An EVEBO-Based BTS Localization Algorithm
Koorosh Navi, Manoochehr Kelarestaghi and Farshad Eshghi
Electrical & Computer Eng. Dept., Kharazmi University, 15719-14911 Tehran, Iran
Keywords:
BTS Localization, EVEBO, Election Inspired, Evolutionary Algorithm, Meta-Heuristics, NP-Hard.
Abstract:
In this paper, we use EVEBO, an election-inspired optimization algorithm, to solve the BTS (i.e. transceiver)
localization problem. The proposed method tries to solve the classic and very important problem of achieving
maximum coverage with minimum number of BTSs in a specified geographical area. It also tries to reduce the
over-coverage rate, one of the undesirable phenomena in cellular networks. The EVEBO’s merit in solving
the problem is measured by a common fitness function, and speed of convergence. Simulation results show
that EVEBO solves the problem in much less number of evaluations compared to the best results reported in
the literature for square-coverage transceivers. We also show that it can be used in a scenario involving more
challenging non-square-coverage (almost circular) transceiver type with satisfactory results.
1 INTRODUCTION
Optimization problems are one of the most common
problems in science and engineering. Achieving the
exact solution, in too many cases, is almost impos-
sible due to the high complexity and multiplicity of
dimensions of the problem in hand. So, solving the
problem comes down to searching for the best possi-
ble solution.
NP-hard problems, Mathematical Programming,
Regression Analysis, and etc are different types of op-
timization problems. (Luke, 2009)
NP-hard problems are the ones we try to solve by
searching for and finding the optimum solution(s) and
not necessarily the exact one, because of the inher-
ent complexity involved. Adding more dimensions
to a problem, makes it harder to solve (Luke, 2009).
Therefore, researchers try to devise new algorithms
and techniques regularly, in hope of solving them
nicely.
Some of the most popular methods to solve NP-
hard problems, particularly those involve multiple so-
lutions, are Evolutionary Algorithms (EA), which try
to evolve a population of individuals (solutions) by it-
erative execution of a set of simple operations. They
do this based on a fitness function that shows how
much an individual in population is adequate. The
operation will continue until a termination condition
is satisfied (Eiben, 2003).
EAs are a subset of a more general category called
Meta-Heuristics, which try to find better and better
solutions by using simple search mechanisms in the
problem’s defined search space, based on the evo-
lution of a population of solutions (Bianchi et al.,
2009). Genetic Algorithm (GA), Evolution Strategy
(ES), Evolution Programming (EP), and Genetic Pro-
gramming (GP) technique (Beyer, 2013) and other
population-based methods such as: Differential Evo-
lution (DE) (Simon, 2013), and Swarm intelligence
algorithms like Particle Swarm optimization (PSO),
and Ant Colony are the most common evolutionary
algorithms (Yu and Gen, 2010).
Ever-increasing wireless devices usage has made
the optimization problem of estimating the number of
base transceiver stations (BTSs) in an area very rele-
vant (called BTS localization). In this kind of prob-
lems, the goal is to find the location of the transceivers
in a specified area that ensures maximum coverage
with minimum number of units. Due to its NP-
hard complexity nature (Vega-Rodr
´
ıguez et al., 2007),
most of the BTS localization solutions in the literature
are meta-heuristic-based algorithms. In this work,
we employ EVolutive-Election Based Optimization
(EVEBO), a most recently devised evolutionary algo-
rithm, to solve the similar problem due to its capabil-
ity in solving large-size(dimension) problems and its
low dependency on initial problem parameters values.
We will show that our new proposed method
which uses EVEBO algorithm on binary representa-
tion space can find the optimum solution in a accept-
able evaluation numbers (computational efforts) and
also shows better result in some competitions. Be-
Navi K., Kelarestaghi M. and Eshghi F.
An EVEBO-Based BTS Localization Algorithm.
DOI: 10.5220/0006500902650272
In Proceedings of the 9th International Joint Conference on Computational Intelligence (IJCCI 2017), pages 265-272
ISBN: 978-989-758-274-5
Copyright
c
2017 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
sides that we will try to minimize over-coverage rate
(coverage overlap), one of the unpleasant parameters
in this issue.
It should be mentioned that we consider this prob-
lem as a permutation NP-hard (which based on a bi-
nary representation) issue and thus we try to find the
optimum solution regardless of considering any spe-
cial telecommunication parameters.
The rest of this paper is organized as follows. In
the next section, the motivation of authors regard-
ing solving this classic problem will be expressed.
Thereafter, some relevant works are briefly explained.
A short description of EVEBO algorithm come in
section 4. Application of the EVEBO along with
some adaptations towards the BTS localization prob-
lem will be introduced in section 5. Simulation results
and comparisons against other meta-heuristic meth-
ods appear in section 6. Concluding remarks are men-
tioned in the last section.
2 MOTIVATION
Increasing mobile usage in the daily life necessitates
more wireless coverage. Accordingly, one of the most
challenging optimization problems in recent years,
and years to come, is to estimate the minimum re-
quired number of BTSs and their locations for a max-
imum coverage in a specific geographical area.
Regarding maximizing the coverage area, speci-
fying the locations of a set of BTSs is an NP-hard
optimization problem (Vega-Rodr
´
ıguez et al., 2007).
Moreover, looking at the problem as to select the lo-
cations of BTSs from all possible locations, makes
this problem to be seen as a permutation optimization
problem.
We believe that EVEBO, a recently introduced
election-inspired evolutionary algorithm, is a good
candidate for solving this kind of problems due to its
distributed nature and low sensitivity to initial values
of problem parameters.
3 RELATED WORKS
Solving BTS localization problem will lead to deter-
mination of a set of optimal BTS locations in a ge-
ographical area ensuring a satisfactory coverage (not
necessarily a total coverage) with minimum number
of transceivers.
Find a set of optimized BTS locations in a radio
network design using a distributed steady state (GA)
in (Alba, 2004) is one of the first EA-based efforts for
solving the problem.
Another radio network design by some meta-
heuristics approaches such as GA, DE, PBIL
(Population-Based Incremental Learning) which is a
combination of GA and competitive learning, CHC
(it is similar to EAs but with no mutation), and Sim-
ulated Annealing (SA) were introduced in (Vega-
Rodr
´
ıguez et al., 2007). These methods try to achieve
the maximum coverage with minimum number of
square-coverage BTSs, without considering the over-
coverage in their fitness functions. Simulation results
show that PBIL, SA and CHC have obtained the opti-
mal fitness function value (with full coverage), while
DE gives better convergence speed performance (less
evaluations). (Cal
´
egari et al., 1997) tried to solve
the problem by proposing a parallel island-based GA
wherein the population of solutions are distributed
over some workstations called islands.
There are other related works that try to find ade-
quate solutions by considering specific telecommuni-
cation factors such as signal strength, power level at
specified locations, and etc. Amongst them, a global
optimization for multiple transmitter locations is pro-
posed by (Nelson et al., 2006) which uses particle
swarm optimization to find the transmitter locations.
It tries to minimize the difference between the true
received power, measured by a set of sensor nodes
in the specified area, and the estimated power with
considering initial smart clustering conditions. An
Expectation-Maximization (EM) technique for locat-
ing multiple transmitters, based on power levels ob-
served by a set of arbitrarily-placed receivers, is pro-
posed by (Nelson and Gupta, 2007). Finally, (Nelson
et al., 2009) proposes a quasi EM method for estimat-
ing multiple transmitter locations based on received
signal strength measurements by a sensor network of
randomly located receivers in the area. Simulation re-
sults show its outperformance compared to methods
presented by (Nelson et al., 2006) and (Nelson and
Gupta, 2007).
4 EVEBO: EVOLUTIVE
ELECTION-BASED
OPTIMIZATION
One of the most recent meta-heuristic evolutionary
algorithms is EVEBO which was inspired by man-
kind electoral systems and was modified for becom-
ing capable of solving some optimization problems
(Pourghanbar et al., 2015). The idea of EVEBO is
based on a common society feature, called collective
behaviour, which uses the aggregation of human opin-
ions to determine a winner person(s) over a number
of nominated candidates, through an official election.
Similar to other EAs, EVEBO starts with a popula-
tion of initial individuals (non-optimized solutions) in
a problem-specific defined search space called Belief
Space (BS). The individuals are sorted using a fitness
function values. Some better solutions are marked
as candidates and each of the remaining individu-
als moves towards each candidate inversely related to
their inter-distance in the BS (campaign). Then, each
individual votes for its closest candidate(s) in the BS.
The candidate(s) (solution(s)) with the highest num-
ber of votes is(are) elected as the winner(s). In the
next step, the post-election, each winner moves to-
wards his fans (individuals who voted for him) and
other non-fan individuals. The whole process com-
prising campaign, voting, and post-election steps is
considered one epoch of running EVEBO. The above
cycle continues until a termination condition is satis-
fied. A brief description of how EVEBO transforms a
real life election phenomenon into a tool for solving
an optimization problem is illustrated in Figure 1.
Figure 1: Election entities correspondence between real life
election and EVEBO.
EVEBO evaluation steps are described as follows.
•· INITIALIZATION. A population of initial solu-
tions will be generated randomly with respect to
the predefined conditions for problem in hand.
•· UTILITY MATRIX. All evolutionary algorithms
involve some stochastic(Simon, 2013). In
EVEBO, each individual in the population has
a probabilistic parameter called Utility Matrix
(UM). The number of rows in UM is equal to
the number of solutions in the population and
the number of its columns is equal the dimension
of solutions. UM elements are randomly gener-
ated [0, 1] at the beginning of each evaluation.
Each element of the UM determines the probabil-
ity with which modifications in the corresponding
element of the solution takes place (for more de-
tails see (Pourghanbar et al., 2015)).
•· ELECT ORAL SYSTEM SELECTION. In this
step, an electoral system will be randomly
selected from those systems which are suited,
in terms of modality (uni-modal (one optima)
or multi-modal (more than one optima)), to the
specific problem in hand. For uni-modal prob-
lems which is our interest herein, we randomly
select one from FPTP (First Past the Post), TRS
(Two-Round System), and IRS (Instant-Runoff
System) electoral systems described in Figure 2.
Figure 2: Electoral systems suited to problems seeking one
optimal solution (uni-modal).
•· ELECT ORAL LEGISLATIONS. Based on the na-
ture of the problem, some pre-defined conditions
should be verified and enforced on solutions. For
instance, those individuals which are not valid
based on our problem conditions are removed and
replaced by another random ones (to ensure that
the population size remains fixed).
•· SETTING CANDIDATES AND CAMPAIGNING.
After selecting the electoral system, the number
of candidates will be determined according to the
population size. The candidates will be selected
based on their fitness values. Then, as a result
of campaigning, each non-candidate individual
will be affected by its nearest (in distance)
individual, and its corresponding solution is
updated according to their fitness values. Finally,
for each candidate, a Gaussian Impact Function
(GIF) of distance is calculated. All non-candidate
individuals are updated based on these GIF
values.
•· VOTING. Each individual votes for the nearest
candidate(s). The candidate(s) with the highest
number of votes is(are) selected as the winner so-
lution(s) in this evaluation.
•· POST-ELECTION. Because the winner solution(s)
is(are) not necessarily the optimum one(s), so, in
this step, the winner solution(s) is(are) updated
according to its(their) distance(s) from all other
individuals.
As mentioned before, solution update in this algo-
rithm is stochastic and based on a utility matrix. Also,
EVEBO employs a tolerance parameter which con-
trols the solution progress in evaluations (Tolerance
in Figure 1).
The flowchart of Figure 3 illustrates the imple-
mentation of EVEBO.
Figure 3: EVEBO’s functional flowchart (Pourghanbar
et al., 2015).
5 BTS LOCALIZATION USING
EVEBO
In this work, we use EVEBO to solve BTS-
localization problem with some modification in the
original algorithm. First we try to estimate the
square-coverage BTS locations in a discretized area
aiming at maximum coverage with minimum num-
ber of transceivers. To be more realistic, thereafter,
we solve the problem for circular-coverage BTSs as
well. When a circular or any non-square-coverage
transceiver is employed, it is impossible to get full
coverage without having any over-coverage (Cal
´
egari
et al., 1997) (Figure 4).
In what follows, first, we express the essentials of
the problem and then proceed with applying EVEBO
steps to it.
Figure 4: Coverage and over-coverage in non-square
transceiver cellular networks. Left: Partial coverage and
a no over-coverage case. Right: Full coverage and partial
over-coverage case.
•· SOLUTION REPRESENTATION: We consider
each individual solution X as a binary vector of n
elements (the total number of different potential
BTS locations) where each element x
i
can be 1
or 0 which shows whether a transceiver has been
positioned in that location or not:
X =
x
1
x
2
...x
n
(1)
In fact, the one dimensional vector X is the linear
representation of the 2-D grid of BTS locations.
This will reduce the complexity of the problem
significantly by replacing euclidean distance com-
putations with Hamming distance. Each vector’s
element is a pointer to the two dimensional BTS
location in the grid space. A genotype/phenotype
solution representation of the problem is illus-
trated in Figure 5.
Besides, the binary/1-D representation of the
problem has the benefit of fairer comparison with
the related works using similar representations.
•· FITNESS FUNCTION DEFINITION. Our prob-
lem has 3 objective parameters: Coverage,
over-coverage and number of BTSs. These
parameters can be unified into one objective
criterion f (.), called fitness function, as proposed
by (Cal
´
egari et al., 1997):
f (X) =
(CR(X) k.OCR(X))
2
N
BT S
(2)
in which X is an individual solution in our popula-
tion described before, and CR, OCR, and N
BT S
are
Figure 5: An example of corresponding binary vector X
(genotype solution representation) to the 2-D placement of
transceivers in a discretized grid area (phenotype solution
representation).
coverage rate, over-coverage rate, and the number
of BTSs respectively.
Our goal is to maximize f (X). There is another
non-objective weighing parameter in the fitness
function, k, where k [0,1] states the importance
of the over-coverage rate in the fitness function. It
is obvious that setting k = 0 will ignore the over-
coverage factor in the problem.
•· UNCERTAINTY PARAMETER. In this work, we
replace the utility matrix with a stochastic vector
P(X), p
i
[0,1], for each X in the population.
For large problems like ours, creating a matrix for
each solution would increase memory usage and
computational complexity. This was confirmed
by our simulation results which are not presented
herein for the sake of brevity.
The application of modified-EVEBO to the BTSs
localization problem proceeds through the following
steps:
1. Initial Individuals. A population of initial solu-
tions is generated randomly. The size of the pop-
ulation (number of solutions) is a constant value
(See Table 2).
2. Electoral System Selection. In a flat grid area
with no limitation in BTS locations(i.e. uni-
form nature of the problem), the uni-modal con-
sideration is a right choice since there are not
much difference between solutions out of a multi-
modal consideration of the problem. Amongst
FPTP, TRS and IRS electoral systems, one is ran-
domly selected. If the best solution does not im-
prove (based on the fitness value) during a pre-
determined number of evaluations, represented
by a Tolerance threshold, the electoral system is
switched to another one (corresponding to revolu-
tion in EVEBO).
3. Legislations. For the problem in hand, all indi-
viduals in the population will be verified for du-
plicate solutions.
4. Fitness Calculation and Candidates Setting. In
this step, the fitness values of all solutions in the
population will be calculated. Thereafter, a num-
ber of highest-in-fitness solutions will be selected
as the candidates in the current evaluation. Then,
P(X), the uncertainty parameter, is generated for
each solution X in the population.
5. Campaigning. Each solution X takes a move,
with the probabilistic influence of P(X), towards
its nearest (in terms of hamming distance) neigh-
bor/each candidate by randomly selecting m(X)
elements of X and setting them equal to the cor-
responding elements in that neighbor/candidate
(Figure 6). The value of m(X) is calculated as
below:
m(X) = b
f it(NN/C)
f it(NN/C)) + fit(X)
size(X)c (3)
Figure 6: An example of campaigning effects on an indi-
vidual solution X
i
in a binary belief space: a) X
0
i
moves
under effect of and towards its nearest neighbor (based on
Hamming distance) to the new position X
i
(m(X
i
) =2).
b) X
1
i
moves towards a candidate to the new position X
2
i
(m(X
i
) =3).
where NN and C represent the nearest neighbor
and each candidate respectively. It is obvious that
the higher is m(X), the closer X moves towards its
nearest neighbor or a candidate. It should be noted
that, herein, the above campaigning method has
replaced the continuous Gaussian Impact Func-
tion (GIF) in the original EVEBO. Since GIF is a
continues function, so it works just when proxim-
ity criteria is a continues distance in an euclidean
space. However, as was mentioned earlier, we use
binary vectors with Hamming-distance proximi-
ties in this problem for ease of implementation
and fairer comparison to the related works.
6. Voting: Each individual X identifies and votes for
its nearest candidate. The candidate with the high-
est number of votes will be announced as the win-
ner solution in the current evaluation.
7. Post Election: Finally, the winner solution is
updated by considering the impacts of all other
individuals. Particularly, a light mutation-like
correction will be probably (according to P(X))
performed on the winner. As a result, some
new BTSs will be randomly placed and some al-
ready existing ones will be randomly removed. It
should be noted that each occurred mutation is
also counted as one more evaluation. The off-
springs will remain in the next evaluation only if
they are better than their parents (Elitism in EAs
(Yu and Gen, 2010)).
The pseudo-code of the above steps appear in Algo-
rithm 1.
Algorithm 1: EVEBO-Based BTS localization.
1: Parameters initialization.
2: Generating initial solutions and first fitness calcu-
lation.
3: Evaluation 0
4: while Termination conditions not reached do
5: System Selection
6: Tolerance t
0
7: while Tolerance > 0 do
8: Legislations
9: for each solution X
i
in population do
10: p(X) rand [0,1]
11: Set candidates based on fitness function.
12: (*) Campaigning - Update solutions
13: Voting - Set Winner
14: (*)Post election: Update winner and other
individual
15: if Mutation then
16: Evaluation Evaluation + 1
17: Fitness values calculation
18: if f it(winner) > f it(Best) then
19: Best winner
20: Elitism: Always save best
21: if f it(winner) <= f it(Best) then
22: Tolerance Tolerance 1
23: Evaluation Evaluation + 1
(*) All changes on the solution X
i
will be enforced
with probability P(X
i
).
6 SIMULATION RESULTS
To verify the performance of EVEBO-based BTS lo-
calization algorithm, it is compared to the methods
introduced in (Vega-Rodr
´
ıguez et al., 2007). Herein,
we intend to estimate the optimum number and loca-
tions of square-coverage BTSs in a discretized square
flat area. For a fair comparison, we use the clas-
sic 287 287-grid-point area and the maximum pos-
sible of 349 BTS locations as in (Vega-Rodr
´
ıguez
et al., 2007). Finally, we will consider a more
realistic and challenging (in the sense of coverage
and over-coverage) circular-coverage BTS case. As
mentioned earlier, there are no report of any previ-
ous meta-heuristic-based works on BTS-localization
problem with circular-coverage BTSs(the only re-
ports of circular-coverage BTSs involve communica-
tion signal parameters). All simulations were done in
Java with external JFree chart library.
6.1 Numerical Results
Table 1. summarizes the simulation results of the pro-
posed EVEBO method and the two best methods in
(Vega-Rodr
´
ıguez et al., 2007). We chose two best
methods (one for its better fitness value and another
for less number of evaluations) in (Vega-Rodr
´
ıguez
et al., 2007). For a fair comparison and statistical
purposes, 30 independent runs have been performed.
To be consistent with the results in (Vega-Rodr
´
ıguez
et al., 2007), the over-coverage was excluded by set-
ting k = 0 in the equation (2). So now the fitness func-
tion will be only a relation between coverage and the
number of transceivers.
Table 1 suggests that EVEBO and PBIL outper-
form DE in fitness value, coverage, and convergence
speed. EVEBO is doing significantly better in con-
vergence speed (computational efforts) compared to
PBIL. This outperformance becomes noticeably im-
portant in problems of larger sizes.
The fitness value, coverage rate, and number of
BTSs in PBIL and our proposed EVEBO-based al-
gorithm are the same. This is due to employing the
same grid size, the same list of predefined BTS loca-
tions, and an identical fitness function. It is impor-
tant to note that equal optimum results does not mean
same solutions since the final optimized BTS loca-
tions most probably differ due to non-deterministic
nature of these two algorithms.
There is another work which presents its cover-
age results only in graphical forms ((Cal
´
egari et al.,
1997)) and for this reason it cannot be used as a com-
parison reference.
Now we start the circular-coverage BTS case. In
our simulation, for ease of visualization we assume
that BTSs can be placed on any 3-by-3-pixel boxes
which gives us 9604 different potential BTS locations
which is also the size of our solution X . To display
the circular-coverage area on our adopted discretized
Table 1: A comparison between the best results in (Vega-Rodr
´
ıguez et al., 2007) and our proposed EVEBO-based method
with square-coverage BTSs with 30 independent runs.
Parameters / Method PBIL DE EVEBO
· Fitness Value 204.082 163.48 204.082
· Number of BTSs 49 49 49
· Coverage 100% 89.5% 100%
· Number of Evaluations 276,345 9,363 8,079
Figure 7: Some simulation evaluations for a specific inde-
pendent run.
Figure 8: Final result after the 1000th evaluation (k = 0.5).
area with square pixels, we use the midpoint circle
algorithm in (Pitteway, 1967) and (Van Aken, 1984).
All initialization parameters are tabulated in Table
2. In this case, by adopting k = 0.5 the over-coverage
factor in the fitness function is also considered. To
make results more reliable, each run is repeated 50
times and the corresponding results is shown in Table
3.
The results in Table 3 show that the proposed
method does not show much variations throughout 50
runs. While satisfactory coverage and over-coverage
rates are achieved, they cannot reach perfection due
to their conflicting natures (see Figure 4).
For clarity, some intermediate results correspond-
ing to the 1st, 100th, 400th, and 800th evaluation of an
independent run are shown in Figure 7. The final so-
lution corresponding to the 1000th evaluation is illus-
trated in Figure 8. Also for this run, the average rates
of coverage and over-coverage in each evaluation (av-
erage rates over all solutions in the population) is cal-
culated and plotted on two diagrams shown in Figure
9. As seen, coverage rate increases almost monoton-
ically while EVEBO tries to keep over-coverage low.
Both rates demonstrate stabilization after some num-
ber of evaluations.
Figure 9: Average rates of coverage and over-coverage over
all solutions in the population in each evaluation(k = 0.5).
We repeated all simulations with combinations
of different initial values of parameters in Table 2.
Table 2: Initial parameters values for circular-BTS-
coverage localization problem.
Parameter Value
Population size 200
Over-coverage parameter (k) 0.5
Tolerance 4
BTS coverage radius 24 Pixels
Termination condition # of Evals.>1000
Table 3: Simple statistics of circular-BTS-coverage local-
ization results for 50 separate runs each after 1000 evalua-
tions (k = 0.5).
Results Min Max Average
Fitness 141.42 152.35 147.37
Active BTS 42 51 48
Coverage 81.41% 91% 86.53%
Over-Coverage 4.31% 8.06% 5.64%
Specifically, we tried population sizes equal to 100,
400, and 500 and tolerance values of 2, 5, and 10, and
we observed no significant changes in final solutions
and number of evaluations. This demonstrates, at
least in a simulation sense, low sensitivity of EVEBO
algorithm to initial values of parameters.
7 CONCLUSION
In this paper, EVEBO was employed to solve the
prevalent problem of BTS localization in cellular net-
works. We show that EVEBO is a good candidate
for solving this kind of problems due to its speed of
convergence and low sensitivity to initial values of pa-
rameters. Simulation results show EVEBO’s superi-
ority in comparison to the best of the related works.
In addition, we have also tried the more challenging
circular-coverage BTS where we show that EVEBO
can produce stable results with adequately fast con-
vergence. We have shown that EVEBO can produce
better than or repeat the best results in the literature in
much less computational effort. Herein, we have also
shown good over-coverage rate results of the EVEBO
which is not usually addressed in similar works.
For future works, we are interested in running
EVEBO to optimize radio network design by con-
sidering signal and telecommunication factors in real,
larger and more challenging terrains.
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