Abstract

In the presented paper, the functioning and the results of the work of two metaheuristic algorithms, namely cuckoo search algorithm (CS) and firefly algorithm (FA), are described using the apparatus of generalized nets (GNs), which is an appropriate and efficient tool for describing the essence of various optimization methods. The two developed GN-models mimic the optimization processes based on the nature of cuckoos and fireflies, respectively. The proposed GN-models execute the two considered metaheuristic algorithms conducting basic steps and performing optimal search. Building upon these two GN-models, a universal GN-model is constructed that can be used for describing and simulating both the CS and the FA by setting different characteristic functions of the GN-tokens. Moreover, the universal GN-model itself can be transformed to each of the herewith presented GN-models by applying appropriate hierarchical operators. In order to validate the proposed universal GN-model, numerical experiments are performed for the operating of the universal GN-model (CS and FA) on benchmark mathematical functions. The obtained results are compared with the results of the GN-model of CS, GN-model of FA, as well as the results of the standard CS and FA.

中文翻译：

---

基于广义网络理论的布谷鸟搜索和萤火虫算法

摘要

在本文中，使用通用网络（GNs）的设备描述了布谷鸟搜索算法（CS）和萤火虫算法（FA）这两种元启发式算法的功能和工作结果，这是一种适当而有效的方法描述各种优化方法本质的工具。这两个已开发的GN模型分别根据杜鹃和萤火虫的性质模拟了优化过程。拟议的GN模型执行两种基本的启发式算法，进行基本步骤并执行最佳搜索。在这两个GN模型的基础上，构建了通用GN模型，该通用GN模型可通过设置GN令牌的不同特征函数来描述和模拟CS和FA。而且，通用通过应用适当的层次运算符，可以将GN模型本身转换为本文提出的GN模型。为了验证所提出的通用GN模型，针对通用GN模型（CS和FA）在基准数学函数上的运行进行了数值实验。将获得的结果与CS的GN模型，FA的GN模型以及标准CS和FA的结果进行比较。