基于核模糊聚类的动态多子群协作骨干粒子群优化

针对骨干粒子群优化（BBPSO）算法易陷入局部最优、收敛速度低等问题，提出了基于核模糊聚类的动态多子群协作骨干粒子群优化（KFC-MSBPSO）算法。该算法在标准骨干粒子群算法的基础上，首先，采用核模糊聚类方法将主群分割为多个子群，令各个子群协同寻优，提高了算法的搜索效率。然后，引入非线性动态变异因子，根据子群内粒子数以及收敛情况动态调节子群粒子变异概率，通过变异的方式使子群粒子重新回到主群，提高了算法的探索能力；进一步采用主群粒子吸收策略与子群合并策略加强了主群与子群之间、子群与子群之间的信息交流，提高了算法的稳定性。最后，利用子群重建策略，结合主群与子群搜索到的最优解，调节子群重建的间隔代数。通过Sphere等6个标准测试函数进行对比实验，结果表明，KFC-MSBPSO算法和经典BBPSO算法以及反向骨干粒子群优化（OBBPSO）算法等改进算法相比寻优准确率至少提高了约11.1%，在高维解空间内测试结果的最佳均值占到83.33%并且具有更高的收敛速度。这说明KFC-MSBPSO算法具有良好的搜索性能与鲁棒性，可应用于高维复杂函数的优化问题中。

Dynamic multi-subgroup collaborative barebones particle swarm optimization based on kernel fuzzy clustering

To solve problems such as easily getting trapped in local optimum and slow convergence rate in BareBones Particle Swarm Optimization (BBPSO) algorithm, a dynamic Multi-Subgroup collaboration Barebones Particle Swarm Optimization based on Kernel Fuzzy Clustering (KFC-MSBPSO) was proposed. Based on the standard BBPSO algorithm, firstly, kernel fuzzy clustering method was used to divide the main group into several subgroups, and the subgroups optimized collaboratively to improve the searching efficiency. Then, nonlinear dynamic mutation factor was introduced to control subgroup mutation probabilities according to the number of particles and convergence conditions, the main group was reconstructed by means of particle mutation and the exploration ability was improved. The main group particle absorption strategy and subgroup merge strategy were proposed to strengthen the information exchange between main group and subgroups and enhanced the stability of the algorithm. Finally, the subgroup reconstruction strategy was used to adjust the iterations of subgroup reconstruction by combining the optimal solutions. The results of experiments on six benchmark functions, such as Sphere, show that the accuracy of KFC-MSBPSO algorithm has improved by at least 11.1% compared with classical BBPSO algorithm, Opposition-Based Barebones Particle Swarm Optimization (OBBPSO) algorithm and other improved algorithms. The best mean value in high dimensional space accounts for 83.33% and has a faster convergence rate. This indicates that KFC-MSBPSO algorithm has good search performance and robustness, which can be applied to the optimization of high dimensional complex functions.