Layout of Routers in Mesh Networks with Evolutionary Techniques
Pedro Henrique Gouvea Coelho, J. F. M. do Amaral, K. P. Guimarães and Matheus C. Bentes
State Univ. of Rio de Janeiro, FEN/DETEL, R. S. Francisco Xavier, 524/Sala 5001E, Maracanã, RJ, 20550-900, Brazil
Keywords: Genetic Algorithms, Artificial Intelligence Applications, Evolutionary Techniques.
Abstract: Wireless Mesh Networks show cost-efficient and fast deployment characteristics, however their major
problem is mesh router placement. Such optimal mesh router placement ensures desired network performance
concerning network connectivity and coverage area. As the problem is NP hard, a motivation to solve the
mesh router placement problem and seek optimal solution with suitable performance is to follow a heuristic
approach using evolutionary techniques involving genetic algorithms including fuzzy aggregation. Two case
studies are considered in this paper. The first one deals with a genetic algorithm application for spatial layout
of routers in a two dimensional, obstacle free, wireless mesh network model. The second one considers a
hybrid fuzzy-genetic scheme based on a fuzzy aggregation system that assesses the fitness of a genetic
algorithm. The hybrid system carries out the routers layout evolution within an area with localization
constraints where the placements of such routers are high cost. The results indicate the feasibility of the
proposed method for this type of application.
1 INTRODUCTION
A wireless mesh network (WMN) can be seen as a
communications network made up of radio nodes
planned in a mesh topology. There are two types of
nodes in WMNs: mesh routers and mesh clients. A
group of mesh routers, connecting to each other
wirelessly constitutes a backbone to serve a set of
mesh clients. A few mesh routers with Internet
connections act as Internet Gateways to pass on the
traffic between the Internet and the WMN. Low cost
design characteristics and fast set up of WMNs is that
make them a cost-effective option to establish
wireless Internet connectivity for mobile users at
anytime and anywhere. These features mainly would
be useful in developing regions or countries,
decreasing costs of deployment and maintenance of
wired Internet infrastructures. The good quality and
operability of WMNs widely depends on placement
of mesh routers nodes in the desired area to achieve
network connectivity, stability and user coverage.
The purpose is to seek an optimal and strong topology
of the mesh network to allow desired services to
clients. But, in a practical deployment of WMN the
purely random node positioning may end up in poor
performance WMN since the final placement could
be far from optimal. Besides, real deployment of
WMNs may need taking into account some
restrictions and features of a specific geographic area
and thus one require to seek different topologies for
distributing mesh routers. As a matter of fact, node
layout is a critical aspect in WMNs. The purpose of
this paper is to deal with the mesh router placement
issue. As such problem is NP hard, a motivation to
solve the mesh router placement problem and seek
optimal solution with suitable performance is to
follow a heuristic approach using evolutionary
techniques involving genetic algorithms including
fuzzy aggregation. The positioning of routers in a
mesh network is not a trivial problem. Several studies
using computational intelligent systems for this
purpose have been carried out by universities and
research centers around the world. (Girgis et al.,
2014) uses a genetic algorithm and simulated
annealing in order to search for a low-cost WMN
configuration with constraints and determine the
number of used gateways.
(Rezaei et al., 2011) proposes a genetic algorithm
in connection with circle packing problem techniques
that consist in packing non-identical circles without
overlap inside the smallest containing circle C. Their
model maximizes network connectivity and coverage
area.
(Praba and Rani, 2013) focus their interest on the
efficient route construction of the networks. The
efficient route can be constructed by choosing the
438
Coelho, P., M. do Amaral, J., Guimarães, K. and Bentes, M.
Layout of Routers in Mesh Networks with Evolutionary Techniques.
DOI: 10.5220/0007739204380445
In Proceedings of the 21st International Conference on Enterpr ise Information Systems (ICEIS 2019), pages 438-445
ISBN: 978-989-758-372-8
Copyright
c
2019 by SCITEPRESS Science and Technology Publications, Lda. All rights reser ved
best neighbor for transmitting the packets. Their
method is designed for finding the route from the
source to the destination nodes using minimum-hop
count.
In this paper, we will use genetic algorithms to
determine the location of routers in a mesh network
in connection with evolutionary techniques
associated with fuzzy aggregation methods. Details of
the modeling are discussed in section 3.
This paper is organized in five sections. The
second section describes the basics of mesh networks.
Section three deals with the modeling of the problem
followed by section four which discusses case studies
in connection with the routers layout problem. Finally
section five ends the paper with the conclusions.
2 MESH NETWORKS BASICS
Wireless Mesh Networks (WMN) can be considered
self-configured and dynamically self-organized, with
the nodes in the network automatically establishing
and maintaining mesh connectivity among
themselves. Wireless Mesh Networks have two types
of nodes: routers and clients. Routers show minimal
mobility and form the backbone of mesh networks.
Multi-hop communication is employed in WMNs and
the gateway/bridge functionalities in routers make
possible the integration of WMNs with several
existing wireless networks such as Internet, Wi-Fi,
cellular, and so on. The structure of a mesh network
resembles the structure of an ad hoc network, where
all the nodes of the network are in the same hierarchy
without a server that manages the whole network.
Basically, a mesh network consists of nodes that use
the offered service - the clients - and by nodes in
charge of transmitting or passing on the information
that will be served by network clients - the Access
Points, or APs, also referred as routers. Routers have
multiple network interfaces and communicate to
maintain network connectivity. They have a small
transmission power and, in general, use multihop
technology, which transmits the desired information
from AP to AP until it reaches the desired client.
These routers have technology for transmitting on
multiple radio channels and can be connected to other
similar devices and are responsible for
communicating the clients to the network. There are
several models and manufacturers of mesh routers in
the market, such as Google wifi, Deco M5 (TPLink),
Eero, Lyra Trio (Asus), Orbi (Netgear), Luma and
LinkSys Velop. Table 1 shows typical signal
transmission power of routers from several
manufacturers. Wireless mesh technology allows
Table 1: Typical routers signal transmission power.
Frequency
Manufacturer|
2,5 GHz
5GHz
Google WIFI
-46 dBm
- 38 dBm
ASUS
-41 dBm
-39 dBm
Luma
-57 dBm
-59 dBm
TPLink
-20 dBm
-23 dBm
networks to be built in areas with large coverage,
where conductive cables are difficult to install and in
locations that are in an emergency situation. Three
standards are usually adopted for wireless mesh
networks - the IEEE 802.16a standard, which covers
WiMAX networks, IEEE 802.11s, better known as
Wi-Fi networks and IEEE 802.15.5, which
correspond to ZigBee networks (Lee et al., 2006). A
survey on WMNs can be found in (Benyamina et al.,
2012). In recent years, a number of university campi
and research centers around the world have developed
and widely used mesh networks such as campus
access networks by users residing in their vicinity.
Examples of pilot mesh wireless mesh networks are
ReMesh in Niterói / RJ-Brazil (Saade et al., 2007),
RoofNet at MIT-USA, Google Mesh in California-
USA, VMesh in Greece, MeshNet at UCSB-USA
(Lundgren et al, 2006), Microsoft Mesh- USA,
among others.
Mesh networking technology is ideal for building
community access networks, allowing Internet access
for those who cannot afford the high costs of a
traditional Digital Subscriber Line (DSL) or cable
broadband connection. Because of this, another
potential use of mesh networks is the construction of
digital cities, providing wireless communication
infrastructure in a metropolitan environment to all
citizens, which has already been carried out in cities
such as Dublin, Taipei, Pittsburgh and Philadelphia.
Wireless mesh technology allows networks to be built
in areas with large coverage, where conductive cables
are difficult to install and in locations that are in an
emergency situation. Three standards are usually
adopted for wireless mesh networks - the IEEE
802.16a standard, which covers WiMAX networks,
IEEE 802.11s, better known as Wi-Fi networks and
IEEE 802.15.5, which correspond to ZigBee
networks (Lee et al., 2006). A survey on WMNs can
be found in (Benyamina et al., 2012). In recent years,
a number of university campi and research centers
around the world have developed and widely used
mesh networks such as campus access networks by
users residing in their vicinity. Examples of pilot
mesh wireless mesh networks are ReMesh in Niterói
/ RJ-Brazil (Saade et al, 2007), RoofNet at MIT-USA,
Google Mesh in California-USA, VMesh in Greece,
Layout of Routers in Mesh Networks with Evolutionary Techniques
439
MeshNet at UCSB-USA (Lundgren et al, 2006),
Microsoft Mesh- USA, among others.
Mesh networking technology is ideal for building
community access networks, allowing Internet access
for those who cannot afford the high costs of a
traditional Digital Subscriber Line (DSL) or cable
broadband connection. Because of this, another
potential use of mesh networks is the construction of
digital cities, providing wireless communication
infrastructure in a metropolitan environment to all
citizens, which has already been carried out in cities
such as Dublin, Taipei, Pittsburgh and Philadelphia.
To perform the geographic configuration of the
routers in a network we must take into account some
aspects of the network, for example:
- Composition
· Homogeneous: all routers have the same feature.
· Heterogeneous: composed of different routers.
- Organization
· Flat: networks without grouping.
· Hierarchical: networks with clusters
- Distribution
· Regular: nodes are evenly distributed in the
monitoring area.
· Irregular: nodes are distributed randomly in the
monitoring area.
The coverage area of a router is specified by the
manufacturer and can be calculated as the area of a
circle, where R is the coverage radius of the router, as
shown in Figure 1a. Figure 1b shows an example of
coverage area.
Figure 1: a) Coverage radius of a Router; b) Example of a
coverage area.
Figure 2: (a) Routers in regular distribution; b) Routers in
irregular distribution.
The coverage area is closely linked to the way the
routers are distributed in the area. Figure 2 shows two
examples of routing distribution in the coverage area.
3 PROPOSED MODEL
The core model used for solving the mesh router
placement is based on genetic algorithms. The genetic
algorithm (GA) is inspired by biological evolution, as
it makes use of a selection of individuals, uses genetic
operators and operates in a random and oriented way,
seeking an optimal solution within a population. The
main application of genetic algorithms is in
optimization problems with very large or complex
search spaces, which makes the use of traditional
techniques unfeasible. In the case of the search
method, a comparison is made between the evolution
of the species and the problem in question a
population of individuals (possible solutions)
identified by chromosomes, are evaluated and
associated with an aptitude and subjected to a process
of evolution, through selection and reproduction, for
several generations. Aptitude is the quality of its
results, in relation to the transfer of aptitude, the
crossing is modeled by an operator called crossover
and adaptive modifications are modeled by mutation
operators. Statistically, over several generations, the
results tend to converge to the fittest results. The
typical flowchart of a GA is shown in Figure 3.
Figure 3: Typical flowchart of a Genetic Algorithm.
The objective or fitness function is defined based
on the specification of the problem and is
fundamental to a successful implementation. In
general, the objective function involves only a single
criterion. However, most of the real problems involve
more than one objective to be considered, so the
ICEIS 2019 - 21st International Conference on Enterprise Information Systems
440
objective function must use methods for converting a
measure of vector fitness into a scalar one(Davis,
1990).The general GA parameters influence its
performance and can be used to establish a stopping
criterion for executing the algorithm. Such
parameters include population size, maximum
number of generations and operator application rate.
The choice of parameters must meet the established
empirical criteria or the specific characteristics of the
specific problem.
In order to carry out case studies with multiple
objectives in genetic algorithms we can use fuzzy
aggregation methods.
3.1 Fuzzy Aggregation Methods
The use of fuzzy systems makes it possible to
simultaneously evaluate all the objectives, integrating
the preferences of the user in relation to each
objective and to each situation. This feature is a good
advantage over Pareto optimality multi-objective
methods, since it does not require user interference to
choose the best solution at the end of the process,
since preferences or specifications are inserted before
evolution in a more simple and interpretable fashion
through fuzzy logic and thus the process of evolution
is guided in the direction of pre-established
preferences. Each individual in the GA population
represents a possible solution to the problem. During
the evaluation process, individuals are applied to the
function or model that describes the problem and the
results obtained in relation to each objective are used
as inputs to the fuzzy system. For each individual of
the population the fuzzy aggregation method is
applied yielding a single fitness value. Figure 4
illustrates the evaluation model using the Fuzzy
Aggregation method. The rates of selection
operations, crossover, mutation on the current
population, population size and the maximum number
of generations are defined by the designer before the
start of the algorithm.
The evolution ends when a certain stop criterion
is reached. The most frequent stopping criterion is
specified by a certain maximum number of
generations. Another possibility is to establish an
aptitude value to be reached or stop the execution of
the algorithm when there is no evolution for a certain
number of generations. After the evaluation of all
individuals of the current generation, the genetic
algorithm continues the evolution process.
The fuzzy aggregation system has the normal
operation of a fuzzy inference system. Each input of
the system corresponds to an objective and the
membership functions have triangular or trapezoidal
Figure 4: Evaluation model with Fuzzy aggregation.
Figure 5: GA model with Fuzzy aggregation.
format. The genetic algorithm used in this paper
follows the model presented in Figure 5 in the
traditional way, until the evaluation of the next
generation, where the evaluation process through the
fuzzy aggregator is again executed for all individuals,
until the stopping criterion is reached.
The rules of the fuzzy aggregator are elaborated in
order to meet the preferences required for the problem
considering each objective.
4 CASE STUDIES
The case studies considered in this paper consist of
positioning routers for a mesh network to be used for
data acquisition in an agricultural environment of size
50m x 50m. All use Matlab Fuzzy Toolbox.
The first study consists of using a traditional
genetic algorithm, with a single objective. The goal is
to position the routers so that each monitoring point
in the field is covered by at least one router.
The second study considers that there are areas in
the field with a higher installation cost. To do so, we
discard areas of the field where the cost for the
installation of routers is high. In this way the
application uses a genetic algorithm together with a
Layout of Routers in Mesh Networks with Evolutionary Techniques
441
Fuzzy aggregation method to carry out a multi-
objective study where it is desired to position routers
so that each monitoring point in the field coverage
area must be in contact with at least one low cost
router.
4.1 First Case Study
The environment of this first case study is an
agricultural area of 2500m², where the spatial
distribution of the routers must be carried out. In this
environment it is necessary that each monitoring
point reaches at least one router. The device
responsible for monitoring has a range of 13 meters.
The organization of the routers is flat (no
clustering), homogeneous (all routers have the same
characteristic) and irregular. In order to achieve these
objectives a traditional single-target genetic
algorithm is used. The 16 monitoring points are
positioned in the area, as shown in figure 6.
Figure 6: Monitoring points (16).
Several tests were carried out changing the values
of the parameters of the genetic algorithm and it was
observed that the parameters presented in table 2
below have met the expectations of solutions to the
problem. Figure 7 shows the curve of the best
individual and the average of the population. It can be
noticed that the best individual reached the maximum
aptitude around the 120th generation and the average
followed this evolution.
Figure 8 shows the location of the monitoring
points and the positioning of the routers for the best
individual which was achieved by the GA.
The green square in figure 8 represents the area
(50m x 50m), the smaller blue circles are the
monitoring points and the larger blue circles represent
the area each of the routers are covering, and the "x"
in red are the routers.
Table 2: Parameters of the GA for case study 1.
Parameters
Values
Number of
generations
200
Search Region
-25 25; -25 25
Precision
50 cm
Population
300 individuals
Fitness
Number of Monitoring Coverage points
Selection
Geometric Normalization of 5%
Crossover Rate
80%
Mutation Rate
1%
Figure 7: Best individual (Red) and average (Blue).
Figure 8: Best individual positioning for the first case study.
It can be seen that the routers were positioned
meeting the established criterion, since each
monitoring point is being covered by a router.
This first study did not take into account
differences in the cost of installing the routers in
relation to the most difficult access areas.
Considering that cost is something that is important
to be reduced in the majority of the projects, in mesh
-25
-20
-15
-10
-5
0
5
10
15
20
25
Position x
-25
-20
-15
-10
-5
0
5
10
15
20
25
Position
y
Positioning of the monitoring points in the coverage region
ICEIS 2019 - 21st International Conference on Enterprise Information Systems
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networks would not be different. Therefore, the
proposal of the second case study is to carry out the
configuration of the network taking into account the
installation costs.
4.2 Second Case Study
One way to reduce the cost of a mesh network is to
define the minimum amount of routers needed to
cover an area without positioning routers in places
where the cost of installation is high.
As in the first case study, the environment of this
second case study is an agricultural area of 2500 m²,
where the spatial distribution of the routers must be
carried out. The device responsible for the monitoring
has a range of 13m and the organization of the routers
is flat i.e. no grouping, homogeneous (all routers have
the same characteristic) and irregular.
For this scenario it is necessary that:
each monitoring point reaches at least one
router;
the routers are not positioned in places where the
installation cost for them is high.
Therefore, we have a multi-objective problem: to
cover the area and reduce costs.
To achieve these objectives a genetic algorithm is
used together with a fuzzy aggregation scheme.
The developed fuzzy system is of Mamdani type,
characterized by being simpler and more interpretable
than TSK type systems, and all the rules have the
same degree of importance, i.e., weights equal to one.
The fuzzy aggregation system has two inputs:
"number of monitoring points served" and "cost". Its
output is the "fitness" that receives an evaluation
between 0 and 10. The defuzzification method is the
average of the maximums. Figure 9 shows the
fuzzy aggregation parameters used in this case study.
Figure 10 shows the membership function of the
input "Number of Monitoring Points Served".
Figure 11 illustrates the membership function of
the cost.
In figure 12 one can see the membership function
of the fuzzy aggregation system output fitness.
The rules of the Fuzzy Aggregator are as
follows:
• 1. If (NumMPattended is low) and (Cost is low)
then (Fitness is bad)
• 2. If (NumMPattended is low) and (Cost is
medium) then (Fitness is bad)
3. If (NumMPattended is low) and (Cost is high)
then (Fitness is bad)
Figure 9: Fuzzy aggregation system parameters.
Figure 10: Membership function of the input - number of
monitoring points served.
Figure 11: Membership function of the input - cost.
Figure 12: Membership function of the fuzzy aggregation
system output - fitness.
• 4. If (NumMPattended is medium) and (Cost is
low) then (Fitness is bad)
• 5. If (NumMPattended is medium) and (Cost is
medium) then (Fitness is bad)
• 6. If (NumMPattended is medium) and (Cost is
medium) then (Fitness is bad)
Low
Medium
High
Low
Medium
High
Medium
Good
Bad
Layout of Routers in Mesh Networks with Evolutionary Techniques
443
7. If (NumMPattended is high) and (Cost is low)
then (Fitness is good)
8. If (NumMPattended is high) and (Cost is
medium) then (Fitness is medium)
9. If (NumMPattended is high) and (Cost is
high) then (Fitness is bad)
The parameter NumMPattended is the number of
monitoring points attended.
Several tests were performed by changing the
values of the parameters of the genetic algorithm and
it was observed that the ones presented in table 3 have
met the expectations of solutions to the problem.
Table 3: Parameters of GA for case study 2.
Parameters
Values
Number of
generations
200
Search Region
-25 25; -25 25
Precision
50 cm
Population
300 individuals
Fitness
Fuzzy aggregation
Selection
Geometric Normalization of 5%
Crossover Rate
80%
Mutation Rate
1%
Figure 13 shows the area, the location of the
monitoring points, and the high-cost installation
regions of routers, regions in which the genetic
algorithm should avoid positioning the routers.
Figure 13: Monitoring points and high cost areas in red for
case study 2.
Figure 14 shows the curve of the best individual
and the mean of the population. From the graphs it
can be seen that the best individual reached the
maximum fitness around the 60th generation and the
mean followed this evolution.
Figure 14: Best and average individual for case study 2.
Figure 15 shows the location of the monitoring
points and the best positioning of the routers for case
study 2.
Figure 15: Best individual positioning for case study 2.
The green square of the figure 15 represents the
coverage area (50m x 50m), the smaller blue circles
are the monitoring points, the larger blue circles
represent the area each of the routers are covering.
The x in red are the routers and the squares in red are
the regions of the area where the cost for installing
routers is high. In the same figure it can be seen that
the routers were positioned according to the
established criteria, since each monitoring point is
being covered by a router and no router was
positioned in the area where the installation cost is
high.
It can also be observed that, with the restriction of
positioning of routers in areas of greater cost, it was
necessary to use one more router to cover the area,
yieldind five routers. Such additional cost of routers
obviously must compensate for the installation of a
router rather than higher cost.
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The results obtained in the simulations fulfilled its
objectives of determining the positioning of routers in
mesh networks.
5 CONCLUSIONS AND FUTURE
WORK
In this paper, two case studies were presented with
applications in mesh networks, whose objective is the
optimization of the positioning of routers in a field
scenario with automation for data acquisition. In the
first case study, with one variable, a genetic algorithm
was used that resulted in satisfactory solutions. In the
second case study, a fuzzy-genetic hybrid
evolutionary technique was applied to a multi-
objective problem, in which the cost variable was
included in the routing question.
For future work in mesh networks it is expected
the inclusion of new targets for the fuzzy aggregation
system and possibly the design of a chromosome of
variable size in the GA modeling may be investigated
so that the evolution can also determine the number
of routers suitable for the field coverage. A
benchmark problem would be useful to compare
different approaches and a way to interpret the results
based on different objectives defined for each
approach proposed by several researchers.
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