The hybrid evolutionary algorithm for optimal planning of hybrid woban

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN

0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME

122

THE HYBRID EVOLUTIONARY ALGORITHM FOR OPTIMAL

PLANNING OF HYBRID WOBAN

Anwar A. Alsagaf1, Yousef Y. Holba

2, Anwar H. Jarndal

3 ,

Gamil R. Salman

4

1,2(Engineering Department of Hodeidah University, Hodeidah, Yemen)

3(Electrical and Computer Engineering Department of University of Nizwa, Nizwa, Sultanate

of Oman) 4(SGGS college of Engineering and Technology, SRTM University, Nanded, Maharashtra

state. India)

ABSTRACT

In the recent few years, the hybrid network deployment is an important problem,

especially, optimal placement problems of WBSs and ONUs in the WOBAN architecture.

The optimal placement problems of WBSs and ONUs will play a key role for overall cost

optimization of a hybrid network architecture. The challenge is to obtain the global optimal

solution, since the objective function is usually high-dimension, highly non-linear, non-

convex, and multimodal, where a local optimum is typically not the global optimal solution.

The traditional local and global algorithms could trap to a local optimum. Thus, in this paper,

we reformulate our problem as multicriteria optimization problem under uncertainty and

represent its by using game model. The two hybrid evolutionary algorithms (HEA) are

proposed for solving the optimal placement problems of WBSs and ONUs, independently.

The results of modeling show that HEA is powerful technique adequate to our proposed

model and give good optimal solutions with comparison by other traditional methods.

Keywords. Hybrid evolutionary algorithm, Optimal placement problem, Hybrid wireless

network, Hill climbing algorithm.

1. INTRODUCTION In the recent few years, the hybrid wireless network deployment is an important problem,

especially, optimal placement problems of wireless base stations (WBSs) and optical

network units (ONUs) in the Wireless Optical Broadband Access Network (WOBAN)

architecture. The optimal placement problems of WBSs and ONUs will play a key role for

overall cost optimization of a hybrid wireless network architecture. This problem has

generated much research interest and challenge instances have been published in the more

literatures [1-9].

These problems belongs to the class of NP-hard optimization problem with multiple

and conflicting objectives. The challenge is to obtain the global optimal solution, since the

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objective function is usually high-dimension, highly non-linear, non-convex, and multimodal,

where a local optimum is typically not the global optimal solution. The WBSs placement

problem involves selecting base station site locations from a set of feasible candidates, which

are normally located irregularly on the geographical area. The selected sites must be

configured to provide adequate required maximum service coverage and capacity at the

lowest possible financial cost with unsplittable demands, and unknown numbers of

subscribers. These two conflicting objectives always exist when setting up cellular network

service, as adding base station to improve coverage inherently increases the total cost of

network.

In this paper, we focus on resolving the two separated fundamental stages of cell

planning problems. First stage, we produce cell planning problems in which WBSs locations

are selected on to the geographical area. The next stage we will providing ONUs optimal

placement. Our goal in this study is finding an optimal locations/positions of WBSs and

ONUs using two hybrid evolutionary optimization technique, satisfy the conflicting

objectives, taking into account the only factors and constraints which have the largest impact

on financial cost and service coverage. These factors are considered in details below. We

reformulate our problem as multicriteria optimization problem under uncertainty and

represent its by using game model presented in [10, 11].

The hybrid evolutionary optimization techniques have successfully been applied to

multicriteria optimization problems. For solving its we will investigate two algorithms based

on combination of global and local search algorithms. The first hybrid evolutionary algorithm

based on combination of multicriteria genetic algorithm(MGA) and hill climbing

algorithm(Topiks-Veinott algorithm ) to solve the WBSs placement problem, when the

second hybrid evolutionary algorithm based on combination of multicriteria genetic

algorithm(MGA) and hill climbing algorithm( Modified Tornqvist algorithm ) to solve the

ONUs placement problem.

In this paper, we propose and investigate clustering architecture for WOBAN which

have focused on the integration of WIMAX 4G and cellular technologies. A hybrid WOBAN

(referred to as a “hybrid network” here) consists of a wireless network at the front end, and it

is supported by an optical access network, viz., the passive optical network (PON) at the back

end. The basic architecture (see Fig. 1). Assume that an Optical Line Terminal (OLT) is

placed in Telecom Central Office (CO) and it feeds several ONUs. Thus, from ONU to the

OLT/ CO, we have a traditional fiber network; and, from ONUs, end users are wirelessly

connected, either directly (in a single hop) or through multihop fashion. In a typical hybrid

network, end users, e.g., subscribers with wireless routers at individual homes, are scattered

over a geographic area.

Fig.1. Hybrid optical-wireless broadband access network architecture[4].

Through performance study on the given two data sets, we show that, the two hybrid

evolutionary algorithms can improve the chances of reaching the global optimum because of

applying the neighborhood search algorithm based on the dominance cone construction from



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each points and using choice technique based on the most best selection mechanism with the

most worst exception function from population pool.

This paper is organized as following: in the section 2 we introduce the problem

statement. The section 3 give the problem formulation as multicriteria optimization problem

under uncertainty. The related works and proposed two HEA are considered in the section 4.

The result of experiments presented in the section 5. The section 6 give the conclusion of our

paper. Acknowledgement is presented in the section 7. In section 8 given the references.

2. PROBLEM STATEMENT

An analysis of numerous scientific studies and works aimed at developing and design of

optimal automatic positioning systems and optimal planning or relocation of some devices

such as WBSs, wireless sensors(WS), antenna configuration(AC), wireless access

points(APs), and automatic transfer machine(ATM), etc in the various telecommunication

networks architecture, especially in the hybrid networks. The problem of optimal design and

optimal planning of the WBSs and ONUs in the proposed WOBAN architecture on the

territorial plane is mostly represented in the form of an optimization problem with many

conditions. This traditional formulation cannot be put to an adequate model because of

problem complexity, multiobjective functionality, multi-crossing of the input-output

parameters of the system optimization and uncertainty in the environment parameters and the

no enough information’s about number of subscribers, user demand, end user etc. Therefore it

is necessary to apply a different simplified and adequate mathematical model, taking into

account conflicting criteria and objectives for uncertain disturbing factors, affecting on the

optimization system as a whole . In addition, satisfying all the designer/planner

requirements, also satisfying both technical and economical constraints and social-technical

requirements.

In this paper, we derive the first objective function for the WOBAN planning and

design which is to minimized the sum of the following items: installation cost for all ONUs

required, plus installation cost for all WBSs required, plus cost of connecting WBSs to an

ONU and sum of cost WOBAN design. This function is defined[4, 6]:

min);,,,( ....

.cos →= ij

design

WBS

design

ONU

inst

WBS

inst

ONU1 dCCCCfJijij

(1)

The second objective is function of functions which is determine the optimal values of all

items that’s affecting in the proposed WOBAN architecture. This function is defined as the

following:

optimalNloslosNSfSDRSIPIRPPTRPLfJ cRxTx2 →= )/,;,,,,,,,,(cov (2)

The parameters in function )(•jf after the “;” are define the uncertainties parameters when

the parameters lie before that may be calculated and/or determined by the designer/planer and

depend on the technical features, specifications and configuration of the devices, where NS

is the numbers of subscribers which is assumed unknown in this paper whereas NlosLos / is

line of sight and Non-line of sight in the geographical environment.

The relation between all parameters and functions defined in (2) have a different

effects and conflict situations, so we need to provide a better combination of the various

dimension of cost and effectiveness. The process of finding the cost-effective design is

further complicated by uncertainty, which is shown in (1) and (2), so the projected cost and

effectiveness of a design are better described by a probability distribution. Distributions

resulting from designs and distributions associated with risky designs may have uncertainty

which cause producing highly undesirable outcomes and presence of low-effectiveness/high

cost.



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We denote that in radio planning the channel modeling requires further

characterization on path loss propagation PL , fading and sometimes interference. PL is a

measure of average radio frequency (RF) attenuation endured by transmitted signal before

arriving at the receiver. For PL model, either empirical (statistical) model or site specific

model can be used. An empirical model is simple to implement, requires less computation

time and is less sensitive to the environment while site-specific models are more accurate and

very complex to implement.

The Stanford University Interim (SUI) models was developed by IEEE802.16

working group are used in this paper, for details information about propagation models which

are used in planning channel modeling can referred to [12]. The basic path loss equation with

correction factors is presented as:

sLLdd10APL hfo10 ++++= )/(logγ (3)

where, d is the distance between the access points and the user terminals’ antennas in meters,

the 0d =100m, )/(log. λπ 010 d420A = and bb hcbha /+−=γ , here, bh is base station height

above the ground in meters between 10m and 80m.

To use this model for higher frequencies(upper 2GHz) and different receiver antenna

heights, correction factors must be included[13].

The correction factors for the operating frequency( fL ), is defined by

)/(log. 2000f06L 10f = and for the receiver antenna height ( hL ) are given by

)/log(. 2000h610L rh = for type A and B while for type C the hL is defined by

)/log(. 2000h610L rh −= and s is a log normally distributed factor that is used to account for

the shadowing fading to trees and other clutter and has a value between 8.2 dB and 10.6 dB.

The grid separation distance(SD) is defined as the physical distance between any two

communicating neighbors, is chosen suitably relative to the transmission range (TR). Assume

that, 0S is SINR threshold which satisfies the required BER, γ is the path loss exponent, NP

is the background noise power, and RxP is the power received at a reference point in the far

field region at a distance refd from the transmitting antenna are given to we can compute the

TR by: γ/)/( 1

N0Rxref PSPdTR =

The grid separation distance equal to half the transmission range; i.e., 2TRSD = .

The interference range, IR is defined as the maximum distance at which the receiver

corresponding to a reference transmission will be interfered with by another source (i.e., the

received SINR at the reference receiver drops below the threshold 0S ), is given by[14]:

γγ /)))/()/()//((( 1

RxNref0 PPdSDS11SDIR −= (4)

To this end, we have to determine a link budget, LB . LB takes all of the gains and

losses of the transmitter through the medium to the receiver into account.

Firstly, we need to calculate the maximum allowable path loss maxPL to which a

transmitted signal can be subjected while still being detectable at the receiver. To determine

maxPL we need to take the parameters into account. It is important to remark, that maxPL is

dependent of the input power TxP of the antenna and thus dependent of the output power of the

power amplifier.

Once we know the value of the maxPL , we can determine the maximum range maxTR ,

so we can reach with the base station of a certain technology[15].



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( )MSBScmax

1 hhfSMPLTR ,,,gmax −= − (5)

The quantity before the ”|” in (5) is a variable and varies over a continuous interval, while the

quantities after the ”|” are parameters which take only one discrete known value. cf is carry

frequency (in Hz). The SM is the shadowing margin (in dB), BSh is the height of the base

station (in meters) and MSh is the height of the mobile station (in meters). The shadowing

margin depends on the standard deviation of the path loss model, the coverage percentage

and the outdoor standard deviation.

The generated interference in the network depends on the network topology used and

the transmission activity of the nodes in the network. This model is an energy-based

interference model which takes into consideration radio related interference due to far away

transmitting nodes. The interference of the wireless link could be assumed to be non-

coherently combined at the receiver, and treat the interference of each node as white noise.

The interference power, IP of all transmit nodes adds up to a total interference power labeled

as totalIP . The totalIP of a random number of interferers )(aN with random interference ( )kRψ

is given by[14]:

( )( )

∑=

=aN

1kktotal RIP ψ ( 6 )

The PDF for the total interference power is only dependent on the transmit node density and

given by: )./.(

)/()(IP4

t

2t

32

3

eIP2IPPDFλπλπ −⋅⋅=

−

( 7 )

Where tλ is the transmit node density. The corresponding cumulative distribution

function(CDF) is given by:

( ) )/.( / IP2erfcIPCDF t

23 λπ=

Besides the above, there are factors which affect the signal received at the receiver

due to obstacles along the signal path for example Reflection and Refraction, Diffraction,

Scattering and Multi-path interference. In addition, if the mobile receiver is moving, it is best

to include the effect of Doppler frequency shift model on the channel characterization.

The receiver sensitivity, RS is defined as the minimum received signal power needed

for the receiver to achieve a given data and bit-error-rate, it is given by WiMAX forum [16]:

Bimplem SNRINFWLSR2kTRS ⋅⋅⋅⋅= .)/( …………….(8)

This is further translated into:

( )( ) ( )Bimplem SNR10I10NF10

WLSR1000102kT10RS

log.)log(.log.

log.)./)/log((.

. +++

++=

L

L……... (9)

or

( ) ( ) ( ) ( )Bimplem SNR10I10NF10WLSR10177RS log.log.log.log. . ++++=

WLSR is wireless link symbol rate, NF is define noise figure, .imolemI is degradation caused by

implementation limitations of noise ratio BSNR . BSNR is determine the theoretical baseband

received signal power to noise ratio. NT is baseband value of thermal noise power and RxP is

define the received signal power. The NTPRx / is needed to operate at the given bit-error-rate.

For an alternative form of this expression, which uses 0s nE / instead of signal power

to noise ratio BSNR , where sE is the symbol energy and 0n is the single sided thermal noise

spectral density. RS is then given by:



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)/log(.)log(.)log(.)log(. . 0simplem nE210I10NF10WLSR10177RS ++++−= ….. (10)

Finally LB with RS can be derived as:

totalRx SMGRSEIRPLB −+−=

Where, RxG is the received antenna gain in dB and totalSM is the total margin in dB including

shadow, interference, fading, etc.

3. PROBLEM FORMULATION

The values of all criteria, objective functions and some parameters which to have been

needed satisfying must be given or calculated by (1)-(10) and expressed as general

performance index in parametric and criteria planes. This index show the efficiency of the

HEA applied onto the WOBAN architecture.

Thus, the task of optimal planning and optimal location of the WBSs and ONUs in order to

achieve optimal solutions can be formulated as following mathematical mapping reflection:

VQPF →×Φ :)( (11)

In (11) is needed to find the optimal positions of WBSs and ONUs under the uncertainty,

where rEP ⊂ is set feasible values of position, qrEQ ⊂ is set feasible values of uncertainty

parameters,

V is set of vector – evaluation functions )(•V , ( ) mEtqpV ∈,, is evaluation function at

moment t , [ ]Ttt ,0∈ , and ( ) miEqpV ∈, is vector of performance index.

By applying some mathematical transformations and computations we obtain the total error

which is needed to achieve:

( ) ( ) ( )Pp

qpqppE∈

= =

→Λ=∑∑ min,,k

1i

m

1j

i

j

iT

j ϕϕ (12)

where, ( )1N1kdiag kk +==Λ ,,λ - diagonal matrix of positions with size ( )( )1N1N ×× .

In this paper, we propose and investigate the game model formulation, which is a

predeployment network optimization scheme, where the cost of WOBAN design is

minimized (by placing reduced number of WBSs and ONUs, and planning an efficient fiber

layout). Also take in account the interference among multiple WBSs and ONUs, and other

affecting factors, and explore several installation and assignment constraints that have to be

satisfied for a better-quality access solution and maximized coverage.

Our proposed game model for optimal WOBAN placement problem is formulated as

the multicriteria optimization problem under uncertainty as shown below[11]

( )qpVQP ,,, (13)

Where:

Pp ∈ is vector of the WBS positions or ONUs locations.

QQq ⊂∈ ˆ is vector of uncertainty parameters.

( )qpV , is vector of evaluation functions.

We assume that, the sets P and Q given as system of nonlinear inequalities-constraints

( ) ,1s1

rpE 0GpP ≤∈= (13a)

( ) ,2

q

s2

rqE 0GqQ ≤∈= (13b)

Where:



128

1

1

s

s E∈0 , 2

2

s

s E∈0 - vectors with non-zeros elements

,p

mE 0BzzΩ ≤∈= (13c)

Ω - is dominant polyhedral cone defined by(13c).

When we assume that, the matrix B with size [ ]ml × and z defined by vv ′−′′=z , then

( ) pvv 0B ≤′−′′

4. THE RELATED WORKS AND PROPOSED HEA ALGORITHMS

In the recent few years the taxonomy of hybrid technology have big interest into specialists

and researchers, so that, especially the hybrid Metaheuristics have received considerable

interest in the field of combinatorial optimization problems [17] such as traveling tournament

problem (TTP) [18], quadratic assignment problem (QAP) [9, 19], antenna placement

problem (APP) [20], node placement problem (NPP)[21, 22], integrated points placement

problem (IPP) [23] and transmitter location problem (TLP)[24] in different fields of

communication systems such as wireless sensor networks (WSN) [15, 21, 22, 24, 25],

wireless local area networks (WLAN) [26, 27] design, and wireless ATM backbone network

design[28-30], femtocells optimization[31] and WOBAN[10] etc. The best results found for

many practical or academic optimization problems are obtained by hybrid algorithms.

Combination of algorithms such as descent local search, simulated annealing, Tabu search,

integer programming, minimax algorithms, and evolutionary algorithms, and/or evolution

strategies have provided very powerful search algorithms[18, 19,24].

Thus, they are not suited for the modeling of the our specific formulated problem

which is considered in the previous section. In this case, the problem formulated in (13)-

(13c) must be separated into two sub problems and each sub problem is solved

independently. The first problem is WBSs placement problem for solving it, we propose the

first hybrid evolutionary algorithm(HEA), denoted by HEA1, it is based on combination of

multicriteria genetic algorithm(MGA) and hill climbing algorithm such as Topiks-Veinott

algorithm (TVA)[11]. Our primary goal is to place multiple WBSs (say N of them) properly

in the selected geographical area. Assume that ),( iii yxP is the position of i-th WBSs, which

will serve users and ),( jjj yxP is the position of j-th ONUs which will serve multiple of

WBSs.

The second problem is ONUs placement problem for solving it, we propose the

second hybrid evolutionary algorithm(HEA), denoted by HEA2, it is based on combination of

multicriteria genetic algorithm and hill climbing algorithm such as modified Tornqvist

algorithm(MTA)[32, 33]. Here, our goal is to place multiple ONUs (say M of them) properly

in a geographical service area, where the user’s locations are known beforehand from last

stage.

The proposed HEA1 has two main phases, a global search phase based on multicriteria

genetic algorithm and a local search phase based on modified Topiks-Veinott algorithm. The

goal of the global search phase is to cover the search space as broadly as possible in order to

identify a good start point for the local search phase initialization. The local search phase then

starts from the starting point which is selected in the global search and applies a gradient-

based method or heuristic search algorithm such as hill climbing algorithm to search around

its neighborhood for finding a better solution or near-optimal solution from optimal feasible

solutions.



129

For both global search and local search phases, we modify both algorithms by applying a

novel neighborhood search technique based on constructing locally a cone dominate space

function from each founded point in each iteration, which leads to better convergence for

overall hybrid evolutionary algorithm.

4.1 The first hybrid evolutionary genetic algorithm (HEA1) for multiple WBSs

placement problem

4.1.1 Global search phase: MGA In this phase is applied the multicriteria genetic algorithm consist of the following blocks:

The first block is randomly generate of the first generation of population and encoded in bit

string such as :

( ) ( ) ( ) LtaN1itatAii === dim;,, (14)

Where: N is population size; L is bit string length; ( )tai

is bit string length; t is number of

current generation , [ ]T1t ,∈ and T is the last generation.

In each of ( )tai

is encoded all information about all vector elements ( )tpi

.

The second block consists of the following two steps:

Step 1 : The population decoding is obtained by:

( ) ( ) Nittaii ,,: 1p =→∆

Each partial n1l i ,, =µµ , bit sting ( )tai

is represented into nature number ( )tC i

µ according to

the following:

( ) ( ) ( )( )

( ) ( ) ( )

=−−

===

+−+=∑

1ta121

0ta0tCandtCtC

i

k

1kM1p

i

ki

k

M

1k

i

k

i

µ

µ

µµµ,

,, (15)

The bit string ( )ta i

µ of the element ( )tpi

µ of the vector ( )tpi

is defined by Grey code.

The coordinate values of the vector ( ) N1itpi ,, = is calculated by:

( ) r12tCt 1

LH

i

L

i ,),/))((( =−+= − µµµµµµµ pppp

Step 2 : Fitness function calculation.

Compute the ( )( ) N1itpVi ,, = . In each of individual ( ) N1itp

i ,, = we must to apply the

−Ω−ε optimal principal condition which is formulated in following such as:

( )( )( ) ( ) ( )( ) ( )( )[ ]p

iiji tttCt 0pVpppVB ≤−−+ ε (16)

For ( ) ijNjtj ≠=∀ ,,, 1p

The number of points ( )tpj

is denoted as ( )tbi , for which it’s in the point ( )tpi

is executed

the inequalities constraints (16).

If ( ) 0=tbi then )(ti

p is −Ω−ε optimal solution for the multicriteria optimization problem

which is formulated in (13 -13c), so that, )(ti

p is −Ω−ε optimal solution for multicriteria

optimization problem which is formulated as:

( )pVPp∈

min (17)

Otherwise, when ( )tip is not −Ω−ε optimal solution for problem (17), to ( ) 10 −≤≤ Ntbi

Thus, the fitness function in this case is formulated such as: ∗≥−+= γq

i

i1Ntb11ta )))/()((/())((Φ (18)



130

Where q is selected from practical and effect on convergence speed of proposed algorithm.

In (18) shown that when 0b =)(ti to ( )( ) 1tai =Φ , and when 1Nti −=)(b to ( )( )

q

ita

2

1Φ = .

The third block is forming the probability selection mechanism of the population in parents

set ( )tΘ . This mechanism based on the best selection of population with exception properties.

This is mechanism is presented by the following steps:

Step (1): The interval ( )[ ]tS,0 is constructed by following recurrent relations:

( ) ( )( )

( ) ( ) ( )( )tatStS

tatS

NNN Φ

Φ

1

1

1

+=

=

−

L

,

We assume that ( ) ( )tStS N= .

Step (2): Generate the points-parents population

First, the random value is generated on the interval ( )[ ]tS,0 . The population is selected in the

parents set, if the random value lies on the subinterval from ( )[ ]tS,0 . After that, the suitable

subinterval was excepted from the interval ( )[ ]tS,0 . This is procedure is repeated 2N / once.

The crossover and mutation operations with analogy the selection mechanism operations

which is above presented. The probability of mutation is selected on the interval [ ]mP,0 . In

this work we apply two types of mutation operations.

The forth block is the stop criteria which is presented such as:

1. Check the following condition ∗≥ δ)/)(( Ntn (19)

Where ( )tn is define the number of individual in the population ( )tA with size N. For that’s it

the inequality: ∗≥ γ))(( ta

iΦ must be executed.

If the(19) is executed, to the set of the points ( ) P⊂tpA is approximation of the −Ω−ε

optimal solution. That is mean that ( )tpP A=Ωεˆ and multicriteria genetic algorithm is

finished. Otherwise, if ∗≥ tt , the set ( )tpA is approximation of the −Ω−ε optimal solution

and multicriteria genetic algorithm is finished.

2. Initial points selection:

This block is needed for initial setting multicriteria local algorithm which is consist of the

following steps:

Step1: The vector performance index ( )pV is normalized with the following representation

operation:

( ) ( )mi

VV

VpVpV

LiHi

Liii ,,

~1=

−

−=

Where LiHi VV , are maximum and minimum of possible values of the ( )pVi

( )pVV ipp

HiΩ∈

=εˆ

max ,

( ) mipVV ipp

Li ,,maxˆ

1==Ω∈ ε

Step2: The initial approximation Ω∈ εP0 ˆp is constructed by applying the following:

( )( ) ( )pVpV iMi

~max

∈=Φ

Find the Ω∈ εP0 ˆp by solving the optimization problem:



131

0

PppPVΦ ⇒

Ω∈))((min

ˆε

(20)

4.1.2 The local search phase: TVA

In this phase is applied the multicriteria local algorithm based on hill- climbing algorithm

such as TVA. The TVA is that, firstly, the optimal solutions are sought along of gradient

direction(algorithm1). If the optimal solutions not found along of gradient direction, then the

direction is changed in to 180, that’s means, the optimal solutions must be sought in the

direction of anti-gradient(algorithm 2). The cycle is repeated until there are the optimal

solutions not found. In this paper, the two cases are considered. In the first case, the searching

of the next better solution is taken along of gradient direction (algorithm 1), while in the

second case the searching of the next better solution is taken anti gradient direction (the

steepest descent algorithm is algorithm 2).

The algorithm1: The search along of gradient direction. This algorithm belongs to the

iterative gradient-based optimization methods and depends on the following rule( ) ( ) ( ) ( )

,kkk1k

dpp α+=+

For finding the next better point using above iterative rule, we construct the polyhedral

dominance cone from approximated pareto set founded in the last phase by MGA and select

feasible directions ( ) rEpΩd ⊂∈ P inside the constructed dominance cone. This algorithm

consist of following steps:

Step1: The selection of ( ) rEpΩd ⊂∈ P when ( )pΩP Ω like the type of (13c) which is

constructed in the space of the locations ip of the WBSs at the current point p . Using the

dominance condition as Hill-down or Hill-up condition, we can be to formulate the problem

of the Hill-down or Hill-up condition direction at the point P∈p inside the dominance cone

such as:

[ ]z

Dz ∈,max

Td

(21)

Where, the D is given as inequalities-constraints:

( ) ( )

( ) ( ) ( )

( )

≤

−≤+∂

∂

≤+∂

∂

c211d

b21pGZdp

pG

a210Zdp

pV

D

k

1S1

pp

1,

,

: B

B

Where 1

1

s

s

p

p EZEZ ∈∈ , is the vector with the same element z and B is quadratic matrix of

the polyhedral dominance cone.

The equation (21a) is denoted by ( )pd PΩ∈ and its means Hill-down direction condition at

inside the cone Ω .

The equation (21b) is the feasible direction d which is taking in account both active and non-

active inequalities-constraints at the point P .

The equation (21c) is the inequality is vector norm condition of d k-th order.

Stop condition of the feasible direction selection algorithm is formulated by the following:

0B =⋅+⋅ ∗∗ νµ )()( pGpV a1

TT && (22)



132

Where ( ) as

a EpG 1

1 ∈∗- constraints vector which is (22) active at point P

*. The following

condition γ≤z is stop criteria of the multicriteria local optimization. Where γ is show the

accuracy of the multicriteria local search.

Step2: step size ( )kα calculation in the selected direction ( )kd

1: firstly, finding the distance to the boundary of the feasible area P is calculated along of

the direction ( )kd

HL

rpppEpP ≤≤∈=

For that, P may be represented by another form:

bCpEpP r ≤∈=

Assume that, [ ] [ ]TTTTTTbbbccc 2121 ,;, == , so that

( ) ( )2

k

21

k

1 bpcandbpc ≤=

The distance ( )k

dλ to feasible area boundaries at the point ( )k

p is defined by:

( )

( )

( )( )

( )

,

ˆ,

ˆˆ

ˆmin

≤∞

≥=

0

0

k

j

k

jk

j

k

j

k

d

dallif

dd

b

λ

Where ( ) ( ) ( ) ( )kkkk

pcbbdcd 222 −== ˆ;ˆ

2: step size selection ( )kα is calculated by following operators dented by OP1-OP4:

OP1:

( ) ( ) ,,min k

d0

k λαα =

OP2: ( ) ( ) ( ) ( )

,kkk1k

dpp α+=+

OP3: ( ) ( )( ) ( )( ) ,k1kk

pp ννν −=∆ +

OP4: ( ) ( )

p

kk 0B ≤∆⇔Ω∈∆ νν

If the OP4 in not excepted to, we increment the ( )kα and step by step repeat the operators

(OP2-OP4).

The algorithm 2: The search of the next better point is taken anti gradient direction(here,

used steepest descent algorithm). This algorithm is similarly to the algorithm 1, but the

iterative rule is changed into ( ) ( ) ( ) ( )kkk1k

dpp α−=+, and the

[ ]z

DzdT ~

,min

∈ instead of (21) and the

(21a-21c) can be changeable and the stop criteria condition (22) is reformulated in another

form. 4.2 The Second hybrid evolutionary algorithm(HEA2) for multiple ONUs placement problem

The HEA2 proposed for solving the multiple ONUs placement problem based on combination of

MGA and MTA. The HEA2 too has two phases. The first phase is the MGA which is considered

before, whereas, the MTA is applied in the second phase.

The modified Tornqvist algorithm(MTA)

The second local phase search algorithm is the modified Tornqvist algorithm adapted to our planar

location model proposed in this paper. The Tornqvist’s algorithm was first defined 25 year ago. It is

deterministic algorithm belonging to a family of local hill-climbing search methods. It has been

proven to perform very well on simple planar location or planar covering our task. In addition, it can

be easily adapted to include not enough information about feasible locations of ONUs, propagation

environment, number of subscribers and service areas etc., which causes uncertainties situation as

well as presented in the problem statement and formulation. The method involved a series of moves

over the search space; where each move attempted to improve the objective function. When no further

move can be found that would result in an improvement or, in instances in which an identified

improvement falls below a pre-determined critical value, the algorithm terminates. The hill-climbing



133

algorithm could be defined asvd

k

j

k

j1j

k

1j sPfPf θ=++ += )()( , πθ 20v ,= , where

)()( j

k

j1j

1k

1j PfPf >++

+ , and )( 1j

1k

1j Pf ++

+ is the values of the objective functions at the next locations.

)( j

k

j Pf is the values of the objective function in the previous locations, andk

s is a step vector and vθ

is the angles of direction, so that, the steps may be taken dynamically adjusted.

In this paper, the MTA is initialized by initial points set of positions obtained by MGA. Then

the algorithm executes a series of moves (steps) according to a search plan (hence, its designation as a

`deterministic' algorithm) in the selected directions until no more improvements can be made. The

MTA includes the neighborhood search method based on dominance cone construction (13c) from

each one of the locations in all steps along of all directions. The general flowchart of the modified TA

can be presented in the following fig.2:

Fig.2 The general flowchart of MTA

Initial set of ONUs position

(obtained before hand by MGA 0P )

Position selection mechanism

Tt0t =→=

Direction change

1dd +←

print the best optimal of the ONUs

positions

Do ),,,( kk

jj dsyxmove

Step change 1ss +←

Dominance cone construction

ΩPfPf +=+ )()( j1j

Fitness function calculations

Evaluation function calculation

kd

k

j

k

1j

1k

θ=++ += sPVPV )()(

)()( j

k

1j

1kk PVPVV −=∆ ++

p

k 0zBΩV <⋅⇔∈∆

stop criteria

p

k 0V >∆

Yes

No



134

Where, in the fig.2. ),,,(v

d

kk

jj dsyxmoveθ= expresses the search from a point ),( jjj yxp ,

with a step s in a direction d , )min(s is a minimum step, )( j

k pf∆ is a change in an objective

function values, change direction vdd θ=∆ is a change in the direction of a search, change step

1sss +←∆ is a change in the search step, and T is the maximum number of iterations allowed.

5. PERFORMANCE STUDY The performance of proposed HEA was evaluated through application of the HEA1 to the

two data sets for WBS locations of Yemen mobile company in Hodeidah City and Hodeidah

Government which are distributed and represented in the Geographical maps as shown as in

the (fig.3.a) and (fig.3.b).

Our experiments for performance investigation of the proposed HEA1 are carried out in two

cases. In the first case, we will use the data sets of WBSs locations for Hodeidah City and

Hodeidah Government installed by Yemen Mobile company. The HEA1 is applied on the

given data sets for finding the optimal locations of WBSs.

The results of the modeling show that the proposed HEA1 finds the optimal locations of

WBSs at the given parameters for Hodeidah City as illustrated in the fig.4.

Fig3.a. Geographical map of Hodeidah city.

fig.3.b. Geographical map of Hodeidah government

Fig.4 Optimal locations of WBs by HEA1 for

Hodeida city

Fig.5 Optimal locations of WiMAX WBs and ONUs by

HEA2 for Hodeida Government



135

ut in the second case, we assume that Yemen Mobile Company want to develop the its

network by applying the new 4G technology by using hybrid WOBAN architecture (which

above introduced) and WiMAX WBSs and ONUs installation for increasing of the overall

network performance. For this reason, we will use the data sets locations of WBSs applied in

the first case as potential locations for WiMAX WBSs and ONUs placement, we use the

methodology presented in [34-36]. For this purpose, the geographical map is separated into

three regions and represented as three quadrates/clusters, where each quadrate/cluster defines

the service area and consists of permissible locations which belong to the feasible location

set. Assume that, each of region, so called cluster with a unknown numbers of WiMAX

WBSs and each one cluster has one a ONU to be providing the maximum connection

between the ONU and other multiple WiMAX WBSs. The network of WiMAX WBSs can be

simulated with a hexagonal model which simplifies calculations of some operational

parameters of the wireless system such as channel interference, power interference, path loss,

interference range and receiver sensitivity etc considered in the section (2).

The quality of the wireless communication network of WOBAN architecture depends,

largely, on the locations of the WiMAX WBSs and ONUs. The WiMAX WBSs located in

favorable locations will assure desirable signal quality and desirable maximum coverage, so a

good quality of service. Conversely, poorly located of WiMAX WBSs will create inadequate

signal coverage, degrading overall network performance. Our proposed algorithm dented by

HEA1 for solving the WiMAX WBSs placement problem takes into account the

environmental factors, economical and technical aspects. In addition, it is takes into account

the uncertainty parameters. After WiMAX WBSs positioning and deployment should be

ONUs placement and deployment, for this purpose, the HEA2 is applied for finding the

optimal locations of ONUs. The fig.5 illustrate the optimal locations of WiMAX WBSs and

ONUs.

The results of our experiments on the selected data set depict the characteristic feature of

proposed HEA1 and HEA2 a relatively small number of generation are necessary for the

algorithm convergence (whereas traditional evolutionary algorithms or local search

algorithms independently may require hundred of generations/iterations) for converge (fig.6).

In addition, our proposed algorithms do not trapping in the local optimum because of the

HEA1 and HEA2 includes the neighborhood search method based on dominance cone

construction (13c) from each one of the locations in all steps along of all directions. Fig7.

Illustrates performance comparison of HEA with MGA and Hill climbing, independently.

20 40 60 80 120 140 180 200 100 160

0.4

0

0.3

0.2

0.1

0.6

0.7

0.8

0.5

1

0.9

0 220

Per

form

ance

in

dex

(%

)

Generations, t

Fig.7 Performance comparison of HEA(MGA+ Hill climbing)

With MGA and Hill climbing independently

Hill climbing.

MGA

HEA (MGA+ Hill climbing)

),,( tqpV

20 40 60 80 120 140 180 200 100 160

0.4

0

0.3

0.2

0.1

0.6

0.7

0.8

0.5

1

0.9

0 220

Cov

erag

e no

rmal

ized

Generations, t

HEA best sol.

HEA opt. sol.

HEA worst sol.

Fig.6 Convergence of HEA

covJ



136

6. CONCLUSION

We investigated two problems of multiple WBSs/WiMAX WBSs and multiple ONUs

optimal placement in the hybrid WOBAN architecture. The HEA1 is applied for solving,

independently, the WBSs/WiMAX WBSs placement problem and the HEA2 is applied for

solving the multiple ONUs placement problem. The results obtained by using the hybrid

evolutionary algorithms performs very well optimization techniques for solving the

multicriteria optimization problems which formulated in this paper. With comparison with

traditional optimization methods the proposed HEA achieve a result close to the global

optimum and require at minimum time consuming. In addition, they reach high accuracy and

satisfy all designer/planner and economic-technical requirements taking in to account the

parameters of uncertainty defined in problem formulation.

7. ACKNOWLEDGEMENT

The authors thank the Yemen Mobile Company for supporting this project, especially, many

thanks to the engineer Sami Kafla for providing the data sets and a great tanks to Professor

Hussein Omar Qadi, President of Hodeidah University for his supporting to develop the

academic research and researchers in the Hodeidah University.

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