Optimizing the controllability of arbitrary networks with genetic algorithm

• The problem of optimizing controllability of arbitrary networks is studied.
• An efficient genetic algorithm oriented controllability optimization framework is proposed.
• The evolution of network topology is captured.
• How a network’s structure affects its controllability is explored.

Recently, as the controllability of complex networks attracts much attention, how to optimize networks’ controllability has become a common and urgent problem. In this paper, we develop an efficient genetic algorithm oriented optimization tool to optimize the controllability of arbitrary networks consisting of both state nodes and control nodes under Popov–Belevitch–Hautus rank condition. The experimental results on a number of benchmark networks show the effectiveness of this method and the evolution of network topology is captured. Furthermore, we explore how network structure affects its controllability and find that the sparser a network is, the more control nodes are needed to control it and the larger the differences between node degrees, the more control nodes are needed to achieve the full control. Our framework provides an alternative to controllability optimization and can be applied to arbitrary networks without any limitations.