Optimal Design of Network Topology for Collaborative Control of Intelligent Group Systems

The collaborative control of intelligent group systems in complex environments relies on efficient network topologies, while existing methods struggle to construct topologies with multiple optimization objectives. This paper proposes a multi-objective optimization model based on connected persistent graph, aiming to abstractly describe the topology generation problem in the formation control of intelligent group systems. By introducing the concept of connected persistent graph, we transform the traditional graph theory model into a large-scale sparse multi-objective optimization problem with strong constraints. Next, an evolutionary algorithm named SparseGR is designed for solving this problem. SparseGR innovates in population initialization, objective switching strategies, and non-dominated sorting, significantly enhancing the algorithm’s optimization ability for large-scale sparse decision variables. Finally, the proposed algorithm is verified in four typical formations and large-scale random formations. Experimental results show that SparseGR outperforms existing algorithms in terms of the topology’s robustness against damage, formation maintenance capability, and rapid response capability. In addition, the algorithm demonstrates advantages in convergence, effectiveness, and timeliness, with improvements of at least 9.86%, 19.44%, and 6.85%, respectively.