Generalized minimum spanning tree problem, which has several real-world applications like telecommunication network designing, is related to combinatorial optimization problems. This problem belongs to the NP-hard class and is a minimum tree on a clustered graph spanning one node from each cluster. Although exact and metaheuristic algorithms have been applied to solve the problems successfully, obtaining an optimal solution using these approaches and other optimization tools has been a challenge. In this paper, an attempt is made to achieve a sub-optimal solution using a network of learning automata (LA). This algorithm assigns an LA to every cluster so that the number of actions is the same as that of nodes in the corresponding cluster. At each iteration, LAs select one node from their clusters. Then, the weight of the constructed generalized spanning tree is considered as a criterion for rewarding or penalizing the selected actions. The experimental results on a set of 20 benchmarks of TSPLIB demonstrate that the proposed approach is significantly faster than the other mentioned algorithms. The results indicate that the new algorithm is competitive in terms of solution quality.

中文翻译：

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基于快速学习自动机的广义最小生成树问题方法

广义最小生成树问题具有组合优化问题，该问题具有电信网络设计等多个实际应用。该问题属于NP-hard类，是一个簇图上的最小树，该图跨越每个簇中的一个节点。尽管已经应用精确的元启发式算法成功解决了这些问题，但是使用这些方法和其他优化工具获得最佳解决方案仍然是一个挑战。在本文中，尝试使用学习自动机（LA）网络来实现次优解决方案。该算法将LA分配给每个群集，以使操作数与相应群集中的节点数相同。在每次迭代中，LA从其集群中选择一个节点。然后，构造的广义生成树的权重被视为奖励或惩罚所选动作的标准。以TSPLIB的20个基准为一组的实验结果表明，所提出的方法比其他提到的算法要快得多。结果表明，新算法在解决方案质量方面具有竞争力。