一种交互演化改进鲸鱼算法及其收敛性分析

针对鲸鱼算法求解稳定性不强、收敛速度有时较慢、易陷入局部极值等缺点,提出一种具有轮盘赌选择和二次插值择优机制的双种群交互演化鲸鱼算法.首先,在搜索觅食阶段引入轮盘赌选择机制,可有效避免劣质解被多次选取的问题,保证算法的收敛性能;在算法进化结构和求解过程中用两种不同演化机制的种群以及它们之间不断的信息交互,可有效地平衡和调节算法的全局搜索与局部搜索能力;在双种群个体演化更新后、信息交互前,利用二次插值策略更新鲸鱼个体的位置,增加种群的多样性,而之后的择优选取新位置可提高算法的收敛速度.然后,给出算法流程并用概率测度法对算法的收敛性进行证明.最后,通过6种代表性算法对CEC2017测试函数集套件中不同特征函数在多个维度上进行仿真实验,结果表明改进算法的收敛速度、寻优精度和求解稳定性均有明显提高,具有很好的收敛性能.

An interactive evolutionary improved whale algorithm and its convergence analysis

Aiming at the disadvantages of the whale algorithm, such as poor stability, slow convergence speed and easy to fall into local extremum, a two-population interactive evolutionary whale algorithm with roulette selection and the quadratic interpolation mechanism is proposed. The roulette selection mechanism is introduced in the searching and foraging stage, which effectively avoids the problem that the poor solution is selected several times and ensures the convergence performance of the algorithm. In the evolutionary structure and solution process of the algorithm, the population of two different evolutionary mechanisms and the continuous information interaction between them are used to balance and adjust the global search and local search ability of the algorithm effectively. The quadratic interpolation strategy is used to update the position of the whale individuals after the evolution update of the two populations and before the information exchange, which increases the diversity of the population, and then the optimal selection of new positions improves the convergence rate of the algorithm. Then the algorithm flow is given and the convergence of the algorithm is proved using the probability measure method. Finally, six representative algorithms are used to simulate different characteristic functions in the CEC2017 test function suite in multiple dimensions. The results show that the improved algorithm has better convergence speed, optimization precision and solution stability, and has good convergence performance.