INFORMS Journal on Computing
A Multicommodity Network-Flow Problem with Side Constraints on Paths Solved by Column Generation
INFORMS Journal on Computing
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part II
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Stabilized branch-and-price for the rooted delay-constrained steiner tree problem
INOC'11 Proceedings of the 5th international conference on Network optimization
A multilevel heuristic for the rooted delay-constrained minimum spanning tree problem
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
Reload cost trees and network design
Networks
On the hop constrained steiner tree problem with multiple root nodes
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
On solving the rooted delay- and delay-variation-constrained steiner tree problem
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
EvoCOP'13 Proceedings of the 13th European conference on Evolutionary Computation in Combinatorial Optimization
The Steiner Tree Problem with Delays: A compact formulation and reduction procedures
Discrete Applied Mathematics
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In this paper we discuss models and methods for solving the rooted distance constrained minimum spanning tree problem which is defined as follows: given a graph G=(V,E) with node set V={0,1,...,n} and edge set E, two integer weights, a cost c"e and a delay w"e associated with each edge e of E, and a natural (time limit) number H, we wish to find a spanning tree T of the graph with minimum total cost and such that the unique path from a specified root node, node 0, to any other node has total delay not greater than H. This problem generalizes the well known hop-constrained spanning tree problem and arises in the design of centralized networks with quality of service constraints and also in package shipment with service guarantee constraints. We present three theoretically equivalent modeling approaches, a column generation scheme, a Lagrangian relaxation combined with subgradient optimization procedure, both based on a path formulation of the problem, and a shortest path (compact) reformulation of the problem which views the underlying subproblem as defined in a layered extended graph. We present results for complete graph instances with up to 40 nodes. Our results indicate that the layered graph path reformulation model is still quite good when the arc weights are reasonably small. Lagrangian relaxation combined with subgradient optimization procedure appears to work much better than column generation and seems to be a quite reasonable approach to the problem for large weight, and even small weight, instances.