ACO FOR OPTIMAL SENSOR LAYOUT

Stefka Fidanova

, Pencho Marinov

and Enrique Alba

Institute for Parallel Processing, Bulgarian Academy of Science, Acad. G. Bonchev str. bl.25A, 1113 Soﬁa, Bulgaria

E.T.S.I. Informatica, Grupo GISUM (NEO), University of Malaga, Malaga, Spain

Keywords:

ACO, Wireless sensor networks.

Abstract:

Metaheuristic methods have frequently been applied to telecommunication problems in the last years. One of

these problems is Wireless Sensor Network (WSN) layout, which is an NP-hard optimization problem. The

sensors sent their sensing results to a special station called the High Energy Communication Node (HECN).

The sensing area of the WSN is the union of the individual sensing areas of the nodes. When deploying

a WSN, the major objective is to achieve full coverage of the terrain (sensor ﬁeld). Another objectives are

also to use a minimum number of sensor nodes and to keep the connectivity of the network. In this paper

we address a WSN layout problem in which full coverage and connectivity are treated as constraints, while

objective function is the number of the sensors. To solve it we propose Ant Colony Optimization (ACO)

algorithm. The terrain is modeled with 500 × 500 points grid and both sensing radius and communication

radius are set to 30. We compare our results with existing evolutionary algorithms.

1 INTRODUCTION

Telecommunications are an important symbol of our

present information society. Telecommunication is a

ﬁeld in which many open research lines are challeng-

ing the research community. Nowadays, the trend in

telecommunication networks is having highly decen-

tralized, multi-node networks. From small, geograph-

ically close, size-limited local area networks the evo-

lution has led to the huge worldwide Internet. This

same path is followed by wireless communications,

where we can already see wireless telephony reach-

ing virtually any city in the world. In this context

WSN have recently become a hot topic in research.

A WSN allows an administrator to automatically and

remotely monitor almost any phenomenon with a pre-

cision unseen to the date. The use of multiple small

cooperative devices yields a brand new horizon of

possibilities yet offers a great amount of new prob-

lems to be solved. WSN have so far been employed

in military activities such es reconnaissance, surveil-

lance, and target acquisition (Deb et al., 2000), en-

vironmental activities such as forest ﬁre prevention,

geophysical activities such as volcano eruptions study

(Werner-Allen et al., 2006), biomedical purposes such

as health data monitoring (Yuce et al., 2007) or civil

engineering (Paek et al., 2004).

When deploying a WSN, the positioning of the

sensor nodes becomes one of the major concerns. The

coverage obtained with the network and the economic

cost of the network depend directly of it. Since many

WSN can have large numbers of nodes, the task of

selecting the geographical positions of the nodes for

an optimally designed network can be very complex.

Therefore, metaheuristics seem an interesting option

to solve this problem.

In this paper we propose a solution method for

the WSN layout problem using ACO. We focus on

minimizing the number of nodes, while the full cov-

erage of the network and connectivity are considered

as constraints.

Jourdan (Jourdan, 2000) solved an instance of

WSN layout using a multiobjectivegenetic algorithm.

In there formulation a ﬁxed number of sensors had

to be placed in order to maximize the coverage. In

(Molina et al., 2008) are proposed several evolution-

ary algorithms to solve the problem.

For solving the WSN layout problem, the cover-

age has to satisﬁed some restrictions and the biggest

possible coverage will be preferred: the number of

sensor nodes should be kept low for economical rea-

sons and the network needs to be connected.

The rest of the paper is organized as follows. In

Section 2 the WSN is described and the layout prob-

lem is formulated. Section 3 presents the ACO algo-

rithm. In Section 4 the experimental results obtained

Fidanova S., Marinov P. and Alba E..

ACO FOR OPTIMAL SENSOR LAYOUT.

DOI: 10.5220/0003057600050009

In Proceedings of the International Conference on Evolutionary Computation (ICEC-2010), pages 5-9

ISBN: 978-989-8425-31-7

 2010 SCITEPRESS (Science and Technology Publications, Lda.)

are shown. Finally, several conclusions are drown in

Section 5.

2 PROBLEM FORMULATION

A Wireless Sensor Network is a wireless network

formed by sensor nodes. Each sensor node sens an

area around itself called its sensing area. A parameter

called sensing radius determines the sensitivity range

of the sensor node and thus the sensing area. The

nodes communicate among themselves using wireless

communication links. These links are determined by

a communication radius. A special node in the WSN

called High Energy Communication Node (HECN) is

responsible for external access to the network. There-

fore, every sensor node in the network must have

communication with the HECN. Since the communi-

cation radius is often much smaller than the network

size, direct links are not possible for peripheral nodes.

A multi-hop communication path is then established

for those nodes that do not have the HECN within

their communication range.

The WSN layout problem amounts to deciding the

geographical position of the sensor nodes that form

a WSN. In our formulation, a non-ﬁxed amount of

sensor nodes has to be placed in a terrain providing

full sensitivity coverage. The positions of the nodes

have to be chosen in a way that minimizes the total

number of sensor nodes, while keeps the connectivity

of the network.

The WSN operates by rounds: In a round, ev-

ery node collects the data from its measurements and

sends it to the HECN. Every node transmits the infor-

mation packets to the neighbor that is closest to the

HECN, or the HECN itself if it is within the commu-

nication range. The sensing area of the WSN is the

union of the individual areas of all nodes. The de-

signer wants the network to cover the complete sens-

ing area. On the other hand, the number of sensor

nodes must be kept as low as possible, since using

many nodes represents a high cost of the network,

possibly inﬂuences of the environment and also pro-

vokes a probability of detection (when stealth moni-

toring is designed). The objective of this problem is

to minimize the number of sensors deployed while the

area is fully covered and connected.

3 ANT COLONY OPTIMIZATION

FRAMEWORK

Many of the existing solutions to this problem come

from the ﬁeld of Evolutionary Computation (Alba and

Molina, 2008; Molina et al., 2008). After analyz-

ing them, we noticed that these interesting develop-

ments are quite similar to ACO algorithms. The re-

lation between ACO algorithms and evolutionary al-

gorithms provides a structural way of handling con-

strained problems. They have in common the use of

a probabilistic mechanisms for recombination of in-

dividuals. This leads to algorithms where the popula-

tion statistics are kept in a probability vector. In each

iteration of the algorithm, these probabilities are used

to generate new solutions. The new solutions are then

used to adapt the probability vector.

Real ants foraging for food lay down quantities

of pheromone (chemical cues) marking the path that

they follow. An isolated ant moves essentially guided

by an heuristic function and an ant encountering a

previously laid pheromone will detect and decide to

follow it with high probability thus taking more in-

formed actions based on the experience of previous

ants (and thereby reinforce it with a further quantity

of pheromone). The repetition of the above mecha-

nism represents the auto-catalytic behavior of real ant

colony where the more the ants followa trail, the more

attractive that trail becomes.

The ACO algorithm uses a colony of artiﬁcial ants

that behave as cooperative agents in a mathematic

space were they are allowed to search and reinforce

pathways (solutions) in order to ﬁnd the optimal ones.

The problem is represented by graph and the ants

walk on the graph to construct solutions. The so-

lution is represented by a path in the graph. After

initialization of the pheromone trails, ants construct

feasible solutions, starting from random nodes, then

the pheromone trails are updated. At each step ants

compute a set of feasible moves and select the best

one (according to some probabilistic rules based on a

heuristic guided function) to carry out the rest of the

tour. The structure of ACO algorithm is shown in Fig-

ure 1. The transition probability p

, to chose the node

j when the current node is i, is based on the heuristic

information η

and on the pheromone trail level τ

of the move, where i, j = 1, . . . . ,n.

∑

k∈allowed

(1)

The higher value of the pheromone and the heuris-

tic information, the more proﬁtable is to select this

ICEC 2010 - International Conference on Evolutionary Computation

move. In the beginning, the initial pheromone level

is set to a small positive constant value τ

and then

ants update this value after completing the construc-

tion stage (Bonabeau et al., 1999). ACO algorithms

adopt different criteria to update the pheromone level.

Ant Colony Optimization.

Initialize number of ants;

Initialize the ACO parameters;

while not end-condition do

for k=0 to number of ants

ant k starts from a random node;

while solution is not constructed do

ant k selects higher probability node;

end while

end for

Local search procedure;

Update-pheromone-trails;

end while

Figure 1: Pseudocode for ACO.

In our implementation we use MAX-MIN Ant

System (MMAS) (Stutzle and Hoos, 2000), which is

one of the more popular ant approaches. The main

feature of MMAS is using a ﬁxed upper bound τ

max

and a lower bound τ

min

of the pheromone trails. Thus

the accumulation of big amounts of pheromone by

part of the possible movements and repetition of same

solutions is partially prevented. The main features of

MMAS are:

• Strong exploration to the space search of the best

found solution. This can be achieved by only al-

lowing one single ant to add pheromone after each

iteration (the best one).

• Wide exploration of the best solution. After the

ﬁrst iteration, the pheromone trails are reinitial-

ized to τ

max

. In the next iteration, only the move-

ments that belong to the best solution receive a

pheromone, while the rest pheromone values are

only evaporated.

The aim of using only one solution is to make the

solution components, which frequently occur in the

best found solutions, get a larger reinforcement. The

pheromone trail update rule is given by:

← ρτ

+ ∆τ

, (2)

∆τ







1/C(V

best

) if (i, j) ∈ best solution

0 otherwise

Where V

best

is the iteration best solution and i, j =

1,...,n, ρ ∈ [0,1] models evaporation in the nature.

To avoid stagnation of the search, the range of pos-

sible pheromone values on each movement is lim-

ited to an interval [τ

min

,τ

max

]. τ

max

is an asymptotic

maximum of τ

and τ

max

= 1/(1 − ρ)C(V

∗

), while

min

= 0.087τ

max

. Where V

∗

is the optimal solution,

but it is unknown, therefore we use V

best

instead of

∗

The WSN layout problem is represented by graph

as follows: the terrain is modeled by grid G =

}

N×M

; the pheromone is related with location

sites Ph = {ph

}

N×M

, the initial pheromone can be

a small value, for example 1/n

ants

. The central point,

where the HECN is located, is included in the solu-

tions like ﬁrst point (zero point). Every ant starts to

create the rest of the solution from a random node

which communicates with central one, thus the differ-

ent start of every ant in every iteration is guaranteed.

The ant chooses the next position by the ACO prob-

abilistic rule (equation 1). It choses the point having

the higher probability.

The used heuristic information is

(t) = s

(1− b

), (3)

where s

is the number of points which the new sen-

sor will cover, and



1 if communication exists

0 if there is not communication

(4)

b is the solution matrix and the matrix element

= 1 when there is sensor on this position other-

wise b

= 0. With s

we try to locally increase the

covered points, with l

we guarantee that all sensors

will be connected; with rule (1 − b

) we guarantee

that the position is not chosen yet. When p

= 0 for

all values of i and j the search stops. Thus, the con-

struction of the solution stops if no more free posi-

tions, or all points are covered or new communication

is impossible.

4 EXPERIMENTAL RESULTS

In this work we solve an WSN problem instance

where a terrain of 500 × 500 meters has to be cov-

ered using nodes with coverage and communication

radii equal to 30 meters. An example of solution that

achieves full coverage of the region is a square grid

formed by the sensors separated by 30 meters.Thus,

the number of sensors is 289 including the HECN.

This result is used for comparison. We apply MAX-

MIN ant algorithm with the following parameters:

ACO FOR OPTIMAL SENSOR LAYOUT

α = β = 1, ρ = 0.5, the number of used ants is 3 and

the maximum number of iterations is 10. In Table 1

are reported best found results (minimal number of

sensors) achieved by several metaheuristic methods.

We compare our ACO algorithm results with results

obtained by the evolutionary algorithms in (Molina

et al., 2008) and the symmetric solution.

Table 1: Experimental results.

Algorithm sensors

Symmetric 289

MOEA 260

NSGA-II 262

IBEA

265

ACO 232

We observe that the ACO algorithm outperforms

the symmetric and the evolutionary algorithms. We

perform 30 independent runs of the ACO algorithm

and the achieved numbers of sensors are in the in-

terval [232,247]. The ACO algorithm outperforms

the evolutionary algorithms, because the worst found

number of sensors by ACO is less than the best found

by the evolutionary algorithms.

The ACO solution is represented on Figure 2.

With black dots are represented the sensors and with

the rings are represented the coverage and connectiv-

ity area by a sensor. We can observe there the cover-

age of the region, positioning of the sensors and con-

nectivity of the network.

Figure 2: ACO solution.

5 CONCLUSIONS

We have deﬁned a coverage problem for wireless sen-

sor networks with its connectivity constraint. A very

large instance consisting of 500 × 500 square meter

area has to be covered using sensors nodes whose

sensing and communication radii are 30 meters. We

propose ACO algorithm to solve this problem and

we compare it with existing evolutionary algorithms.

The ACO algorithm outperforms the evolutionary al-

gorithms. The worst found solution by ACO is bet-

ter than the best found solution by evolutionary al-

gorithms. In a future work we plane to redeﬁne the

problem so as to be able to solve more complex WSN

layout problem with regions in a sensing area where

to put sensors is forbidden and network problem with

obstacles. Other interesting direction is to study the

robustness of the solutions, to minimize the distur-

bance in the network when single sensor fail and thus

to avid segmentation of the network.

ACKNOWLEDGEMENTS

This work has been partially supported by the Bul-

garian National Scientiﬁc Fund under the grants

”Modeling Processes with ﬁxed development rules”

DID 02/29 and ”Effective Monte Carlo Methods

for large-scale scientiﬁc problems” DTK 02/44, and

by Spanish Ministry of Science and Innovation

and FEDER under contract TIN2008-06491-C04-

01 (M-project, http://mstar.lcc.uma.es). It has also

been partially funded by the Andalusian Government

under contract P07-TIC-03044 (DIRICOM project,

http://diricom.lcc.uma.es).

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ACO FOR OPTIMAL SENSOR LAYOUT