The firefly algorithm (FA) is one of the swarm intelligence algorithms which can solve global optimization problems accurately. In the traditional FA, the position of each firefly can only be updated by the brightness of other fireflies around it. As a result, it is simple to update the firefly position but easy to fall into local optimum. In this paper, a novel hybrid firefly algorithm based on the vector angle learning mechanism (HFA-VAL) is proposed, which can combine the advantages of both the firefly algorithm (FA) and differential evolution (DE) by the vector angle learning mechanism. HFA-VAL employs vector angle parameters to adaptively adjust the moving step length of firefly in order to avoid falling into local optimum. In the evolutionary process, the difference method is used to update the dominant leader, so as to improve the moving direction of other fireflies and expand the search ability. In order to understand the strengths and weaknesses of HFA-VAL, several experiments are carried out on 25 benchmark functions in CEC2005. Experimental results show that the performance of HFA-VAL algorithm is better than other the-state-of-art algorithms.

中文翻译：

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一种基于矢量角学习机制的新型混合萤火虫算法

萤火虫算法（FA）是一种能够准确解决全局优化问题的群体智能算法。在传统的 FA 中，每只萤火虫的位置只能通过它周围其他萤火虫的亮度来更新。因此，更新萤火虫位置很简单，但容易陷入局部最优。本文提出了一种新的基于矢量角学习机制的混合萤火虫算法（HFA-VAL），它通过矢量角学习机制结合了萤火虫算法（FA）和差分进化（DE）的优点。HFA-VAL采用矢量角参数自适应调整萤火虫的移动步长，以避免陷入局部最优。在进化过程中，采用差分法更新主导leader，从而改善其他萤火虫的移动方向，扩大搜索能力。为了了解 HFA-VAL 的优缺点，在 CEC2005 中对 25 个基准函数进行了多次实验。实验结果表明，HFA-VAL 算法的性能优于其他最先进的算法。