A matheuristic approach for the minimum broadcast time problem using a biased random‐key genetic algorithm

Abstract

The Minimum Broadcast Time (MBT) is a well‐known data dissemination problem whose goal is to find a broadcast scheme that minimizes the number of steps needed to execute the broadcast operation. The problem has many applications in distributed systems and, in particular, the Industry 4.0 domain. Because Industry 4.0 applications rely primarily on the use of large‐scale machine to machine communications, they need data dissemination techniques that combine high reliability with low communication latency. This work proposes a Biased Random‐Key Genetic Algorithm and a matheuristic for the MBT. We carry out experiments with our algorithms on instances commonly used in the literature (hypercube, shuffle exchange, cube‐connected cycles, de Bruijn, Harary graphs), and also on massive synthetic instances (up to 1000 vertices), allowing to cover many possibilities of real industry topologies. Our proposal is also compared with state‐of‐the‐art exact methods and heuristics. Experimental results show that our algorithm is able to outperform the best‐known heuristics for the MBT, and also that it is a very good alternative for large instances that cannot be solved by current exact methods.

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

“…More recently, Lima et al [95] proposed a metaheuristic algorithm for the MBT problem with GA, namely BRKGA. They suggested various versions of their algorithm while combining it with different decoders, such as first receive first send (FRFS) or an integer linear programming (ILP) method.…”

“…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.…”

“…Assim, desenvolver outros algoritmos não ótimos, mas que possam ter soluc ¸ões melhores do que os algoritmos da literatura. O Biased Random Key Genetic Algorithm [Toso andResende 2015, Resende 2011] (BRKGA) é uma das meta-heurísticas a ser considerada, pois o BRKGA foi utilizado para solucionar o MBT [Lima et al 2022].…”