL-KH。首先，通过余弦递减策略确定步长因子平衡算法的探索与开发能力；然后，加入广义反向学习策略对每个磷虾进行广义反向搜索，增强磷虾探索其周围邻域空间的能力。将改进的算法在15个经典测试函数上进行测试并与KH算法、步长线性递减的磷虾群（KHLD）算法和余弦递减步长的磷虾群（KHCD）算法比较，实验结果表明:GOBL-KH算法可有效避免早熟且具有较高的求解精度。为体现算法有效性，将GOBL-KH算法与K均值算法结合提出HK-KH算法用于解决数据聚类问题，即在每次迭代后用最优个体或经过K均值迭代一次后的新个体替换最差个体，使用UCI五个真实数据集进行测试并与K均值、遗传算法（GA）、粒子群优化（PSO）算法、蚁群算法（ACO）、KH算法、磷虾群聚类算法（KHCA）、改进磷虾群（IKH）算法进行比较，结果表明:HK-KH算法适用于解决数据聚类问题且具有较强的全局收敛性和较高的稳定性。

关键词: 磷虾群算法, 余弦递减策略, 广义反向学习, 数据聚类, K均值聚类算法