Comparison of Metaheuristic Approaches for

Impairment Aware Transparent Optical Networks

Urmila Bhanja1, Debajyoti Mishra

2

1Assistant Professor,

2Senior Lecturer.

Dept. of Electronics and Communication Engineering, Indira Gandhi Institute of Technology, Sarang, Orissa,

759146, India.

E-mail: urmilabhanja@gmail.com, debajyoti_igit@yahoo.co.in Abstract- In this paper two metaheuristic approaches are

compared while solving the dynamic routing and wavelength

assignment (DRWA) problem in wavelength division multiplexing

(WDM) optical network. In this problem, the effect of Four Wave

Mixing (FWM) and amplifier spontaneous emission (ASE) noise

are incorporated while solving the problem. The two

metaheuristic approaches used in this work are evolutionary

programming algorithm (EP) and simulated annealing (SA).

These metaheuristic techniques use a common objective function

that is designed to reduce the effect of FWM noise and ASE noise

on a requested lightpath. The FWM crosstalk products and the

static FWM noise power per link are pre computed in order to

reduce the set up time of a requested lightpath, and stored in an

offline database. These are retrieved during the setting up of a

lightpath and evaluated online taking the dynamic parameters

like cost of the links into consideration.

Keywords-Evolutionary programming algorithm; Simulated

annealing; Impairment aware DRWA problem; Four wave mixing;

ASE noise.

I. INTRODUCTION

An important feature of optical networks is their capability to

deliver data with a low bit error rate (BER) over long distances.

However during the routing of signals, as the transmission

distance increases the optical signal undergoes various physical

impairments that include noise generated in optical amplifiers,

nonlinear crosstalk appearing in WDM or dense wavelength

division multiplexing (DWDM) systems due to the fiber

nonlinear effects like cross phase modulation (CPM) and four

wave mixing (FWM), inter symbol interference because of

fiber chromatic dispersion (CD) and polarized mode dispersion

(PMD), etc. These impairments affect the optical networks and

their effects increase with an increase in the propagation

distance. The quality of signals in an optical network, which is

measured by the BER, is therefore dependent on the network

state. Unlike linear impairments, non-linear impairments affect

not only each optical channel individually, but they also cause

disturbance and interference among them. One such

impairment is FWM, in which signals at different wavelengths

interact resulting in generation of new signals called the FWM

components. Some of these FWM components interfere with

the original signals and degrade their quality [13]. The number

of FWM components generated increases with the increase in

the number of users. FWM severely degrades the network

performance if the input power is large and/or the channel

spacing is narrow [13]. Although, nonlinear impairments like

self phase modulation (SPM) and cross phase modulation

(XPM) that come into play only at high data rates, are

considered by some of the authors, the effect of four wave

mixing (FWM), which may degrade the signal quality in a

WDM or a DWDM system even at moderate powers and bit

rates, has received very little attention while addressing the

dynamic routing and wavelength assignment (DRWA)

problem. However, very few papers consider nonlinear effect

like FWM on a DRWA problem [4, 5, 8, 9, 14].

As reported by Azodolmolky et al., there are very few papers

available that use metaheuristics to solve the impairment aware

DRWA problem [2]. Tan et al. have reported an FWM aware

wavelength assignment using Ant colony optimization (ACO)

[14]. They have tried to correlate the input signal power with

FWM crosstalk power. Marsden et al. have proposed a DRWA

algorithm assuming that the quality of service (QoS) of

lightpaths are degraded mainly due to the FWM generated

noise [8]. The same authors have also reported a mechanism to

reduce the set up time for a lightpath in this FWM aware

DRWA algorithm by pre computing the FWM crosstalk power

[9]. However in this work, the authors have assumed the link

lengths to be the same. The main objective of the work

reported in this paper is to compare two FWM aware

metaheuristic approaches to investigate the wavelength routed

optical network design for a non ideal physical layer. The

proposed algorithms such as evolutionary programming

algorithm (EP) [4, 5] and simulated annealing approach

consider the ASE noise and the crosstalk components due to

the FWM effect while minimizing the connection blocking

probability. Simulated annealing (SA) has been used

extensively for modeling many of the optimization problems in

optical network. However, the potential of SA for solving an

impairment aware DRWA problem is not explored yet in the

literature. Therefore, in this work FWM aware SA for the

DRWA problem is developed and compared with EP [4, 5] in

terms of network performance metrics such as mean blocking

probability and mean execution time. Unlike an earlier

approach reported in [8, 9], this work is focused on a network

with variable link lengths, which makes the problem more

complex. In order to reduce the set up time of a lightpath, the

FWM crosstalk products and the static partial powers of all the

FWM terms are calculated offline and are stored in a database.

During the online evaluation of signal quality, the FWM

crosstalk power for the corresponding links are retrieved from

978-1-4673-1989-8/12/$31.00 ©2012 IEEE

the database and then the quality of signal is evaluated

dynamically taking the link length into consideration [4, 5]. In

the proposed approach, the signal quality measured in terms of

BER, is also evaluated, in addition to finding a wavelength

continuous path. If the BER is found to be below a threshold

value then the call request is accepted.

II. FOUR WAVE MIXING CROSSTALK IN A MULTICHANNEL

SYSTEM

FWM is one of the nonlinear effects in optical fiber, in which

three signals of different wavelengths interact to generate a

fourth wavelength that can interfere with the information signal

and result in performance degradation [8, 13].

III. SYSTEM AND PROBLEM MODEL

A. Problem definition

For the impairment aware DRWA problem the lightpath

requests are assumed to arrive at the network dynamically

according to a Poisson process with an average arrival rate of

Λ. A lightpath request is specified by three attributes: S, D, and

Th, which respectively represent the source node, the

destination node, and the holding time, for the request. The

source and the destination for each request are uniformly

randomly distributed. The holding time for a lightpath request

are assumed to be exponentially distributed with fixed mean,

T_hold=E[Th]. During this holding time duration, the network

resources are reserved for the connection request. Once the

holding time expires, the network resources are released to be

used later by other incoming lightpath requests. The network

load is defined as: Network load= Λ ×T_hold, the mean

blocking probability, and the mean execution time, are defined

as (Number of requests blocked ⁄Total number of requests

processed), (Total simulation time⁄ Total number of requests)

respectively [6].

B. The network model

It is assumed that the reduced version of NSFNET used to

illustrate the proposed algorithm can be modeled as a graph

G(V, E), where V is the set of nodes, representing N

wavelength routing nodes (WRNs), and E is the set of fiber

links, representing physical connectivity between the nodes.

Fig.1 shows the network model assumed in this work [10]. The

components present in a wavelength routing node (WRN)

include a cross connect switch (XCS), optical power taps for

monitoring signal, and a pair of EDFAs on either side of the

XCS for signal amplifications.

In the proposed model, the WRN also contains a transmitter

array and a receiver array that helps in adding or dropping a

local signal at any of the wavelengths at the node [10]. The

WRN’s are connected through non-zero dispersion shifted

optical fibers (NZDSF). It is assumed that there are no in-line

amplifiers in the network. In this work, the effect of signal

leaks in the optical cross connect switches and the effect of

non-ideal filtering at the demultiplexers, are neglected. In this

model the effect of chromatic dispersion (CD) and polarized

mode dispersion (PMD) are neglected.

Fig.1. Architecture of a wavelength routing node (WRN) [10]

.

C. The routing and wavelength assignment model

The routing and wavelength models assumed in this work are

identical to that used in [1, 3, 4, 5, 12].

D. Online signal power and noise power evaluation module

The calculation of received signal power, FWM crosstalk

power, and ASE noise power along a lightpath during a call

admission step is dynamic in nature. The signal power and the

ASE noise power depend on the number of links traversed by

the lightpath during the call admission phase and the associated

link cost. The FWM crosstalk power depends on the number

of different signals present in a link and the length of the

associated links that a lightpath traverses during the call

admission phase. The signal power, the ASE noise power at the

output of the kth intermediate node, and the FWM crosstalk

power for the multichannel system are expressed for the xth

individual as in [8, 10].

In a multichannel system, each lightpath traverses H hops or

links until it reaches its destination node. The accumulated

FWM crosstalk power at the destination node, PDNx(fr+fl-fm), is

the sum of all the crosstalk components generated in the links

traversed by the lightpath for the xth individual or solution and

is given by

1

( ) ( , , )r l

H

DNx r l m rlmx r l m

c f f fm

P f f f P f f f=

+ − =∑∑∑∑ , (1)

The FWM crosstalk power per link at the kth node for the xth

individual due to the three co-propagating signals at

wavelengths , ,r l mλ λ λ is given by [8,9],

2 2 ( 1, ) 2 2( , , , ) ( ( ) ( ) ( ) ( ) ( ))/9.0r L k k

rlmx r l m rlm r l m eff in tap mx dm sw outP k D PPPe L G k L L k L k L kG kαλ λ λ η γ − −=

(2)

The effective length Leff for the kth node is expressed as

-αL(K -1,K)

eff

(1- e )L =

α (3)

In the above equations, L(k-1,k) denotes the length of the link

between the (k-1)th node and the kth node. ( , )sigx i

p k λ

represents the signal power of kth node at wavelength λi,

( 1, )sigx i

p k λ− represents the signal power of (k-1)th node at

wavelength λi, ( 1, )fx

L k k− represents the fiber loss between

the (k-1)th and the kth node, and Gin(k) and Gout(k)

respectively represent the gain of the EDFAs at the input and

output of the kth node for any wavelength, ( )dmL k represents

the demultiplexer loss at the kth node, ( )swL k represents the

switch loss at the kth node, ( )mxL k represents the multiplexer

loss at the kth node, tap

L represents the tap loss,

( , )asex ip k λ represents the ASE noise power of kth node at

wavelength λi, ( 1, )asex ip k λ− represents the ASE noise power

of (k-1)th node at wavelength λi, h is Planck’s constant, iν is

the optical frequency at iλ , spη represents the spontaneous

emission factor for the EDFAs, Bo represents the optical

bandwidth, and Drlm represents the degeneracy factor in the

presence of the frequencies fr, fl, and fm.

E. Online bit error rate evaluation model

Optical signal received at the destination node in the presence

of ASE noise and FWM crosstalk power can be expressed as

( ) ( ) ( )( ) cos(2 ( )) ( ) ( )R x i ase x fwm x

E t A t t E t E tπν φ= + + + (4)

The first term in (4) represents the signal component at

frequency νi for the xth individual, A is the signal amplitude,

and φ(t) is its phase. The second and the third terms

respectively represent the received ASE noise power and the

FWM crosstalk power at the receiver node for the xth

individual. The photodetector is a square law device and hence

the received lightwave after photodetection produces a

photocurrent given by,

1 1 1

1

( ) 1( ) ( ) ( ) ( ) ( )

( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

d x x sig ase x sig fwm x ase ase x fwm fwm x

fwm ase x th shot x

i t i t i t i t i t i t

i t i t i t

− − − −

−

= + + + +

+ + +

(5)

Equation (5) represents the signal current received for bit ‘1’

after photo detection, along with the beat noise components.

Equations (6) and (7) below represent the corresponding noise

variances.

The first term in (5) represents the signal component and the

rest of the terms represent the beat noise components for the

xth individual. The last two terms represent the thermal noise

current and the shot noise current respectively. The combined

noise can be modeled as a zero mean Gaussian random process

with a variance given by,

1 1

2 2 2 2 21

2 2

( ) ( ) ( ) ( ) ( )

( )

sig ase ase ase sig fwm fwm ase

thermal shot

x x x x x

x

σ σ σ σ σ

σ σ

− − − −= + + +

+ +

(6)

In (6), σ2

sig-ase(x) represents signal-ASE beat noise components,

σ2ase-ase(x) denotes ASE-ASE beat noise, σ

2sig-fwm1(x) denotes

signal-FWM beat noise, σ2

fwm1-ase(x) represents FWM-ASE

beat noise in the presence of signal, σ2

thermal represents thermal

noise variance, σ2

shot(x) represents shot noise variance for the

xth individual or solution and are expressed as in [7,13]. Equation (7) below represents the variance due to the beat

noise components at the receiver when bit ‘0’ is received by

the photodetector.

0

2 2 2 2 2

0( ) ( ) ( ) ( )ase ase ase fwm thermal shotx x x xσ σ σ σ σ− −= + + + (7)

In (7), σ2ase-fwm0(x) represents ASE-FWM beat noise variance

for bit ‘0’ for xth individual. These are expressed as in [7, 13]. The receiver BER due to the xth individual can be expressed

as,

1( ) ( ) ( )

1 0

( )0.25[ ( ) ( )]

2 ( ) 2 ( )

x th x th x

x

i t i ierfc erfc

x xξ

σ σ

−= +

(8)

The receiver BER is evaluated with a fixed decision threshold

ith(x). By suitably selecting the threshold, one can minimize the

BER. In this work, the threshold value is fixed at i1(x)(t)/2 [10].

IV. THE PROPOSED ALGORITHMS

This section briefly explains the mechanism of the proposed

evolutionary programming algorithm (EP) [3, 4, 5] and

simulated annealing (SA).

A. Chromosome representation

A chromosome represents a route or a path encoded from

source to destination as described in [3, 4, 5].

B. Population initialization and fitness calculation

The population that consists of a single individual is generated

randomly so as to satisfy the given constraints within the

threshold time of T1.

The fitness function for the problem is formulated as follows

[4, 5]:

1

2 2

( ), ( 1)

1 ( , )

2 2 2 2

1 1

[ ( ) ( )

( ) ( ) ( )]

xk

x x gx j gx j ijx shot sig ase

j i j E

ase ase thermal sig fwm fwm ase

f W C H x x

x x x

σ σ

σ σ σ σ

−

+ −= ∈

− − −

= + + +

+ + + +

∑ ∑

(9)

In the above equation, fx represents the fitness value of the xth

chromosome or path. In this work, the objective is to minimize

the fitness function. In (9) the first term represents the total cost

of a path, the second term represents the total number of hops

in the path, and the rest of the terms represent different noise

variances for the lightpath. Wx represents the free wavelength

factor for the lightpath, xk is the length of the xth chromosome

or path, and ( )x j

g and ( 1)x j

g + respectively represent the gene

of the jth locus and the (j+1)th locus of the xth chromosome

Wx, The free wavelength factor, is set to one if the wavelength

continuity constraint is satisfied for all the links of a

chromosome; else, it is set to 0.

C. Mutation

The mutation operation used in the FWM aware DRWA

algorithm is identical to that described in [3, 4, 5] and the

threshold time is fixed at T2 during this process. The threshold

times T1 and T2 attempt to reduce the execution time of the

algorithm during initialization and the mutation process.

D. Wavelength assignment algorithms

The wavelength assignment techniques investigated in this

work are the Random technique, and an FWM aware priority

based wavelength assignment technique [15, 4].

V. THE PROPOSED SIMULATED ANNEALING APPROACH

A. Initialization

The initial temperature Temp is set to 10,000 and the cooling

rate ∆ is set to 0.95.

B. Chromosome generation

A chromosome is generated as in [3, 4].

C. Energy function calculation

It is identical to the fitness function of EP.

D. Selection

In this step the difference between the energy functions

corresponding to the two chromosomes are found out. If the

second chromosome or solution is better than the first, then the

second one is selected. If it is worse than the first solution, the

solution is accepted with a probability of exp(-∆E/Temp). Here

∆E represents the difference in energy functions corresponding

to the two solutions and Temp is the temperature.

E. Termination

Steps are repeatedly executed till the final temperature Temp

becomes 0.000001. With each iteration, the temperature is

updated as Temp = ∆*Temp.

VI. THE ALGORITHM IMPLEMENTATION

The proposed algorithms are simulated using Microsoft Visual

C++ on an Intel Core i3 processor (2.4 GHz clock and 3 GB

RAM). The reduced version of 14-node NSF network topology

is used and the cost values are assigned as reported in [6]. The

threshold times T1 and T2 are fixed at 0.5 sec and 1.5 sec,

respectively. The hop count bound, h0, is kept at 4 [3]. The hop

count bound tries to minimize the ASE noise and FWM

crosstalk noise as the lightpath now traverses limited number

of hops and hence, minimizing the mean blocking probability.

VII. COMPUTATIONS OF CROSSTALK PRODUCTS AND POWERS

A.Offline

The FWM crosstalk power is calculated partially for all the

possible combinations of active lightpaths and stored in an

offline database. As soon as a request arrives, a wavelength

continuous path is found and then on each link in the path, the

wavelengths of the co-propagating signals are identified. The

partial crosstalk power corresponding to these wavelengths is

then retrieved from the offline database and is used in the

online evaluation of the lightpath [4].

Equations (10) and (11) below show the FWM power and the

phase mismatching factor for three different wavelengths at the

kth node respectively.

2 2 2( , , , ) ( ( ) ( ) ( ) ( ) ( ))/9.0rlmx r l m rlm r l m in tap mx dm sw outP k D PPPG k L L k L k L k G kλ λ λ γ= (10)

2 2

0 00 0

2( )( )( ( )( )[( ) ( )])

2

cr m l m c r l

dDf f f f D f f f f

c c d

πλ λβ

λ= − − + − + − (11)

B. Online

In the proposed work, a simple search technique is used for the

faster retrieval of data from the offline database. At any

instant, the corresponding partial FWM power and the phase

mismatching factor for the existing combination of wavelengths

in a link are retrieved from the offline database. The FWM

efficiency, the FWM crosstalk power per link, and the total

accumulated crosstalk power for the lightpath, are computed

online as expressed below in (12), (13) and (14) for any request.

It is assumed that the total number of hops a lightpath traverses

is denoted by ‘H’ [4].

The system parameters and the values used in the model are as

referred in [7, 13].

2 2

2 2 2

4 sin ( . / 2)1

(1 )

L

L

e L

e

α

α

α βη

α β

−

−

= +

+ − (12)

2 2 ( 1, ) 2 2( , , , ) ( ( ) ( ) ( ) ( ) ( ))/(9.0)L k k

rlmx r l m rlm r l m eff in tap mx dm sw outP k D PPPe L G k L L k L k L kG kαλ λ λ η γ − −=

(13)

1

( ) ( , , )r l

H

DNx r l m rlmx r l m

c f f fm

P f f f P f f f=

+ − =∑∑∑∑ (14)

VIII. RESULTS AND DISCUSSIONS

This section compares the simulation results exhibited by EP

and SA. As the proposed algorithms are randomized

approaches, each of the experiments are run ten times and the

average is estimated to plot the results. The results are also

analyzed statistically to estimate the margin of error for each of

the experiments. The proposed FWM aware assignment

technique tries to minimize the effect of FWM crosstalk. In this

work, Random and FWM aware priority based wavelength

assignment techniques are considered as these two techniques

are found to give better network performance compared to

other assignment techniques [4]. Fig.2 depicts the mean

blocking probability for Random wavelength assignment

technique and for FWM aware wavelength assignment

technique for a total of 50,000 requests. As expected the FWM

aware priority based wavelength assignment technique

provides the lowest mean blocking probability for both the type

of algorithms EP and SA. The mean blocking probability of the

order of 10-2

even with the estimated margin of error of value

±9.59527519 x 10-4

and ±7.17498651 x 10-2

for 95% of time

obtained by EP and SA respectively when integrated with the

FWM aware priority based wavelength assignment technique

and are found to be better compared to that of heuristic [8] and

metaheuristic approaches [14] at network load of 90 Erlang.

50 60 70 80 90 100 11010

-3

10-2

10-1

100

Network Load (Erlangs)

Me

an

Blo

ck

ing

Pro

ba

bil

ity

Random EP

Random SA

FWM aware EP

FWM aware SA

Fig.2. Mean blocking probability for different network loads

Fig.3 depicts the mean execution time for Random wavelength

assignment technique and for FWM aware wavelength

assignment technique for a total of 50,000 requests. It is

observed from the experiment that FWM aware wavelength

assignment technique for both EP and SA can be used for real

time application for a network load less than 90 Erlang [11]. The margin of error for EP and SA was estimated and found to

be ±0.0098998108 and ±0.0076812385 respectively for a

network load of 80 Erlang for 95% of time. Fig.4 below depicts

the fitness convergence curve for the FWM aware EP and SA. The estimated margin of error was found to be ±0.001568204

and ±0.0093206151 for the EP and SA respectively at the point

of convergence for 95% of time.

50 60 70 80 90 100 1100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Network Load (Erlangs)

Me

an

Ex

ec

uti

on

tim

e (

se

co

nd

)

FWM aware EP

FWM aware SA

Random EP

Random SA

Fig.3. Mean execution time for different network loads

1 2 3 4 5 6 7 8

102.82

102.83

102.84

102.85

102.86

102.87

Generations

Avera

ge f

itn

ess s

co

re

FWM aware EP

FWM aware SA

Fig.4. The fitness convergence curve

IX. CONCLUSION

Two different metaheuristic approaches are compared in terms

of network performance metrics such as mean blocking

probability and mean execution time. The FWM aware EP is

found to give better results compared to the FWM aware SA.

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