# Wide area telecommunication network design: application to the Alberta SuperNet

TL;DR: A tabu search algorithm heuristic is developed and tested on randomly generated instances and on Alberta SuperNet data, and Mathematical models are described for these two subproblems.

Abstract: This article proposes a solution methodology for the design of a wide area telecommunication network. This study is motivated by the Alberta SuperNet project, which provides broadband Internet access to 422 communities across Alberta. There are two components to this problem: the network design itself, consisting of selecting which links will be part of the solution and which nodes should house shelters; and the loading problem which consists of determining which signal transport technology should be installed on the selected edges of the network. Mathematical models are described for these two subproblems. A tabu search algorithm heuristic is developed and tested on randomly generated instances and on Alberta SuperNet data.

## Summary (1 min read)

### 1. Introduction

- The NDP considered in this article is NP-hard because it subsumes several NP-hard problems like the STP.
- Wide area telecommunication network design 1461 due to the complexity of the resulting formulation.
- Instead, the authors opted for a decomposition approach in which they first solve the topological design problem (TDP) and then solve the loading problem (LP) on the TDP solution.
- The authors present models and algorithms for these problems in the next two sections, followed by computational results.

### 2. Model and heuristic for the TDP

- The objective minimizes the total edge and shelter costs.
- These two constraints lead to the correct cost calculation.
- The authors provide the above formulation for precision in problem definition.

### 2.1. Greedy heuristic

- It works on the directed graph in which each edge has been replaced by two opposite arcs.
- The SPPR determines the shortest origin-destination path and the relay locations on 1.
- When applied to a particular (o(k), d(k)) pair, the SPPR problem is denoted as SPPR(&).

### 3.2. Formulation

- If 16) ensure that sufficient fibre is installed on arc (i, j) to carry the flow passing on that arc; whereas constraints (17) guar antee that an appropriately sized cable is installed on (i, j) to accommodate the required number of fibre optical strands.
- This integer program is of large scale even for small net work examples, and is impractical for the Alberta SuperNet project.

### 3.3. TS algorithm

- The authors have also tested two stopping criteria with several parameter values: the total number of iterations spent in the search and the total number of iterations without improve ment in the value of the best known solution.
- The authors found that the second criterion with a value of 50 produced the best results.

### 4. Computational results

- As one can observe from Table 4 , the LP routines DBH, DBESH, SH, and SingleTS were very fast, usually per forming calculations in seconds even for the largest test set problems.
- TrunkTS and SingleTrunkTS were comparatively slower, with an average of 8.5 min and of over an hour in the worst case scenario.
- By comparing the gaps of Table 5 , one can see that neither the TrunkTS nor the SingleTrunkTS algorithms yielded solutions that were significantly better than the SingleTS algorithm.
- Figures 8 and 9 show that the SingleTS heuristic is the most promising.
- Each execution of the algorithm described in Figure 2 took, on average, 43 min, and the total gap between the best and the worst solution was 2.55%, corresponding to $3.25 million.

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##### Citations

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...It has been introduced and studied in [4, 5], and applied to several contexts in [2, 7, 6]....

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...[6] develop a two-step method for the design of a wide area broadband internet network in Alberta, CA....

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### "Wide area telecommunication network..." refers methods in this paper

...TS is a metaheuristic introduced by Glover (1986), which has become one of the most popular tools to a host of hard combinatorial optimization problems....

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### "Wide area telecommunication network..." refers background in this paper

...A large body of the research addresses pure topological problems like the Steiner tree problem (STP) (eg Koch and Martin, 1998; Lucena and Beasley, 1998; Patterson et al, 1999; Polzin and Vahdati Daneshmand, 2001a,b, 2003; Costa et al, 2006) or problems defined on particular topologies like trees (Randazzo and Luna, 2001; Gzara and Goffin, 2005), rings (eg Armony et al, 2000; Chamberland and Sansò, 2000), or meshes (Costa, 2005; Kerivin and Mahjoub, 2005; Magnanti and Raghavan, 2005)....

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...…Daneshmand, 2001a,b, 2003; Costa et al, 2006) or problems defined on particular topologies like trees (Randazzo and Luna, 2001; Gzara and Goffin, 2005), rings (eg Armony et al, 2000; Chamberland and Sansò, 2000), or meshes (Costa, 2005; Kerivin and Mahjoub, 2005; Magnanti and Raghavan, 2005)....

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