Design of capacitated degree constrained min-sum arborescence

The capacitated degree constrained min-sum arborescence problem consists of finding a directed spanning tree in a network to connect a set of terminal nodes to a central node with minimal total cost where the links in the network are directed away from the central node. The number links incident on each terminal node is limited by the number of ports available on them (degree constraint). Additionally, the reliability and response time constraints limit the number of nodes in the sub-trees rooted at the central node (capacity constraint). This problem is formulated as an integer-programming problem and a branch exchange heuristic embedded in the Lagrangian relaxation method is used to find a good feasible solution. The lower bound found as a byproduct of this solution method is used to estimate the quality of the solution given by our heuristic. Experimental results over a wide range of problem structures show that our heuristic method gives good solutions to this problem.