A rapid learning automata-based approach for generalized minimum spanning tree problem

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.