Network Topology Optimization for Energy-Efficient Control

Controlling the dynamics of complex networks with only a few driver nodes is a significant objective for system control. However, the energy required for control becomes prohibitively large when the fraction of driver nodes is small. Previous methods to reduce control energy have mainly focused on increasing the number or altering the placement of driver nodes. In this paper, a novel approach is proposed to reduce control energy by rewiring networks while keeping the number of driver nodes unchanged. We model network rewiring to an optimization problem and develop a memetic algorithm to solve it accurately and efficiently. Specifically, we introduce a connectivity-preserving crossover operator to avoid searching in invalid solution space and design a local search operator to accelerate the convergence of the algorithm according to the network heterogeneity. Experimental results on both synthetic networks and real networks demonstrate the effectiveness of the proposed approach. Notably, our findings reveal that networks with low control energy tend to exhibit a âcore-chainâ structure, where control nodes and high-weight edges form a densely connected core, while other nodes and edges form independent chains connected to the core's boundaries. We further analyze the statistical description and formation mechanism of this structure.