Given a connected, weighted, undirected graph G = (V, E) and an integer D ≥ 2, the bounded diameter minimum spanning tree (BDMST) problem seeks a spanning tree of minimum cost, whose diameter is no greater than D. The problem is known to be NP‐hard, and finds application in various domains such as information retrieval, wireless sensor networks and distributed mutual exclusion. This article presents a two‐phase memetic algorithm for the BDMST problem that combines a specialized recombination operator (proposed in this work) with good heuristics in order to more effectively direct the exploration of the search space into regions containing better solutions. A parallel meta‐heuristic is also proposed and shown to obtain very good speedups – super‐linear, in several cases – vis‐à‐vis the serial memetic algorithm. To the best of the authors' knowledge, this is the first parallel meta‐heuristic proposed for the BDMST problem, and potentially paves the way for handling much larger problems than reported in the literature. Some observations and theorems are presented in order to provide the underlying framework for the proposed algorithms. Further, the proposed memetic algorithm and parallel meta‐heuristic are shown, in the course of several computational experiments, to in general obtain superior solution quality with much lesser computational effort in comparison to the best known meta‐heuristics in the literature over a wide range of benchmark instances.

中文翻译：

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有界直径最小生成树问题的串行和并行模因算法

给定一个连接，加权无向图G ^ =（V，ê）和一个整数d  ≥2时，有界直径最小生成树（BDMST）问题寻求最小成本的生成树，其直径不大于d。已知该问题是NP难题，可在信息检索，无线传感器网络和分布式互斥等各个领域找到应用。本文提出了一种针对BDMST问题的两阶段模因算法，该算法结合了专门的重组算子（本工作中提出）和良好的启发式方法，以便更有效地将搜索空间的探索定向到包含更好解的区域中。还提出了一种并行元启发式方法，并证明了相对于串行模因算法，这种方法获得了非常好的加速比（在某些情况下为超线性）。据作者所知，这是针对BDMST问题首次提出的并行元启发式方法，并有可能为处理比文献中报道的更大的问题铺平道路。为了提供所提出算法的基础框架，提出了一些观察和定理。此外，与多种文献中最著名的元启发式算法相比，在多次计算实验过程中，所提出的模因算法和并行元启发式算法总体上显示出优异的解决方案质量，而运算量却要少得多基准实例的数量。