Browsing by Subject "Network flows"

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    The multi-terminal maximum-flow network-interdiction problem
    (2011) Akgün, İ.; Tansel, B. Ç.; Wood, R. K.
    This paper defines and studies the multi-terminal maximum-flow network-interdiction problem (MTNIP) in which a network user attempts to maximize flow in a network among K ≥ 3 pre-specified node groups while an interdictor uses limited resources to interdict network arcs to minimize this maximum flow. The paper proposes an exact (MTNIP-E) and an approximating model (MPNIM) to solve this NP-hard problem and presents computational results to compare the models. MTNIP-E is obtained by first formulating MTNIP as bi-level min-max program and then converting it into a mixed integer program where the flow is explicitly minimized. MPNIM is binary-integer program that does not minimize the flow directly. It partitions the node set into disjoint subsets such that each node group is in a different subset and minimizes the sum of the arc capacities crossing between different subsets. Computational results show that MPNIM can solve all instances in a few seconds while MTNIP-E cannot solve about one third of the problems in 24 hour. The optimal objective function values of both models are equal to each other for some problems while they differ from each other as much as 46.2% in the worst case. However, when the post-interdiction flow capacity incurred by the solution of MPNIM is computed and compared to the objective value of MTNIP-E, the largest difference is only 7.90% implying that MPNIM may be a very good approximation to MTNIP-E. © 2011 Elsevier B.V. All rights reserved.
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    New formulations for the hop-constrained minimum spanning tree problem via Sherali and Driscoll's tightened Miller-Tucker-Zemlin constraints
    (Elsevier, 2010) Akgün, İbrahim
    Given an undirected network with positive edge costs and a natural number p, the hop-constrained minimum spanning tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, the new models based on the Miller-Tucker-Zemlin (MTZ) subtour elimination constraints are developed and computational results together with comparisons against MTZ-based, flow-based, and hop-indexed formulations are reported. The first model is obtained by adapting the MTZ-based Asymmetric Traveling Salesman Problem formulation of Sherali and Driscoll [18] and the other two models are obtained by combining topology-enforcing and MTZ-related constraints offered by Akgün and Tansel (submitted for publication) [20] for HMST with the first model appropriately. Computational studies show that the best LP bounds of the MTZ-based models in the literature are improved by the proposed models. The best solution times of the MTZ-based models are not improved for optimally solved instances. However, the results for the harder, large-size instances imply that the proposed models are likely to produce better solution times. The proposed models do not dominate the flow-based and hop-indexed formulations with respect to LP bounds. However, good feasible solutions can be obtained in a reasonable amount of time for problems for which even the LP relaxations of the flow-based and hop-indexed formulations can be solved in about 2 days. © 2010 Elsevier Ltd. All rights reserved.