基于中心点双阈值模糊子群的混合蛙跳算法

摘要

To overcome the demerits of basic shuffled frog leaping algorithm( SFLA) , such as low optimization precision and falling into local optimum easily, a shuffled frog leaping algorithm based on central point double thresholds and fuzzy subgroups( CDTFSFLA) is proposed. The distance between frogs and central point in one subgroup is computed to measure compactness degree by selecting the central point randomly in each subgroup. The absolute threshold and the relative threshold of each subgroup are computed by the optimization method, and a strategy of fuzzy grouping with central point double thresholds and fuzzy subgroups is proposed to partition frogs into different fuzzy subgroups. In every local search, the update method of the worst individual in subgroups is improved according to the relation among central point membership, absolute threshold and relative threshold. The simulation results show that the proposed strategy and the update method are effective and feasible. CDTFSFLA can effectively improve convergence speed and precision in the optimization of unimodal and multimodal functions with fixed parameters, and it can maintain optimal performance under the condition of high dimensions, especially under the fitting condition that the number of neighborhood frogs is between 30 and 40 with dynamic parameters. The proposed algorithm improves the optimization performance of basic shuffled frog leaping algorithm effectively.%针对基本混合蛙跳算法寻优精度不高和易陷入局部最优的缺陷，提出一种基于中心点双阈值模糊子群的混合蛙跳算法。通过随机方式选择各子群中心点，利用青蛙到各子群中心点的距离度量子群内青蛙的紧密程度。用优化方法计算各子群的绝对阈值和相对阈值，提出中心点双阈值模糊子群划分策略对青蛙群体划分子群。在一次局部搜索中，依据中心点隶属度与绝对阈值、相对阈值之间关系对子群最差个体更新方法进行改进。仿真结果表明，中心点双阈值模糊子群划分策略和子群最差个体更新方法有效可行。固定参数时算法在单峰值和多峰值函数寻优问题上收敛速度和精度均有显著提高，变化参数时算法在高维函数上保持较好的优化性能，在适宜的邻近青蛙个数条件下优化性能最优。