In many engineered and natural networked systems, there has been great interest in leader selection and/or edge assignment during the optimal design of controllable networks. In this paper, we present our pioneering work in leader–follower network design via memetic algorithms, which focuses on minimizing the number of leaders or the amount of control energy while ensuring network controllability. We consider three problems in this paper: (1) selecting the minimum number of leaders in a pre-defined network with guaranteed network controllability; (2) selecting the leaders in a pre-defined network with the minimum control energy; and (3) assigning edges (interactions) between nodes to form a controllable leader–follower network with the minimum control energy. The proposed framework can be applied in designing signed, unsigned, directed, or undirected networks. It should be noted that this work is the first to apply memetic algorithms in the design of controllable networks. We chose memetic algorithms because they have been shown to be more efficient and more effective than the standard genetic algorithms in solving some optimization problems. Our simulation results provide an additional demonstration of their efficiency and effectiveness.

中文翻译：

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通过模因算法设计可控的领导者-跟随者网络

在许多工程和自然网络系统中，在可控网络的优化设计过程中，人们对领导者选择和/或边缘分配产生了极大的兴趣。在本文中，我们通过模因算法展示了我们在领导者 - 追随者网络设计方面的开创性工作，其重点是在确保网络可控性的同时最大限度地减少领导者的数量或控制能量的数量。我们在本文中考虑三个问题：（1）在保证网络可控性的预定义网络中选择最小数量的领导者；(2) 在一个预定义的网络中选择具有最小控制能量的领导者；（3）在节点之间分配边（交互），形成一个控制能量最小的可控领导者-跟随者网络。所提出的框架可以应用于设计有符号、无符号、有向、或无向网络。应该注意的是，这项工作是第一个将模因算法应用于可控网络设计的工作。我们选择了模因算法，因为它们已被证明在解决一些优化问题方面比标准遗传算法更有效。我们的模拟结果进一步证明了它们的效率和有效性。