Models and Implementation Techniques for Local Access Telecommunication Network Design
This paper presents models, algorithms and implementation techniques for Local Access Telecommunication Network (LATN) Design and Expansion problems. In particular, we develop detailed algorithms for implementing the so-called Limited Column Generation approach. We first formulate both problems into a tree—partitioning problem with an exponential number of variables. A dedicated column generation procedure is developed so that the master tree partitioning linear program can be solved in just n pivots, where n is the number of nodes in the network. As only a limited number of columns are generated, we call such a procedure Limited Column Generation. Prior to each pivot, an entering variable is selected by detecting the Locally Most Violated (LMV) reduced profit (reduced cost), which is equivalent to solve a subproblem in pseudo—polynomial time. In particular, for the LATN Design problem, the corresponding subproblem is the Tree Knapsack Problem. As dual variables are updated at each pivot, the reduced profits have to be computed in an on-line fashion. An efficient implementation is developed to execute such a task so that the LATN Design problem can be solved in O(n 2 H), and the LATN Expansion problem can be solved in O(n 2 δH) time, where b is the largest existing cable capacity and H is the maximum capacity of concentrators. Our computational experiments indicate that our algorithm delivers outstanding performance. For instance, the LATN Design and Expansion problems with 200 nodes can be solved in approximately 90 seconds and 484 seconds, respectively, on a SUN SPARC 1000 workstation.
KeywordsColumn Generation Dynamic Programming Algorithm Lagrangian Relaxation Chordal Graph Expansion Problem
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