Degree-constrained minimum spanning tree problem with uncertain edge weights

Uncertainty theory has shown great advantages in solving many nondeterministic problems, one of which is the degree-constrained minimum spanning tree (DCMST) problem in uncertain networks. Based on different criteria for ranking uncertain variables, three types of DCMST models are proposed here: uncertain expected value DCMST model, uncertain α-DCMST model and uncertain most chance DCMST model. In this paper, we give their uncertainty distributions and fully characterize uncertain expected value DCMST and uncertain α-DCMST in uncertain networks. We also discover an equivalence relation between the uncertain α-DCMST of an uncertain network and the DCMST of the corresponding deterministic network. Finally, a related genetic algorithm is proposed here to solve the three models, and some numerical examples are provided to illustrate its effectiveness.

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