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

 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

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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

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

Position x

-25

-20

-15

-10

-5

Position

Positioning of the monitoring points in the coverage region

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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

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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

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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