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

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

can be 1

or 0 which shows whether a transceiver has been

positioned in that location or not:

X =



...x



(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))

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

∈ [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

in a binary belief space: a) X

moves

under effect of and towards its nearest neighbor (based on

Hamming distance) to the new position X

(m(X

) =2).

b) X

moves towards a candidate to the new position X

(m(X

) =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

7: while Tolerance > 0 do

8: Legislations

9: for each solution X

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

will be enforced

with probability P(X

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

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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