Capacitated power dominating set problem: a solution approach based on forbidden propagation sets
For researchers and practitioners in power system monitoring, this provides a more efficient solution to a realistic variant of the power dominating set problem that accounts for device capacity constraints.
The paper introduces forbidden propagation sets for the capacitated power dominating set problem, enabling new integer linear programming formulations that avoid big-M constraints. The method achieves an average 1.7x speedup over existing approaches on instances with up to 14,000 vertices.
The optimal placement of measurement devices in electrical power systems is commonly modeled through the power dominating set problem. However, in real-world applications, these devices have limited capacities, leading to a capacitated variant of the problem that has received little attention in the literature. In this work, we introduce forbidden propagation sets, novel combinatorial structures that cannot occur simultaneously in any feasible solution. This notion enables a new class of integer linear programming formulations. They combine infection-based variables with exponentially many constraints, while avoiding big-$M$ constraints. We derive structural properties, valid inequalities, and redundancy-breaking constraints, and design an efficient lazy-separation procedure based on cycle detection. Computational experiments on benchmark instances with up to 14,000 vertices show that the proposed method achieves an average execution-time improvement of 1.7x over existing approaches adapted from the literature. Moreover, the results indicate that performance depends not only on network size, but also on capacities.