改进的灰狼优化算法及其高维函数和FCM优化

灰狼优化算法(GWO)具有较强的局部搜索能力和较快的收敛速度,但在解决高维和复杂的优化问题时存在全局搜索能力不足的问题.对此,提出一种改进的GWO,即新型反向学习和差分变异的GWO(ODGWO).首先,提出一种最优最差反向学习策略和一种动态随机差分变异算子,并将它们融入GWO中,以便增强全局搜索能力;然后,为了很好地平衡探索与开采能力以提升整体的优化性能,对算法前、后半搜索阶段分别采用单维操作和全维操作形成ODGWO;最后,将ODGWO用于高维函数和模糊C均值(FCM)聚类优化.实验结果表明,在许多高维Benchmark函数(30维、50维和1000维)优化上,ODGWO的搜索能力大幅度领先于GWO,与state-of-the-art优化算法相比,ODGWO具有更好的优化性能.在7个标准数据集的FCM聚类优化上, 与GWO、GWOepd和LGWO相比,ODGWO表现出了更好的聚类优化性能,可应用在更多的实际优化问题上.

Improved grey wolf optimizer and its application to high-dimensional function and FCM optimization

The grey wolf optimizer (GWO) algorithm proposed recently has strong local search ability and fast convergence, but it has some defects, such as poor global search ability in solving high-dimensional functions and complex optimization problems.Therefore, this paper proposes an improved GWO, namely GWO with opposition- learning and differential mutation (ODGWO). Firstly, a max-min opposition learning strategy and a dynamical and random differential mutation operator are proposed, which are integrated with GWO to enhance its global search ability. Then, in order to balance exploration and exploitation well to improve the overall performance, one-dimensional operation and full-dimensional operation are applied to the first half and the latter one of the search phase respectively to form the ODGWO consequently. Finally, the ODGWO is used for the high-dimensional function and fuzzy C-means (FCM) clustering optimization.The experimental results on many high-dimensional (30, 50 and 1000 dimension) benchmark functions show that the ODGWO has significantly higher global search ability than the GWO does, and the ODGWO outperforms the state-of-the-art algorithms.As for FCM optimization on seven standard datasets, the ODGWO shows better clustering optimization performance compared with the GWO, the GWOepd and the LGWO, and it will be applied to more real-world optimization problems.