A new Lagrangean relaxation approach for the hop-constrained minimum spanning tree problem

Article Abstract:

A new Lagrangean relaxation approach for the hop-constrained minimum spanning tree problem is proposed. The findings suggest that the approach is superior to other Lagrangean relaxations for problems with a large number of edges.

Methods

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Multicommodity flow models for spanning trees with hop constraints

Article Abstract:

Linear programming relaxations of multicommodity flow models for the terminal layout problem expressed as a hop constrained minimal spanning tree problem (HMST) were evaluated. Specifically, it was proven that LP relaxations lead to sharp lower bounds for the network design problem and large LP models. Consequently, Lagrangean relaxation-based schemes for obtaining the bounds were developed after proving the equivalency of undirected and directed models.

Case studies, Integer programming, Relaxation methods (Mathematics), Trees (Graph theory)

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Designing reliable tree networks with two cable technologies

Article Abstract:

An NP-Hard hop and primary connectivity constrained two level minimal spanning tree problem was created as a directed multicommodity flow model. A Lagrangean relaxation was formulated from the model which is associated with a centralized network with reliability requirements and two cable technologies. Results from the derived Lagrangean heuristic show gaps to be close to zero for levels up to 40 nodes.

Operations Research, Heuristic, Reliability (Engineering), Heuristics (Psychology)

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