The hybrid evolutionary algorithm for optimal planning of hybrid woban (1)

International Journal of Electronics and Communication Engineering & TechnologyAND
INTERNATIONAL JOURNAL OF ELECTRONICS (IJECET), ISSN
0976COMMUNICATION ENGINEERING &3, October- December (2012), © IAEME
– 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue TECHNOLOGY (IJECET)

ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 3, Issue 3, October- December (2012), pp. 122-138
IJECET
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THE HYBRID EVOLUTIONARY ALGORITHM FOR OPTIMAL
PLANNING OF HYBRID WOBAN

Anwar A. Alsagaf1, Yousef Y. Holba2, Anwar H. Jarndal3 , Gamil R. Salman4
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

122

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

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]:
J cos. = f 1 (CONU j , CWBS.i , CONU j . , CWBSi . ; d ij ) → min
inst . inst design design
(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:
J cov = f 2 ( PL, TR, PTx , PRx , IR, IP, RS , SD, f c ; NS , los / Nlos) → optimal (2)
The parameters in function f j (•) 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 Los / Nlos 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:
PL = A + 10γ log 10 (d / d o ) + L f + Lh + s (3)
where, d is the distance between the access points and the user terminals’ antennas in meters,
the d 0 =100m, A = 20. log 10 (4πd 0 / λ ) and γ = a − bhb + c / hb , here, hb 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( L f ), is defined by
L f = 6.0 log 10 ( f / 2000 ) and for the receiver antenna height ( Lh ) are given by
Lh = 10.6 log( hr / 2000 ) for type A and B while for type C the Lh is defined by
Lh = −10.6 log( hr / 2000 ) 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, S is SINR threshold which satisfies the required BER, γ is the path loss exponent, P
0 N

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

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

TR by:
TR = d ref ( PRx / S0 PN )1 / γ
The grid separation distance equal to half the transmission range; i.e., SD = TR 2 .
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 S0 ), is given by[14]:
IR = SD (1 /((1 / S0 ) − ( SD / d ref )γ ( PN / PRx )))1 / γ (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 PLmax to which a
transmitted signal can be subjected while still being detectable at the receiver. To determine
PLmax we need to take the parameters into account. It is important to remark, that PLmax is
dependent of the input power PTx of the antenna and thus dependent of the output power of the
power amplifier.
Once we know the value of the PLmax , we can determine the maximum range TRmax ,
so we can reach with the base station of a certain technology[15].

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TRmax = g −1 (PLmax − SM , f c , hBS , hMS ) (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. f c is carry
frequency (in Hz). The SM is the shadowing margin (in dB), hBS is the height of the base
station (in meters) and hMS 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 IPtotal . The IPtotal of a random number of interferers N (a ) with random interference ψ (Rk )
is given by[14]:
N (a )
IPtotal = ∑ψ (Rk ) (6)
k =1
The PDF for the total interference power is only dependent on the transmit node density and
given by:
3
−3 .λ2 / 4. IP )
PDF ( IP) = (π / 2)λt ⋅ IP 2
⋅ e − (π t
(7)
Where λt is the transmit node density. The corresponding cumulative distribution
function(CDF) is given by:
CDF (IP ) = erfc(π 3 / 2 .λt / 2 IP )
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]:
RS = (kT / 2) ⋅ WLSR ⋅ NF ⋅ I implem. ⋅ SNRB …………….(8)
This is further translated into:
RS = 10. log((kT / 2) / 0.001) + 10. log(WLSR ) + L
……... (9)
L + 10. log( NF ) + 10. log(I implem. ) + 10. log(SNRB )
or
RS = 177 + 10. log (WLSR ) + 10. log ( NF ) + 10. log (I implem. ) + 10. log(SNRB )
WLSR is wireless link symbol rate, NF is define noise figure, I imolem. is degradation caused by
implementation limitations of noise ratio SNRB . SNRB is determine the theoretical baseband
received signal power to noise ratio. NT is baseband value of thermal noise power and PRx is
define the received signal power. The PRx / NT is needed to operate at the given bit-error-rate.
For an alternative form of this expression, which uses Es / n0 instead of signal power
to noise ratio SNRB , where Es is the symbol energy and n0 is the single sided thermal noise
spectral density. RS is then given by:
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RS = −177 + 10. log(WLSR ) + 10. log( NF ) + 10. log( I implem. ) + 10. log(2 Es / n0 ) ….. (10)
Finally LB with RS can be derived as:
LB = EIRP − RS + GRx − SM total
Where, GRx is the received antenna gain in dB and SM total 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:
Φ( F ) : P × Q → V (11)
In (11) is needed to find the optimal positions of WBSs and ONUs under the uncertainty,
where
r
P ⊂ E r is set feasible values of position, Q ⊂ E q is set feasible values of uncertainty
parameters,
V is set of vector – evaluation functions V (•) , V ( p, q, t ) ∈ E m is evaluation function at
( )
moment t , t ∈ [t0 , T ] , and V p, q i ∈ E m is vector of performance index.
By applying some mathematical transformations and computations we obtain the total error
which is needed to achieve:
k m
( )
E ( p ) = ∑ ∑ ϕ T p, q i Λϕ j p, q i → min
j ( ) p∈P
(12)
i =1 j =1

( )
where, Λ = diag λkk , k = 1, N + 1 - diagonal matrix of positions with size ( N × 1)( N × 1) .
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]
P , Q ,V ( p, q ) (13)
Where:
p ∈ P is vector of the WBS positions or ONUs locations.
ˆ
q ∈ Q ⊂ Q is vector of uncertainty parameters.
V ( p, q ) is vector of evaluation functions.
We assume that, the sets P and Q given as system of nonlinear inequalities-constraints
{
P = p ∈ E r G1 ( p ) ≤ 0 s , 1
} (13a)
Q ={ ∈E G2 (q ) ≤ 0s 2 },
rq
q (13b)
Where:
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0s1 ∈ E s1 , 0s 2 ∈ E s 2 - vectors with non-zeros elements
{
= z ∈ E m Bz ≤ 0 p ,} (13c)
- is dominant polyhedral cone defined by(13c).
When we assume that, the matrix B with size [l × m] and z defined by z = v′′ − v′ , then
B (v ′′ − v ′ ) ≤ 0 p

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 Pi ( xi , yi ) is the position of i-th WBSs, which
will serve users and Pj ( x j , y j ) 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.

128


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 :
{
A(t ) = a i (t ), i = 1, N ; dim a i (t ) = L }
(14)
Where: N is population size; L is bit string length; a (t ) is bit string length; t is number of
i

[ ]
current generation , t ∈ 1, T and T is the last generation.
In each of a (t ) is encoded all information about all vector elements pi (t ) .
i

The second block consists of the following two steps:
Step 1 : The population decoding is obtained by:
∆ : a i (t ) → pi (t ) , i = 1, N
Each partial lµ , µ = 1, n , bit sting ai (t ) is represented into nature number Cµ (t ) according to
i i

the following:
M 0, aµk (t ) = 0

i

C µ (t ) = ∑ Cµk (t ), and Cµk (t ) = 
i i i
(15)
k =1 (− 1) 2

p +1
(
M − k +1
)
− 1 , aµk (t ) = 1
i

The bit string aµ (t ) of the element pµ (t ) of the vector pi (t ) is defined by Grey code.
i i

The coordinate values of the vector p i (t ), i = 1, N is calculated by:
pµ (t ) = pLµ + (C µ (t )( pHµ − pLµ ) / 2 µ −1 ), µ = 1, r
i i

Step 2 : Fitness function calculation.
( )
Compute the V p i (t ) , i = 1, N . In each of individual p i (t ), i = 1, N we must to apply the
ε − Ω − optimal principal condition which is formulated in following such as:
[(( ( )) ) ( )]
B V p i (t ) + Cε p j (t ) − p i (t ) − V p i (t ) ≤ 0 p
(16)
For ∀p (t ), j = 1, N , j ≠ i
j

The number of points p j (t ) is denoted as bi (t ) , for which it’s in the point pi (t ) is executed
the inequalities constraints (16).
If bi (t ) = 0 then pi (t ) is ε − Ω − optimal solution for the multicriteria optimization problem
which is formulated in (13 -13c), so that, pi (t ) is ε − Ω − optimal solution for multicriteria
optimization problem which is formulated as:
min V ( p ) (17)
p∈P

Otherwise, when pi (t ) is not ε − Ω − optimal solution for problem (17), to 0 ≤ bi (t )≤N − 1
Thus, the fitness function in this case is formulated such as:
Φ (a i (t )) = 1 /(1 + (bi (t ) /( N − 1))) q ≥ γ ∗ (18)
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Where q is selected from practical and effect on convergence speed of proposed algorithm.
1
( ) ( )
In (18) shown that when bi (t ) = 0 to Φ ai (t ) = 1 , and when bi (t ) = N − 1 to Φ a i (t ) = q .
2
The third block is forming the probability selection mechanism of the population in parents
set Θ(t ) . 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 [0, S (t )] is constructed by following recurrent relations:
S 1 (t ) = Φ (a 1 (t )),
L
S N (t ) = S N −1 (t ) + Φ (a N (t ))
We assume that S (t ) = S N (t ) .
Step (2): Generate the points-parents population
First, the random value is generated on the interval [0, S (t )] . The population is selected in the
parents set, if the random value lies on the subinterval from [0, S (t )] . After that, the suitable
subinterval was excepted from the interval [0, S (t )] . This is procedure is repeated N / 2 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 [0, Pm ] . 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 (n(t ) / N ) ≥ δ ∗ (19)
Where n(t ) is define the number of individual in the population A(t ) with size N. For that’s it
the inequality: Φ(a i (t )) ≥ γ ∗ must be executed.
If the(19) is executed, to the set of the points p A (t ) ⊂ P is approximation of the ε − Ω −
optimal solution. That is mean that PεΩ = p A (t ) and multicriteria genetic algorithm is
ˆ
finished. Otherwise, if t ≥ t ∗ , the set pA (t ) is approximation of the ε − Ω − 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 V ( p ) is normalized with the following representation
operation:
~ V ( p ) − VLi
Vi ( p ) = i , i = 1, m
VHi − VLi
Where VHi , VLi are maximum and minimum of possible values of the Vi ( p )
VHi = max Vi ( p ) ,
p∈ pεΩ
ˆ

VLi = max Vi ( p ) , i = 1, m
p∈ pεΩ
ˆ
0ˆ
Step2: The initial approximation p ∈ PεΩ is constructed by applying the following:
~
Φ (V ( p )) = max Vi ( p )
i∈M
0 ˆ
Find the p ∈ PεΩ by solving the optimization problem:

130


min Φ (V ( P )) ⇒ p0
ˆ
(20)
p∈PεΩ

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
p ( k +1 ) = p ( k ) + α ( k ) d ( k ) ,
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 d ∈ P ( p ) ⊂ E r inside the constructed dominance cone. This algorithm
consist of following steps:
Step1: The selection of d ∈ P ( p ) ⊂ E r when P ( p ) like the type of (13c) which is
constructed in the space of the locations pi 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:
max z (21)
[d , z ]∈D
T

Where, the D is given as inequalities-constraints:
 ∂V ( p )
 B ∂p d + Z p ≤ 0 p , (21a )

 ∂G ( p )
D : B 1 d + Z S1 ≤ −G1 ( p ), (21b )
 ∂p
 d ≤1 (21c )
 k

p s1
Where Z p ∈ E , Z s1 ∈ E is the vector with the same element z and B is quadratic matrix of
the polyhedral dominance cone.
The equation (21a) is denoted by d ∈ Ω P ( p ) 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:
& &
V ( p ∗ )T B T ⋅ µ + G1a ( p ∗ ) ⋅ν = 0 (22)

131


∗
( )
s
Where G1 a p ∈ E 1 a - constraints vector which is (22) active at point P*. The following
condition z ≤ γ is stop criteria of the multicriteria local optimization. Where γ is show the
accuracy of the multicriteria local search.
Step2: step size α (k ) calculation in the selected direction d (k )
1: firstly, finding the distance to the boundary of the feasible area P is calculated along of
the direction d (k )
{
P = p ∈ E r pL ≤ p ≤ pH }
For that, P may be represented by another form:
P = p ∈ E r Cp ≤ b { }
Assume that, cT = c1 , c2
T T
[ ] [T T
]
; bT = b1 , b2 , so that c1 p (k ) = b1 and c2 p( k ) ≤ b2
(k ) (k )
The distance λd to feasible area boundaries at the point p is defined by:
 ˆ
b (k ) 

min  j ˆ (k ) d (jk ) ≥ 0 
(k ) 
ˆ
λd =   dj
 ,

 ˆ (k )
∞ , if all d j ≤ 0

ˆ (k )
Where d = c2 d
(k )
; b ( k ) = b2 − c2 p (k )
ˆ
(k )
2: step size selection α is calculated by following operators dented by OP1-OP4:
OP1: α = min{ 0 , λd },
(k ) (k )
α
( k + 1)
OP2: p = p ( k ) + α ( k )d ( k ) ,
(k )
OP3: ∆ν = ν p ( ( k +1 )
) ( )
−ν p ( k ) ,
(k )
OP4: ∆ν ∈ Ω ⇔ B∆ν (k ) ≤ 0 p
(k )
If the OP4 in not excepted to, we increment the α 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 p( k +1) = p (k ) − α ( k )d (k ) , and the min ~ z instead of (21) and the
T
[d , z ]∈D
(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

132


algorithm could be defined as f jk+ 1 ( Pj +1 ) = f jk ( Pj ) + s k d =θ v , { }
θ v = 0, 2π , where
k +1 k k +1
f j +1 ( Pj +1 ) > f ( Pj ) , and f
j j +1 ( Pj +1 ) is the values of the objective functions at the next locations.
k
f ( Pj ) is the values of the objective function in the previous locations, and s k is a step vector and θ v
j
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:

Initial set of ONUs position
(obtained before hand by MGA P 0 )

Position selection mechanism
t =0 →t =T

k k
Do move ( x j , y j , s , d )

Step change s ← s + 1

Dominance cone construction
f j+1 (P ) = f j(P ) +

Fitness function calculations

Evaluation function calculation

V k +1 ( P j +1 ) = V k ( Pj ) + s k d =θ k
k k +1 k
∆V = V ( P j +1 ) − V ( P j )
∆V k ∈ ⇔ B ⋅ z <0 p Direction change
d ← d +1
k
No
∆V > 0p

Yes

stop criteria

print the best optimal of the ONUs
positions

Fig.2 The general flowchart of MTA

133


Where, in the fig.2. move ( x j , y j , s k , d k d =θ v ) expresses the search from a point p j ( x j , y j ) ,
with a step s in a direction d , min(s ) is a minimum step, ∆f k ( p j ) is a change in an objective
function values, change direction ∆d d =θ v is a change in the direction of a search, change step
∆s s ← s +1 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).

Fig3.a. Geographical map of Hodeidah city.
fig.3.b. Geographical map of Hodeidah government

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.

Fig.4 Optimal locations of WBs by HEA1 for Fig.5 Optimal locations of WiMAX WBs and ONUs by
Hodeida city HEA2 for Hodeida Government
134


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.

J cov V( p, q,t)
1 1
0.9 0.9
Hill climbing.
P erform ance index (% )

0.8
Coverage normalized

0.8 MGA
0.7 0.7 HEA (MGA+ Hill climbing)
0.6
0.6 HEA best sol.
HEA opt. sol. 0.5
0.5
0.4
0.4 HEA worst sol.
0.3
0.3
0.2
0.2
0.1
0.1 0
0 0 20 40 60 80 100 120 140 160 180 200 220
0 20 40 60 80 100 120 140 160 180 200 220
Generations, t
Generations, t
Fig.7 Performance comparison of HEA(MGA+ Hill climbing)
Fig.6 Convergence of HEA With MGA and Hill climbing independently

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.

135


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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