Heuristic and Exact Method for the Minimum Broadcast Center

The Minimum Broadcast Center (MBC) problem, which involves selecting a set of source nodes and determining the Minimum Broadcast Time (MBT) from that set. This problem is relevant to the design of networks in smart cities and distributed systems, especially with the Internet of Things (IoT). Two methods have been proposed to solve MBC: a Linear Integer Programming (ILP) model and a metaheuristic based on a Genetic Algorithm with Biased Random Keys (BRKGA). The comparative analysis between ILP and BRKGA in 111 instances showed that both methods are efficient, but BRKGA demonstrated greater consistency and speed in obtaining optimal solutions, especially in larger instances where ILP had difficulty. This comparison underscores the efficacy of BRKGA as a heuristic for the MBC problem.