A genetic algorithm for the minimum broadcast time problem using a global precedence vector

Abstract

The problem of broadcasting a message through a network is considered. The objective is to minimize the number of time steps necessary to complete the broadcast. This problem is known as the Minimum Broadcast Time Problem or the Local Broadcasting Problem. Finding an optimal broadcast using a local broadcasting scheme is known to be NP-Complete. A genetic algorithm (GA) is used as a heuristic technique to find near optimal solutions to this problem. The GA is compared to a variant of a recent heuristic technique presented in the literature.

HUB-GA: A heuristic for universal lists broadcasting using genetic algorithm

“…Broadcasting: In the area of broadcasting, Hoelting et al proposed a GA for the problem of minimum broadcast time (MBT) [94]. They tested their algorithm for random graphs on 10 to 500 nodes, as well as three contrived sets of networks on 40, 80, and 120 nodes.…”

“…Moreover, Hasson and Sipper [4] proposed ACS: an ant colony system for the MBT problem. They compared the performance of their algorithm with that of [94] and AM [24] for random graphs on 15 to 250 nodes and edge probability in the range of (0.05 − 0.1). In most cases, the achieved broadcast time was better or the same, while the running time was enhanced compared to both algorithms.…”

“…Their results show that BRKGA is able to outperform all counterpart heuristics for the MBT problem, while it can also be an alternative for larger networks where the exact methods cannot be applied. Finally, we should point out that the goal of [4], [94], [95] is to minimize the classical broadcast time of a particular vertex under the classical model, not to optimize the broadcast time of all network members at the same time.…”

“…1) The first heuristic for this problem: As mentioned in Section III, there are several heuristics for classical broadcasting, such as [32], [33], even some researchers consider GA [94], [95], or other evolutionary algorithms [4]. However, to the best of our knowledge, there is no similar study on the problem of broadcasting with universal lists.…”

Um modelo de programação matemática para o problema Weighted Minimum Broadcast Time

“…Os problemas MBT e WMBT atraíram interesse de vários pesquisadores devido ao seu potencial para modelar muitas aplicac ¸ões do mundo real. Para o MBT, existem prospostas de algoritmos exatos [Scheuermann and Wu 1984, de Sousa et al 2018, Ivanova 2019, algoritmos aproximados [Elkin andKortsarz 2003, Kortsarz andPeleg 1992], heurísticas, metaheurísticas e matheuristic [Scheuermann and Wu 1984, Hoelting et al 1996, de Sousa et al 2018, Hasson and Sipper 2004, Harutyunyan and Wang 2010, Harutyunyan and Jimborean 2014, Lima et al 2022.…”