A Parallel Genetic Algorithm for Solving the Probabilistic Minimum Spanning Tree Problem

Zhurong Wang, Changqing Yu, Xinhong Hei, Bin Zhang
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Abstract

The probabilistic minimum spanning tree (PMST) problem is NP-complete and is hard to solve. However, it has important theoretical significance and wide application prospect. A parallel genetic algorithm based on coarse-grained model is proposed to solve PMST problem in this paper. Firstly, we discuss several problems of determinant factorization encoding, and develop repairing method for illegal individuals. Secondly, a coarse-grained parallel genetic algorithm, which combines message passing interface (MPI) and genetic algorithm, is designed to solve probabilistic minimum spanning tree problems. Finally, the proposed algorithm is used to test several probabilistic minimum spanning tree problems which are generated by the method introduced in the literature. The statistical data of the test results show that the expectation best solution and average best solution obtained by the proposed algorithm are better than those provided in the literature.
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求解概率最小生成树问题的并行遗传算法
概率最小生成树(PMST)问题是np完全问题,很难求解。但它具有重要的理论意义和广阔的应用前景。提出了一种基于粗粒度模型的并行遗传算法来解决PMST问题。首先讨论了行列式分解编码的几个问题,并提出了针对非法个体的修复方法。其次,将消息传递接口(MPI)与遗传算法相结合,设计了一种求解概率最小生成树问题的粗粒度并行遗传算法。最后,利用本文提出的算法对几种概率最小生成树问题进行了测试。测试结果的统计数据表明,本文算法得到的期望最优解和平均最优解均优于文献提供的最优解。
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