Biased random-key genetic algorithms for the weighted minimum broadcast time problem

Broadcasting is an essential operation in distributed systems, with a wide range of applications. This study is focused on solving the Weighted Minimum Broadcast Time (WMBT), a problem that extends the classical Minimum Broadcast Time problem (MBT) by incorporating costs associated with each communication operation. We propose five contributions to the WMBT: (i) an integer linear programming model, (ii) two greedy algorithms, (iii) two Biased Random-Key Genetic Algorithms (BRKGAs), (iv) a lower bound algorithm, (v) a reduction rule to decrease an instance size, and (vi) a method to create instances with known optimal solutions. Our novel approaches are compared with state-of-the-art methods using large-scale synthetic instances. The experimental results demonstrate the effectiveness of our proposals. The greedy algorithms attains the best known solutions in a significant number of instances, while the two BRKGAs further enhance this performance, surpassing the greedy algorithms in many of the tested instances.