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Journal ArticleDOI

Wide area telecommunication network design: application to the Alberta SuperNet

01 Nov 2008-Journal of the Operational Research Society (Palgrave Macmillan UK)-Vol. 59, Iss: 11, pp 1460-1470

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.

AbstractThis 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.

Topics: Wide area network (56%), Telecommunications network (52%), Network planning and design (51%), Internet access (51%)

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  • It works on the directed graph in which each edge has been replaced by two opposite arcs.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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Wide Area Telecommunication Network Design: Application to the Alberta SuperNet
Author(s): E. A. Cabral, E. Erkut, G. Laporte and R. A. Patterson
Source:
The Journal of the Operational Research Society,
Vol. 59, No. 11 (Nov., 2008), pp.
1460-1470
Published by: Palgrave Macmillan Journals on behalf of the Operational Research Society
Stable URL: http://www.jstor.org/stable/20202230
Accessed: 06-09-2017 07:46 UTC
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Journal of the Operational Research Society (2008) 59, 1460-1470 ? 2008 Operational Research Society Ltd. All rights reserved. 0160-5682/08
www.palgrave-journals.com/jors
Wide area telecommunication network design:
application to the Alberta SuperNet
EA Cabrai1, E Erkut2, G Laporte3* and RA Patterson1
1 University of Alberta, Edmonton, Canada; 2Bilkent University, Ankara, Turkey; and
3HEC Montr?al, Montr?al, Canada
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.
Journal of the Operational Research Society (2008) 59, 1460-1470. doi:10.1057/palgrave.jors.2602479
Published online 12 September 2007
Keywords: heuristic; network design; telecommunications
1. Introduction
Network design problems (NDPs) are central to planning
telecommunication systems (see, eg Balakrishnan et al, 1997;
Raghavan and Magnanti, 1997). Most network design re
search focuses on extracting from a network an optimal sub
network that will satisfy various requirements. Here we use a
broader network design definition that goes beyond the topo
logical component and encompasses the loading aspect, that
is the choice of equipment to be installed on the subnetwork.
Telecommunication networks are generally classified ac
cording to their geographical span. They include local area
networks (LANs) connecting small areas, usually a single
building or a set of buildings, metropolitan area networks
(MANs) covering a city or a metropolitan area, and wide area
networks (WANs) spanning large territories made up of sev
eral cities, states, or countries. Another important classifica
tion in network design is the subnetwork topology. The most
common topologies are trees, rings, meshes and unstructured
networks. Telecommunication networks are often composed
of a backbone network linking primary nodes and of an ac
cess network, but this distinction does not apply to our study.
This article considers the design of a WAN tree network
with a technological choice component. Our study is moti
vated by the Alberta SuperNet project, a partnership between
the Alberta provincial government and a private consortium
led by Bell West Inc. Their goal is to provide broadband
Internet access to 422 communities across Alberta. Optical
* Correspondence: G Laporte, HEC Montr?al, 3000 chemin de la C?te
Sainte Catherine, Montr?al, Quebec H3T 2A7, Canada.
E-mail: gilbert@crt.umontreal.ca
fibres in the SuperNet will be installed along existing roads,
and therefore, the design problem uses the road network
as an input. According to our GIS database, the Alberta road
network comprises approximately 80000 nodes and 280000
edges. In practice, we solve the problem on a simplified net
work containing 21714 nodes and 22871 edges. The edges
correspond to the shortest tree spanning the 422 communi
ties; the nodes include these communities and intermediary
locations on the spanning tree.
The Alberta SuperNet project requires no alternative paths
or redundancy for communication flow, in the event of hard
ware or fibre failure. Thus the most cost-effective topology
is a tree structure in which the digging and fibre installa
tion costs are minimized, as suggested by Chamberland et al
(2000). The project also allows for the coexistence of tech
nologies along the same cable in different strands of optical
fibres. With such freedom, signals can travel in parallel, as
long as a sufficient number of fibres are available in the link
for all signals. Because of multiple technologies, switches
must sometimes be installed at the nodes to allow signals to
pass between fibres of different transmission capacities. How
ever, the presence of switches induces transmission delays.
Also, it is sometimes necessary to locate multiplexers at the
nodes to regenerate the signals.
The use of multiple technologies renders the telecommuni
cation NDP complex. Our goal is to design a least-cost sub
network that spans all communities and satisfies a number of
technological constraints. Although the Alberta SuperNet is
assumed to be tree-shaped, our formulations and algorithms
do not assume any particular topology. They can therefore be
applied to general contexts (Figure 1).
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A a A A **?
A A-4T
A / A A A AAA ?
Communities
Calgary
? Major communities
* Other communities
Major Roads
I I Alberta
+ % A* A A a. A
* -A / A Q A
A A A A A .<
600 Kilometers
Figure 1 The simplified Alberta SuperNet.
An abundant literature exists on NDPs, particularly in
the telecommunications area. A large body of the research
addresses pure topological problems like the Steiner tree prob
lem (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 par
ticular topologies like trees (Randazzo and Luna, 2001 ; Gzara
and Goffin, 2005), rings (eg Armony et al, 2000; Cham
berland and Sans?, 2000), or meshes (Costa, 2005; Kerivin
and Mahjoub, 2005; Magnanti and Raghavan, 2005). Several
papers address hierarchical problems that associate a par
ticular technology with each level (eg Balakrishnan et al,
1998; Chamberland et al, 2000; Chamberland and Sans?,
2001; Chopra and Tsai, 2002; Labb? et al, 2004). Research
on hierarchical network design is relevant to our case, but
no existing paper addresses the problem we study. General
articles and books on NDPs in telecommunications include
Doverspike and Saniee (2000), Gavish (1992), and Sans?
and Soriano (1999).
The NDP considered in this article is NP-hard because it
subsumes several NP-hard problems like the STP. Although
it may be possible to integrate all aspects of the problem
into a single formulation and to design a heuristic to generate
solutions, such an approach would be ineffective in our case,
EA Cabrai et al?Wide area telecommunication network design 1461
due to the complexity of the resulting formulation. Instead,
we opted for a decomposition approach in which we first
solve the topological design problem (TDP) and then solve
the loading problem (LP) on the TDP solution. We present
models and algorithms for these problems in the next two
sections, followed by computational results.
2. Model and heuristic for the TDP
The TDP is defined on an undirected network G = (V, E, K),
where V is a node set, and E = {(/, j) : i, j e V, i < j} is
an edge set. The set K = [(o(k), d(k))} is a set of communi
cation pairs in which o(k) and d(k) are the respective origin
and destination of the kth communication request. With each
edge (/, j) is associated a cost c?j and a length d?j. Node j is
associated with a fixed cost fj of locating a shelter to house
a multiplexer, a switcher, or both. Every o(k) and d(k) node
requires a shelter. The TDP consists of determining a mini
mum cost subnetwork of G and of locating a shelter at some
of its nodes in such a way that: (1) for every (o(k),d(k))
pair, the length of a path between o(k) and the first shelter,
between the last shelter and d(k), or between two consecu
tive shelters does not exceed a preset bound /; and (2) the
total cost of the subnetwork, made up of edge costs and shel
ter fixed costs, is minimized. In the Alberta SuperNet project,
the value of A is 70 km. Note that this problem formulation
disregards multiplexers. In other words, only shelters chosen
by the TDP can house multiplexers in the solution of the LP.
The TDP can be formulated as an integer linear program
in which the main variables correspond to directed paths
associated with (o(k),d(k)) pairs. In order to handle direc
tions, the number of communication pairs is first doubled,
that is, we define K' = {(o'(k), d'(k)), (o"(k), d"(k))}, where
(o'(k), d'(k))=(o(k), d(k)), and (o"(k), d"(k))=(d(k), o(k)),
with (o(k),d(k)) e K. Each edge (i, j) e E is replaced
with two opposite arcs (/, j) and (j, i), with respective
costs c'y = c'jj = Cij/2 and respective lengths d\- = d'}i = d?j.
Denote the set of arcs by A. The problem definition is
otherwise unchanged.
For each communication pair k e K', let P(k) be the set
of feasible paths from o(k) to d(k); given a path p e P(k),
let R(p) denote the set of feasible relay patterns of path p,
that is an ordered subset of vertices on p separated by at most
? distance units, and let r e R(p) be a. feasible relay pattern
for path p. Define the binary variables
1 if arc (/, j) belongs to the solution
0 otherwise
1 if a shelter is located at node i
0 otherwise
r 1 if path p with relay pattern r is used by
zpkr = communication pair (o(k), d(k))
. 0 otherwise
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1462 Journal of the Operational Research Society Vol. 59, No. 11
and the binary coefficients
1 if arc (/, j) belongs to path p
<$
0 otherwise
# =
1 if a shelter is located at node i in relay pattern r
0 otherwise
The formulation of the TDP is then:
(TDP)
Minimize ^ c\-x{j + J^fyi (1)
(i,j)eA ieV
subject to
E %:
PeP(k)
reR(p)
1 (* K') (2)
Y,a?j4r^xa (d,j)eA,keK') (3)
peP(k)
reR(p)
J^b^r^yi (ieV,keK') (4)
PeP(k)
reR(p)
Xij=0orl ((iJ)eA) (5)
y? = 0 or 1 (i g V) (6)
zf=0orl (hr). (7)
In this formulation, the objective minimizes the total edge and
shelter costs. Constraints (2) ensure that each (o(k), d(k)) pair
is connected by a path. Constraints (3) imply that x?j takes the
value 1 whenever arc (/, j) belongs to path p, and constraints
(4) guarantee that yt is equal to 1 if a shelter is located at
node i in path p. These two constraints lead to the correct cost
calculation. We provide the above formulation for precision in
problem definition. We do not use this formulation in solving
the problem; instead we implement a heuristic.
2.1. Greedy heuristic
The heuristic we employ to solve the TDP was developed
by Cabrai et al (2007). It works on the directed graph in
which each edge has been replaced by two opposite arcs. The
heuristic is based on a procedure put forward by Takahashi
and Matsuyama (1980) for the STP, which constructs a sub
network in a greedy fashion, one (o(k), d(k)) pair at a time
for every k e Kf. Because of the constraint imposed on the
interspacing of shelters, the (o(k),...,d{k)) paths are con
structed by using the auxiliary pseudo-polynomial procedure
suggested by Cabrai et al (2005) for the shortest path problem
with relays (SPPR). The input of the SPPR is a graph with
arc (or edge) costs and weights, an interspacing limit of X,
and an origin-destination pair (o, d). The SPPR determines
the shortest origin-destination path and the relay locations on
1. Set E := 0, V := 0 and Q = 0.
2. /or eac/i /c G K do {
call SPPR(/c) to find a path p(k) and a relay pattern r(k)
for each (i,j) G p(k) do
{Q := Q + Cij\ Cij = 0;}
for each i G r(k) do
{Q:=Q + fi;fi = 0;}
}
Figure 2 Pseudo-code of the construction heuristic.
some of its nodes in such a way that the interspacing con
straint is satisfied. When applied to a particular (o(k), d(k))
pair, the SPPR problem is denoted as SPPR(&). In the fol
lowing description of the TDP heuristic, Q denotes the solu
tion cost and a relay pattern r(k) is a set of nodes on a path
p(k) = (o(k),..., d(k)) that satisfies the interspacing con
straint. In Step 2, the c?7 and f values of the selected paths
are set equal to zero to avoid multiple counting when several
paths share some arcs or nodes (Figure 2).
3. Model and heuristic for the loading problem
The TDP heuristic returns a directed subnetwork of G with
shelters that houses multiplexers located at some of its nodes.
This topology remains unchanged in the LP. We now need
to decide which fibre types to install along the edges of the
subnetwork and in which shelters to locate the switchers.
We consider three different types of optical signal trans
port technologies: Gigabit Ethernet (GE), Synchronous
Optical Network (SONET), and Dense Wavelength Division
Multiplex (DWDM). Among these, only GE is Internet com
patible, and therefore, in order to have an Internet network in
place, users must receive and transmit signals in GE techno
logy. SONET and DWDM are well-established technologies
for telecommunication, and provide more capacity per fibre
and add less delay to the signal than GE technology.
GE technology has a per-fibre transmission capacity of
2.5Gbps (Gigabits per second), compared to lOGbps/fibre
for SONET and 40Gbps/fibre for DWDM. The most expen
sive technology is DWDM, followed by SONET, then GE.
Our model assumes the use of simple-mode optical fibres that
are suitable for all three technologies. Our industrial partner
informed us that, compared to GE, SONET and DWDM add
an insignificant delay to the signal, but our model is capable of
distinguishing between different signal delays. We assumed
that GE repeaters, GE/SONET and GE/DWDM switchers add
a delay of 1 ms to the signals, whereas all the other equip
ment add no delay. If a signal leaves an origin in GE or
arrives at a destination in GE, no switcher is necessary at these
nodes. However, if another technology is used, a switcher is
necessary.
We used the following equipment prices: a GE repeater
costs $10 000 (all montetary amounts are in Canadian dollars),
a SONET repeater costs $15 000, a DWDM repeater costs
$35 000, a GE/SONET switcher costs $20000, a GE/DWDM
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Table 1 Costs per metre in $ per strand
Cable type 1 2 3 4 5 6 1
h
zh:#o? 12 24 36 48 72 96 144
strands/
cable
?h: cost/ 2.25 2.85 3.58 5.35 6.50 7.90 10.63
meter
?L
/
Legend
rg^ Equipment Shelter
_ _ Sequence of edges
from NDP
Figure 3 Subgraph from TDP.
switcher costs $40 000, and a SONET/ DWDM switcher costs
$25 000. Cable prices are a stepwise function of the number
of strands they contain. Table 1 provides costs per metre of
each line of type h e H = {1, 2, 3,4, 5, 6, 7} considered in
our problem. If the transmission load requires a cable with a
minimum of 20 strands on a 1-km road segment, one would
use a type 2 cable, which would cost $2850.
The solution procedure must be able to account for capacity,
cost, and signal delays.
3.1. Network simplification
The subnetwork generated by the TDP heuristic (see Figure 3)
can be simplified to remove intermediate nodes between any
two successive shelter locations / and j on an (o(k), d(k))
path, to yield the simplified network in Figure 4. In other
words, the subpath (/,..., j) is replaced with a single edge
(/, j) of length Cij. This makes sense because it never is sub
optimal to use a single cable type on (/,..., j): if one cable
type is best for a subpath of (/,..., j), then the same type
is best for the entire path. Furthermore, the case of multiple
cable types would require the location of multiplexers along
the way. Thus a shelter exists at all nodes of the network on
which the LP is solved.
3.2. Formulation
Denote by G = (N, A) the subnetwork resulting from the
simplification, when TV is a set of nodes and A is a set of
EA Cabrai et al?Wide area telecommunication network design 1463
E?P
??0???(i
Legend
rf?p Equipment Shelter
_ Edge representing
a subpath
Figure 4 Graph for LP.
Figure 5 Technology pairs along a path (o(k),... ,d(k)).
arcs. For a given k e K', let N'(k) = N\{o(k),d(k)}. Let
T be the set of available technologies. In our application,
r = {l=GE, 2=SONET, 3=DWDM}. Denote by o* the fibre
capacity of technology t. In our application, ox =2.5, o2 = 10,
and o3 = 40. The set T2 = {(t, t') : t,tf e T} represents all
possible technology pairs associated with a shelter: t is the
entering technology and t' is the exiting technology (Figure 5).
l? t ^ t', then a switcher of cost ptt' must be located in the
shelter. With each pair (t, tr) e T2 is associated a delay ?tt .
In order to account for origins and destinations, it is useful
to introduce a technology 0 at these nodes. Consequently,
we define T'= T U {0}, and f2 = {(t, t') : t,t' e T'}. If
t = 1, then ? = <510 = 0 because no switcher is necessary
to send or receive a signal in GE. A communication flow
demand <j)k (in Gbps) is given for each (o(k), d(k)) pair. The
maximum allowed signal delay has the same value Amax for
each (o(k), d(k)) pair. Denote by ?h the cost per meter of
cable of type h.
In order to formulate the LP, we introduce the following
variables:
ykt _
1 if technology t is selected for communication
pair (o(k), d(k)) along arc (i, j) e A
0 otherwise
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Journal ArticleDOI
TL;DR: Four key areas of Integer programming are examined from a framework that links the perspectives of artificial intelligence and operations research, and each has characteristics that appear usefully relevant to developments on the horizon.
Abstract: Integer programming has benefited from many innovations in models and methods. Some of the promising directions for elaborating these innovations in the future may be viewed from a framework that links the perspectives of artificial intelligence and operations research. To demonstrate this, four key areas are examined: 1. (1) controlled randomization, 2. (2) learning strategies, 3. (3) induced decomposition and 4. (4) tabu search. Each of these is shown to have characteristics that appear usefully relevant to developments on the horizon.

3,690 citations


"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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Journal ArticleDOI
TL;DR: An algorithm which is designed for general graphs turns out to be an efficient alternative to the MSTH approach and some new equivalent relaxations of this problem are studied.
Abstract: The bottleneck of the state-of-the-art algorithms for geometric Steiner problems is usually the concatenation phase, where the prevailing approach treats the generated full Steiner trees as edges of a hypergraph and uses an LP-relaxation of the minimum spanning tree in hypergraph (MSTH) problem. We study this original and some new equivalent relaxations of this problem and clarify their relations to all classical relaxations of the Steiner problem. In an experimental study, an algorithm of ours which is designed for general graphs turns out to be an efficient alternative to the MSTH approach.

521 citations


Book
14 Aug 1997
TL;DR: Part I: General methodologies complexity and approximability polyhedral combinatorics branch-and-cut algorithms matroids and submodular functions advances in linear programming decomposition and column generation stochastic integer programming randomized algorithms local search graphs and matrices.
Abstract: Part I: General methodologies complexity and approximability polyhedral combinatorics branch-and-cut algorithms matroids and submodular functions advances in linear programming decomposition and column generation stochastic integer programming randomized algorithms local search graphs and matrices. Part II: Specific topics and applications sequencing and scheduling "Travelling Salesman Problem" max cut location problems network design flows and paths quadratic and 3-dimensional assignments linear assignment vehicle routing cutting and packing combinatorial topics in VLSI design applications in computational biology.

376 citations


Journal ArticleDOI
Alysson M. Costa1
TL;DR: Network design problems concern the selection of arcs in a graph in order to satisfy, at minimum cost, some flow requirements, usually expressed in the form of origin-destination pair demands.
Abstract: Network design problems concern the selection of arcs in a graph in order to satisfy, at minimum cost, some flow requirements, usually expressed in the form of origin-destination pair demands. Benders decomposition methods, based on the idea of partition and delayed constraint generation, have been successfully applied to many of these problems. This article presents a review of these applications.

248 citations


"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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