Post on 10-Feb-2022
INADYUTI DUTT* et al. ISSN: 2250–3676
[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337
IJESAT | Sep-Oct 2012
Available online @ http://www.ijesat.org 1327
LIGHT TRAIL MINIMIZATION IN ALL-OPTICAL NETWORK USING
CONNECTION MATRIX AND GENETIC ALGORITHM AND THEIR
COMPARISONS WITH THE ALGORITHM ADOPTED BY INTEGER
LINEAR PROGRAMMING
Inadyuti Dutt1, Soumya Paul
2
1Asst. Professor, Dept of Computer Application, B. P.Poddar Institute of Management & Technology, West Bengal
University of Technology BF-142, Salt Lake City, Sector-II, Kolkata, West Bengal-700052, India ,inadyuti@gmail.com 2Assoc. Professor, Dept of Computer Application, B. P.Poddar Institute of Management & Technology West Bengal
University of Technology, KolkatA, West Bengal-700052, India , soumya.paul2000@gmail.com
Abstract Recently a new architecture called “light trail” has been proposed for carrying data traffic in optical networks and has emerged as a
promising candidate for enabling IP over WDM networks. Optimizing the number of light trails that must be setup to service
connection requests as they arrive is an important light trail design problem. Most of the existing light-trail assignment algorithms
adopt ILP (Integer Linear Programming) approach. Due to high complexity such algorithms are not scalable. In this paper, a
heuristic approach with Connection Matrix (CM) and Genetic Algorithm (GA) is proposed for reducing the number of light trails for
given a graph (network) and a number of connection requests, while using minimum network resources that need to be setup in a
survivable optical network. The results are also compared with light trail algorithm adopted by ILP.
Index Terms: Heuristic; Internet Protocol (IP); Wavelength Division Multiplexing (WDM), Lightpath; Light-trail;
Integer Linear Programming (ILP); Genetic Algorithm (GA).
----------------------------------------------------------------------***------------------------------------------------------------------------
1. INTRODUCTION
In an all-optical network (AON), all network-to-network
interfaces are based on optical transmission, all user-to-
network interfaces use optical transmission on the network side
of the interface and all switching and routing within AON
network nodes is performed optically. Optical networks are
high-capacity telecommunications networks based on optical
technologies and components that provide routing, grooming,
and restoration at the wavelength level as well as wavelength-
based services. In a wavelength routed optical network, data
transfer between clients requires setting up a unidirectional
lightpath (channel) in the optical layer. Such a channel allows
source-to-destination transfer optically throughout the course
of the lightpath. This requires that an appropriate path (route)
and a free wavelength on this path be determined such that this
lightpath connects the sending and receiving clients optically.
The process of lightpath determination may be repeated till
either a connection is established or all the options have been
exhausted. Normally it is required that the same wavelength be
allocated on all the fiber links in the lightpath. This is known as
the “wavelength continuity constraint”.
This lightpath approach does not yield good bandwidth usage
due to the burst nature of data traffic and the fact that most
users generate relatively lower bit rate traffic compared to the
bandwidth of the lightpath. A light trail is a unidirectional
optical bus between a convener node (i.e. light-trail head) and
an end node. It is implemented using a wavelength, and allows
the intermediate nodes to share the bandwidth by adding and
dropping traffic, provided that the total traffic load carried is
not more than the bandwidth of the wavelength. At each
intermediate node, this is achieved by splitting a percentage of
transponder. Meanwhile, the rest of the optical signals continue
to propagate along the light-trail. Thus a light trail is similar to
a lightpath, yet it is different in the sense that intermediate
nodes can also access the unidirectional connection for data
transfer, resulting in better source utilization.
INADYUTI DUTT* et al. ISSN: 2250–3676
[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337
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Available online @ http://www.ijesat.org 1328
One of the light trail design problem is to minimize the number
of light trails needed to serve a given number of connection
requests. The proposed heuristic finds a set of light-trails to
cover the given requests in survivable optical networks such
that the total number of light-trails required is minimized using
Genetic Algorithm, Integer Linear Programming.
2. SURVEY STUDY OF EXISTING ALGORITHMS
Ashwin Gumaste and Imrich Chlamtac [1] propose the concept
of light-trails to alleviate the problems in sustaining IP centric
communication at the optical layer. With the principle of
access to the all-optical path at any node, a light-trail offers to
provide full unidirectional optical connectivity, while avoiding
the need for dynamic, burst type, optical paths establishment.
For setting up light-trails as well as signaling purposes within
light-trails an out of band communication channel called
optical service channel (OSC) exists which is dropped and
processed at each node.
Michael T. Frederick, Nathan A. VanderHom and Arun K.
Somani [4] discuss the advantage of light-trail over MPLS
(Multiprotocol Level Switching), OBS (Optical Burst
Switching) and OPS (Optical Packet Switching) as solutions to
realizing an all-optical network. Proposed solutions for all-
optical networks such as MPLS and OBS monopolize a
wavelength throughout connection duration and do not take
advantage of switches that are already configured. An OPS is a
technology that is not mature and most likely will not be in the
near future. Light trail technology attempts to address the
shortcomings of these various technologies by allowing
intermediate connection nodes to also use the unidirectional
bus, as well as maximize the reuse of already configured
optical switches.
Ashwin Gumaste, Gabriel Kuper and Imrich Chlamtac [5] used
the concept of clustered light-trail (CLT). While ring networks,
due to the fact that their nodal degree is 2, can support only
linear light-trails, mesh networks, on the other hand can
support tree shaped light-trails which are called clustered light-
trails (CLT). A Clustered Light-trail is a tree rooted at a node
called the convener. The end nodes of the branches may be
distinct, and so the CLT can have multiple end nodes.
Wensheng He, Jing Fang, Arun K. Somani [6] focus on the
optimal design of survivable light trail optical network. Two
protection schemes, namely connection based protection and
link based protection, that can achieve 100% protection against
single link failure are proposed and compared. Connection
based protection scheme is more practical for light trail
architecture where the hop-length is limited due to power loss.
Jing Fang, Wensheng He, Arun K. Somani [7] present light-
trail architecture and its optimal design. A two-step approach
for solving the light trail design problem -the first step is called
traffic matrix preprocessing; it divides single longhop paths
into several shorter paths that satisfy the hop-length constraint.
In the second step, the light trail design problem is formulated
as an integer linear programming (ILP) optimization problem.
Bin Wu and Kwan L. Yeung [9] introduce an efficient heuristic
algorithm to solve static light-trail assignment problem. The
problem is solved based on three key factors. These factors
include the request discreteness, the shortest path length of
each request, and the flow volume. The importances of the
three factors are ranked in the same order as they are
mentioned. This algorithm also adopts a reference node
mechanism to address the request discreteness issues.
Weiyi Zhan, Guoliang Xue, Jian Tang, Krishanaiyan
Thulasiraman [10] considers the dynamic light-trail routing
problem where the connection request comes and leaves
dynamically. For each dynamically arriving connection request
a light-trail is found to carry it with the objective of consuming
a minimum number of free wavelengths. Protection issues in
light-trail routing in WDM networks with dynamic traffic also
has been considered.
Akhil Lodha, Ashwin Gumaste, Paresh Bafna and Nasir Ghani
[12] consider an optimization technique; the uncertain nature of
traffic is called stochastic optimization. Stochastic optimization
is based on a multi-stage model reducible to a two-stage model.
The stages involve computation of an optimal solution
followed by estimation and recourse taking future uncertainties
into consideration.
Arun K. Somani [11] discusses an important problem in optical
networks with wavelength-division multiplexing is that of
traffic grooming. Traffic grooming is a technique for
multiplexing different sub wavelength capacity traffic
requirements onto a single wavelength so that the wavelength
and hence the capacity requirements of the whole network are
minimized.
Dzmitry Kliazovich, Fabrizio Granelli, Hagen Woesner and
Imrich Chlamtac [16] present a novel solution of bidirectional
high speed communications for IP traffic transport over WDM
networks. Bidirectional light-trail (BDLT) is an organization of
two separate light-trails connecting a set of nodes in two
directions (downlink and uplink) allowing bidirectional
communication. Broadcasting and multicasting in BDLT
architecture is performed by simultaneous transmission in both
directions for any node of the light-trail.
INADYUTI DUTT* et al. ISSN: 2250–3676
[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337
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Available online @ http://www.ijesat.org 1329
3. PROPOSED HEURISTIC IN SURVIVABLE
OPTICAL NETWORK
3.1 Problem Definition
Given a graph (network) and a number of connection requests,
the problem is to find a set of light-trails to cover the given
requests, such that the total number of light-trails required is
minimized. Additionally the blocking problem of the network
has been considered. Number of blocked links or connections
has been reduced with minimized light-trails and the
percentage of reduction of blocking is calculated here.
3.2 Problem Description
Consider G (V, E) is a graph (unidirectional or bidirectional)
which represents a topology, where V represents the set of n
nodes and E represents the set of m links. The maximum length
(in hop) of a light-trail is denoted by Lmax. The set of existing
request for the network is taken in a request matrix which is
denoted by rqst_mtrx and the set of connections among the
nodes of the network is represented by another matrix denoted
by connectivity matrix or shortly cntv_mtrx. As G is a directed
graph, so connections among the nodes do not only indicate the
links among those nodes but their directions also. Each request
in rqst_mtrx is served by only one light-trail and one light-trail
is used to serve only one request. So, here the number of light-
trail is equal to the number of existing request in rqst_mtrx. So,
the set of light-trails denoted by LT is actually the set of
existing requests in rqst_mtrx.
3.2.1 Assumptions
1. Traffic-matrix Preprocessing: Normally due to power losses,
there is a limit on the maximum hop length of a connection.
The hop length is generally restricted to a maximum of 5. Thus
if the number of hops in the shortest path between a pair of
nodes exceeds this limit, then a connection request between
them must be broken down into two or more connection
requests. The algorithm that preprocesses the connection
request is discussed in [6]. It was not implemented as the part
of the work.
2. Assignment constraint: each request is assigned to one and
only one light-trail.
3. Light Trail Capacity Constraint: The aggregated request
capacity on a light trail should not exceed the full wavelength
capacity.
4. Link-disjoint Light trail Constraint: In order to provide
connection based protection, primary and backup connection
request should be accepted and maintained as link-disjoined
light trails.
3.3 Algorithm
3.3.1 Light-trail implementation with Connection
Matrix (CM)
INPUT: Graph G (V, E); the set of existing light-trails LT
from request matrix rqst_mtrx; connectivity matrix cntv_mtrx;
the maximum hop-length of a light-trail Lmax.
OUTPUT: The set of light-trails (final_lt) that cover the given
requests having following properties:
1. The length of each light-trail is no longer than Lmax.
2. Total number of light-trails required is minimized.
Step1: Checking of blocking
1. If, any light-trail of rqst_mtrx is blocked, keep it in
blocked_lt.
else, keep the light-trail in nonblocked_lt.
2. Split each link of each light-trail of blocked_lt.
3. Check, whether these links are covered by the light-trails of
nonblocked_lt either directly or via nodes.
if not, the links are kept in blocked_links.
Step2: Minimization of light-trails of nonblocked_lt with CM.
1. Determine the hop-length of each light-trail of
nonblocked_lt.
2. Compare the hop-length of each light-trail with Lmax.
(i) if hop-length < Lmax, select the corresponding light-trail.
(ii) else if hop-length ==Lmax, add the corresponding light-
trail to temp1.
3. Concatenate the light-trails selected from step2 (i) with each
other and store the result in temp2.
4. Each node of the light-trails of temp2 are checked.
If, two consecutive nodes are same (same node
number), consider them as one node (uniqueness).
5. Again count the hop-length of each light-trail of temp2.
6. Compare the hop-length of each light-trail of temp2 with
Lmax.
(i) if hop-length > Lmax, cancel out the
corresponding light-trail.
(ii) else, the remaining light-trails are kept in temp3.
7. Check the connection of each light-trail of temp3 by
cntv_mtrx.
(i) if the connection of light-trail is not valid
according to cntv_mtrx, cancel out the light-trails.
(ii) else, keep it in temp4.
8. Check uniqueness of the light-trails of temp4.
If, two or more light-trails are same consider them as
one unique light-trail.
9. Selection of proper light-trails from temp4 and kept in
temp5.
(i) Check for the requests which are served by only
one light-trail, select the light-trails first.
INADYUTI DUTT* et al. ISSN: 2250–3676
[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337
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Available online @ http://www.ijesat.org 1330
(ii) Find out other requests which are also served by
theses selected light-trails and cancel out the other light-trails
which serve only these requests.
(iii) Now if any request is left that is served by two or
more light-trails select any one from them.
10. Match each light–trail of temp5 with each light-trail of
temp1.
(i) if a match is found the corresponding light-trail is
cancel out from temp5.
(ii) else keep the light-trail of temp5 in new_lt.
11. Check whether all the requests in the rqst_mtrx are served
by the light-trails of new_lt.
If not, then the request is added to the final_lt.
12. Add temp1 and new_lt and also blocked light-trails to
final_lt.
13. Return final_lt.
Step3: Reduction of blocking with minimized light-trail.
1. Check whether the links of blocked_links are covered by
the light-trails of new_lt either directly or via nodes.
if not, the links are kept in finally_blocked.
2. Calculate the percentage of reduction of blocking using the
following equation.
Consider, total number of links of blocked_links = bl
total number of links of finally_blocked =fb
So, reduction of blocking (%) =
3.3.2 Example Illustrating Proposed Heuristic with
CM
The directed (unidirectional) graph G, representing mesh
topology is depicted in figure1. The request matrix denoted by
rqst_mtrx containing all the requests and the connectivity
matrix denoted by cntv_mtrx representing all the connections
between the nodes of network G are given as:
Here, the size of the rqst _mtrx is 8x4. So, at the beginning the
total number of light-trails needed to serve all the requests is 8.
Now consider the first two light-trail of rqst_mtrx are blocked.
So each link of these two light-trails is blocked.
The rest of the light-trails of rqst_mtrx are kept in
nonblocked_lt. The links of blocked light-trails which are not
covered by the light-trails of nonblocked_lt (either directly or
via nodes) are considered as blocked_links. Here, [2 3] is
covered by 2nd light-trail of nonblocked_lt.
(bl - fb)
bl X 100
Fig: 1.Unidirectional graph G representing mesh topology
INADYUTI DUTT* et al. ISSN: 2250–3676
[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337
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Available online @ http://www.ijesat.org 1331
In this example, the value of Lmax is considered 3. The first two
light-trails (that served first four requests) having Lmax=3, will
be a part of final result. But the rest four having hop-length <3,
will be concatenated with each other. The steps are shown
below:
Now request 3-1-5 is only served by the light-trail 0-3-1-5. So
this light-trail is considered first. 0-3 and 1-5 are also served by
this light-trail. So, we don‟t need to consider the light-trail 1-5-
0-3 anymore. Now 2-4 can be served by both 1-5-2-4 and 2-4-
1-5. So, any one of them can be selected. The minimized light-
trails are kept in new_lt.
So, in this example finally the total number light-trails required
to serve all the requests is reduced from 8 to 6.
Now [0 1] link of the blocked_links is covered by 1st
light-trail
of new_lt through node 3 and [1 2] link of the blocked_links is
covered by 2nd
light-trail of new_lt through node 5.
finally_blocked will contain the links of blocked_links which is
not covered by new_lt. So, finally_blocked = 4 1
Total number of links of blocked_links (bl) =3; Total number
of links of finally_blocked (fb) =1. So, reduction of blocking
(%) = ((3 -1)/3)*100=66.67%
Similarly another example is given for NSF network shown in
figure2. Hence also the value of Lmax is 3.
Fig 2.NSF network
The request matrix rqst_mtrx and the connectivity matrix
cntv_mtrx of this network are given below:
So, finally_blocked =
Total number of links of blocked links (bl) =4; Total number
of links of finally blocked (fb) =2
So, reduction of blocking (%) = ((4 -2)/4)*100=50%
3.4 Light-trail Minimization Using Genetic Algorithm
Step1 and step 3 are same as previous algorithm. So, they are
not mentioned here. Only step 2 is implemented using GA.
Step2: Minimization of light-trails of nonblocked_lt with
Genetic Algorithm.
(i) Set generation number t 0; Set maximum generation
max_gen 10; Set string length xlen (Lmax +1); Set
crossover probability pcross 0.98; Set mutation probability
pmut 0.001; Set crossover site xsite2;
0 3 1 5 1 5 2 4
new_lt =
INADYUTI DUTT* et al. ISSN: 2250–3676
[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337
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(ii) Initial population:
(a) Calculate the value of WL for each light-trail in
rqst_mtrx,
where WL= 𝑊𝑖𝑗Lmax +1𝑗=𝑖+1
Lmax𝑖=1
and 𝑊𝑖𝑗 =
(b) The light-trail which satisfy WL<Lmax, is considered as a
string Si.
(c) ini_pop {S1, S2,…….,Spop_size} as initial population,
where pop_size denotes total number of strings.
(d) Keep the rest of light-trail of nonblocked_lt in temp1.
(iii) Compute fit (Si) for each string Si (1≤ i≤pop_size) of
initial population, where fitness function
fit (Si) = | Lmax + WL|
(iv) Selection or Reproduction:
The selection operation described below on the string of
ini_pop, generate a mating pool mate_pool of size pop_size.
(a) Calculate the probability Pi of selection of Si
(1≤i≤pop_size)
Pi = fit (Si) / ∑ fit ( Si)
(b) Calculate the expected number of copy E.C.
(expected count) of Si (1≤i≤pop_size).
E.C=
where,
(c) Generate a random number rj from [0,1] for
j=[1,2,………,pop_size] and compute actual number of copies
(actual count) of Si(1≤i≤pp_size).
if rj > (1- fractional remainder of E.C.), then the additional copy
is awarded to the ith
string.
(v) Crossover:
The crossover operation is described below on the strings of
mate_pool and obtains a population of temp_pop of size
pop_size.
(a) Randomly select two strings as pair from mate_pool
such that the total number of each string is equal to the
corresponding actual count and form (pop_size/2) number of
paires.
(b) Generate a random number rk from [0, 1] for k= [1, 2,
(pop_size/2)] for each pair such that, if rk ≤pcross, the
crossover will undergoes at the cut point xsite.
(vi) Mutation:
Mutation operation is described below on the string of
temp_pop and obtains a population new_pop of size pop_size.
Generate a random number rm from [0, 1] for m= [1,
2...pop_size X xlen] for each node nj (1≤j≤xlen) of each string
Si (1≤i≤pop_size) of temp_pop such that,
if rm ≤pmut, exchange node nj of Si with any other
randomly selected node nk of Si where 1≤k≤xlen and k ≠ j.
(vii) Compute fit(Si) for each string Si (1≤i≤pop_size) of
new_pop.
if, fit (Si)=2Lmax, then Si is kept in new_lt.
(viii) Check, whether the requests, served by the light-
trails of ini_pop are now all served by the light-trails of new_lt.
if, yes, then
(a) Light-trails of temp1 and new_lt are kept in
final_lt. The blocked light-trails of blocked_lt are also added to
the final_lt.
(b) Return final_lt.
else
if t< max_gen,
(a) Set tt+1; (b) Rename new_pop as ini_pop; (c) Go to
step (iii).
3.4.1 Example Illustrating Proposed Heuristic with
GA:
WL values of each light-trail of nonblocked_lt of 1st example
(fig.1.) are shown in table1. The last four light-trails having
WL<Lmax (i.e WL<3 as Lmax=3) forms the initial population.
Table2. Computes fitness value of each string.
Table 1: Evaluating
WL value of each
light-trail
Initial Population
rq no. Rqst_mtrx W(Li)
1. 4 1 2 3 3
2. 5 2 3 1 3
3. 3 1 5 - 2
4. 0 3 - - 1
5. 1 5 - - 1
6. 2 4 - - 1
pop_size =
1, if there exists a unidirectional link from node i to node j 0, otherwise
Initial
population
INADYUTI DUTT* et al. ISSN: 2250–3676
[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337
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Table 2: Evaluating fitness value of each string
The considerations are:
(i) Population size (pop_size) = 4; (ii) Maximum number of
generation (max_gen) = 10; (iii) String length = 4; (iv)
Crossover probability (pcross) = 0.98; (v) Mutation
probability (pmut) =0.001; (vi) Crossover site (xsite) = 2.
Selection procedure of individual string is referred in Table 3.
Crossover and offspring generation is shown in table4. Here,
fitness value of each offspring is evaluated.
Table 3. Selection procedure of individual string is being
Table 4: Generating new population
Strings of new population having fitness value equal to 2Lmax
(here Lmax=3, so 2Lmax=6) are considered as light-trails of
new_lt. Now the light-trails of new_lt have served all the
requests which were served by the light-trails of ini_pop. So,
we don‟t need to go in the next generation. The total number of
light-trails required to serve all the requests in the ini-pop is
reduced from 4 to 2. So, total number of light-trail in rqst_mtrx
is minimized from 8 to 6.
Similarly this concept is also applied on NSF network (fig2)
with same rqst_mtrx.
rq
no.
rqst_mtrx fit(Si)
1. 3 1 5 - 5
2. 0 3 - - 4
3. 1 5 - - 4
4. 2 4 - - 4
Strin
g no.
Initial
populatio
n
fit(Si
)
Selection
probabilit
y
Expecte
d count
Rando
m
Actua
l
count
1. 3 1 5
-
5 0.295 1.18 0.67 1
2. 0 3 -
-
4 0.235 0.94 0.28 1
3. 1 5 -
-
4 0.235 0.94 0.55 1
4. 2 4 -
-
4 0.235 0.94 0.98 1
Parents
(with xsite=2)
New population
(Offspring)
fit(Si) New_lt
- 3 1 5
0 3 - -
1 5 - -
- - 2 4
0 3 1 5
- 3 - -
1 5 2 4
- - - -
6
3
6
3
0 3 1
5
1 5 2 4
Sum 17 1.000 4.00 4
Average 4.25 0.25 1.00 1
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[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337
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Available online @ http://www.ijesat.org 1334
Table 5: Evaluating WL value of each light-trail
Table 6: Evaluating fitness value of each string
Table 7: Evaluating Sum and Average fit (Si), Selection
Probability, Expected Count and Actual Count
Sum 25 1.0 6.00
6
Average 4.17 0.167 1.00
1
Table 8: Generating new population
Now the light-trails of new_lt have served all the requests
which was served by the light-trails of initial population. The
total number of light-trails required to serve all the requests in
the ini-pop is reduced from 6 to 3. So, total number of light-
trail in rqst_mtrx is minimized from 14 to 11.
rq
no.
rqst_mtrx W(Li)
1. 0 1 3 4 3
2. 3 4 6 8 3
3. 5 12 11 9 3
4. 13 9 11 12 3
5. 9 8 6 4 3
6. 4 3 1 0 3
7. 3 10 13 - 2
8. 4 5 - - 1
9. 7 9 - - 1
10. 13 12 - - 1
11. 0 8 - - 1
12. 9 13 - - 1
Parents
(with
xsite=2)
New
population
(Offspring)
fit(Si) New_lt
3 10 13
-
- - 13
12
4 5 -
-
- - 7
9
0 8 -
-
- - 9
13
3 10 13 12
- - 13 -
4 5 7 9
- - - -
0 8 9
13
- - - -
6
3
6
3
6
3
3 10
13 12
4 5 7
9
0 8 9
13
rq
no.
rqst_mtrx fit(Si)
1. 3 10 13 - 5
2. 4 5 - - 4
3. 7 9 - - 4
4. 13 12 - - 4
5. 0 8 - - 4
6. 9 13 - - 4
String no.
Initial population
Fit (Si)
Selection probabilit
y
Expected count
Random
Actual count
1. 3 10 13
-
5 0.2 1.2 0.67 1
2. 4 5 -
-
4 0.16 0.96 0.28 1
3. 7 9 -
-
4 0.16 0.96 0.55 1
4. 13 12 -
-
4 0.16 0.96 0.98 1
5. 0 8 -
-
4 0.16 0.96 0.47 1
6. 9 13 -
-
4 0.16 0.96 0.71 1
Initial
population
Sum 25 1.0 6.00 6
Average 4.17 0.167 1.00 1
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4. SIMULATION AND RESULT
As most of the existing light-trail minimization algorithms
adopt ILP (Integer Linear Programming) approach. To
compare the performance of the proposed heuristics with ILP,
consider the example shown in fig1.(mesh topology) and
fig2.(NSF network).
4.1 ILP Formulation
Variables:
µlsd: Binary variable, route indicator, takes value of 1 if request
(s, d) takes light trail l; zero otherwise. This also implies that
node s and d are on trail l and s is d‟s upstream node.
δl: Binary variable, light trail usage indicator takes value of 1 if
trail l is used by any request; zero otherwise.
Wij: Binary variable, link indicator, takes value of 1 if there
exists a link from node i to node j. Here i is upstream node of j.
hl: Hop-length of each light-trail l.
tsd: Traffic flow between node s and node d.
C: Full-wavelength capacity.
Objective: Minimum number of light-trails those are required
in the network.
Subject to following constraints:
1. 1. Hop-length constraint: The hop-length of each light-
2. trail should not exceed the value of Lmax.
hl ≤ Lmax , ⍱l
3. Connectivity constraint: The connections with in a
light-trail l should satisfy the connection matrix.
∑ ∑ Wij = hl
4. Assignment constraint: Each request is assigned to one
and only one light-trail.
5. Light-trail capacity constraint: The aggregated request
capacity on a light-trail should not exceed the full-wavelength
capacity.
6. Light-trail usage constraint: If any of the s-d pair is
assigned on light-trail l, δl is set to 1, otherwise if none of the s-
d pairs picked light-trail l, then δl = 0.
δl ≥ µlsd ⍱ (s,d): tsd єT, δl є {0,1}
We assume Lmax =3 and C=40. Traffic matrix of Fig.1. and
Fig2. are shown in table1. and table3. respectively. The ILP
solutions of these two examples are given in Table 10 and
Table 11 respectively.
Table9.
Traffic
matrix
(TN×N) for
6-node
network
(fig.1)
Table 10. ILP Solution: Resulting Light-trails with Lmax=3, C=40
Table11. ILP Solution: Resulting Light-trails with Lmax=3, C=40
No. Light-
trail
Accommodated s-d pairs Capacity
1. 0-1-3-
4
(0,1)(0,3)(0,4)(1,3)(1,4)(3,4) 38
2. 1-2-5-
7
(1,2)(1,5)(1,7)(2,5)(2,7) 32
3. 3-4-6-
8
(3,6)(3,8)(4,6)(4,8)(6,8) 36
4. 8-9-
11-12
(8,9)(811)(8,12)(9,11)(9,12) 37
5. 5-12-
11-9
(5,9)(5,11)(5,12)(11,9)(12,9)(12,11) 39
6. 13-9-
11-12
(11,12)(13,9)(13,11) 39
7. 9-8-6-
4
(6,4)(8,4)(8,6)(9,4)(9,6)(9,8) 35
8. 4-3-1- (1,0)(3,0)(3,1)(4,0)(4,1)(4,3) 38
0 1 2 3 4 5
0 0 5 15 13 0 18
1 0 0 12 7 12 10
2 0 7 0 14 17 0
3 6 13 4 0 4 8
4 18 5 12 5 0 3
5 9 5 5 7 9 0
No Light-trail Accommodated s-d pair capacity
1. 0-1-2-3 (0,1)(0,2)(1,2)(1,3) 39
2. 3-4-5-0 (3,0)(3,4)(4,0)(4,5)(5,0) 40
3. 4-1-2-3 (2,3)(4,1)(4,2)(4,3) 36
4. 5-2-3-1 (2,1)(3,1)(5,1)(5,2)(5,3) 37
5. 0-3-1-5 (0,3)(0,5)(1,5)(3,5) 39
6. 1-5-2-4 (1,4)(2,4)(5,4) 38
δl
µlsd =1 ⍱(s,d), tsd єT, tsd>0
µlsd tsd ≤ C
INADYUTI DUTT* et al. ISSN: 2250–3676
[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337
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Available online @ http://www.ijesat.org 1336
0
9. 3-10-
13-12
(3,10)(3,12)(3,13)(10,13)(13,12) 40
10. 4-5-7-
9
(4,5)(4,7)(4,9)(5,7)(7,9) 39
11. 0-8-9-
13
(0,8)(0,9)(0,13)(8,13)(9,13) 38
Using ILP, we can see that the 1st example (Fig.1.mesh
topology) needs 6 light-trails and the 2nd
example (Fig.2.NSF
network) needs 11 light-trails to serve all the requests.
Table 12. Traffic matrix (TN×N) for 14-node NSF network(Fig.2)
Table.9 summarizes the result. The 1st, 2nd and 3rd rows give the
number of light-trails required by the Proposed Heuristic with CM and
GA and ILP respectively.
Algorithm
(Fig. 1) N=6 (Fig. 2)
N=14
(Unidirectional)
Biderectional)
Connection Matrix 6 11
Genetic Algorithm 6 11
Integer Linear Programming 6 11
Though all generate same result, but there is no certainty that
the middle approach (GA) will always produce an optimal
solution. Here reduction of blocking is also similar as both
yield same minimized light-trails for a given set of requests for
same blocked light-trails. Complexity of the proposed heuristic
is O(n.k), where n is the number of light-trails assigned to the
network to serve the requests and k is the number of nodes
between source and destination of each light-trail or request,
whereas the complexity of second approach is slightly
increases due to formulation of initial population. But light-
trail implementation with ILP is a NP-Hard problem.
5. CONCLUSION
A heuristic approach with connection matrix and Genetic
Algorithm is proposed for minimizing the number of light trails
for given a graph (network) and a number of connection
requests. Here, mesh topology assuming it as unidirectional
and NSF network which is bidirectional are considered to
illustrate the proposed heuristics. Both the approaches can
solve it in polynomial time, whereas ILP needs exponential
time. Above all, we have tried to develop an algorithm of light-
trail optimization problem which is very efficient and user
friendly such that it will always return an optimal or a sub-
optimal solution with having reasonable lower complexity than
other existing algorithms.
REFERENCES
1. Ashwin Gumaste and Imrich Chlamtac, „Light-trails:
A Novel Conceptual Framework for Conducting
OpticalCommunications‟,Proceedings of HPSR 2003 Torino
Italy, June 2003.
2. Michael T. Frederick, Nathan A. VanderHom and
Arun K. Somani, „Light Trails: A Sub-Wavelength Solution for
Optical Networking‟, HPSR‟2004,pp. 175-179.
3. Ashwin Gumaste, Gabriel Kuper and Imrich Chlamtac,
„Optimizing Light-trail Assignment to WDM Networks for
Dynamic IP Centric Traffic‟, IEEE LANMAN 2004, Apr.
2004,pp 113-118.
4. Wensheng He, Jing Fang, Arun K. Somani, „On Survivable
Design in Light Trail Optical Networks‟, proceeding of 8th
IFIP
Working Conference on Optical Network Design and
Modeling, Feb,2004.
0 1 2 3 4 5 6 7 8 9 10 11 12 13
0 0 5 0 11 8 0 0 0 13 4 0 0 0 8
1 4 0 6 6 2 0 0 9 0 0 0 0 0 0
2 0 0 0 0 0 2 0 8 0 0 0 0 0 0
3 9 4 0 0 6 0 7 0 9 0 3 0 8 10
4 10 9 0 2 0 8 4 6 3 2 0 0 0 0
5 0 0 0 0 0 0 0 12 0 10 0 9 7 0
6 0 0 0 0 4 0 0 0 13 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 11 0 0 0 0
8 0 0 0 0 7 0 9 0 0 9 0 7 6 5
9 0 0 0 0 8 0 5 0 2 0 0 9 6 8
10 0 0 0 0 0 0 0 0 0 0 0 0 0 7
11 0 0 0 0 0 0 0 0 0 3 0 0 11 0
12 0 0 0 0 0 0 0 0 0 4 0 6 0 0
13 0 0 0 0 0 0 0 0 0 13 0 15 12 0
INADYUTI DUTT* et al. ISSN: 2250–3676
[IJESAT] INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & ADVANCED TECHNOLOGY Volume-2, Issue-5, 1327 – 1337
IJESAT | Sep-Oct 2012
Available online @ http://www.ijesat.org 1337
5. Jing Fang, Wensheng He, Arun K. Somani, „Optimal
Light Trail Design in WDM Optical Networks‟, IEEE Intl Conf
on Commun (ICC) 2004 Paris.
6. Bin Wu nad Kwan L. Yeung, „Light-trail assignment in
WDM optical networks‟, IEEE Proc of Globecom 2006 San
Francisco CA.
7. Weiyi Zhan, Guoliang Xue, Jian Tang, Krishanaiyan
Thulasiraman, „Dynamic light-trail routing and protection issue
in WDM optical network‟, IEEE Globecom 2005, vol. 4, pp
1963-1967.
8. Akhil Lodha, Ashwin Gumaste, Paresh Bafna and Nasir
Ghani, „Stochastic Optimization of Light-trail WDM Ring
Networks using Bender‟s Decomposition‟, Indian Institute of
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University Cookeville USA.
9. Arun K. Somani, „Survivability and Traffic
Grooming inWDM Optical Networks‟, Cambridge
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10. Dzmitry Kliazovich and Fabrizio Granelli, „Bidirectional
Light-Trails for Synchronous Communications in WDM
Networks‟, IEEE Globecom 2005.
BIOGRAPHIES
Inadyuti Dutt, has been in the field of
academics and research for more than ten
years and is currently the Assistant Professor
in the Department of Computer Application
of B. P. Poddar Institute of Management &
Technology, Kolkata, West Bengal, India.
.Earlier, she held several technical positions
in National Informatics Centre, Kolkata and Semaphore
Computing Networks Pvt. Ltd. respectively. She has Master‟s
Degree in Computer Application and currently pursuing her
research in Computer Science and Engineering. She is Student
Branch Co-ordinator of CSI Student Branch, B.P.Poddar
Institute of Management & Technology. She has more than 20
publications to her laurels and her research interest is
specifically in the field of Optical Networking, Security and
Neural Networks. She has also been the Technical Reviewer ,
Member, Editorial Board in several journal publications like
International Journal of Software Engineering Research
International Journal of Engineering & Advanced Technology.
Soumya Paul, Associate Professor and
Head, Department of Computer
Application in B. P. Poddar Institute of
Management & Technology, Kolkata,
India, has been in teaching and research
for over 12 years. He holds a Master‟s
Degree in Technology, Computer Application as well as in
Mathematics and has gathered vast experiences in the same. He
received his M.Sc. (Mathematics) from Visva Bharati
University and stood 1st class 1
st. He received MCA from
National Institute of Technology, Rourkela and M. Tech (CSE)
from AAI-Deemed University and pursuing Ph. D in Computer
Science and Engineering. He served as a faculty member and
visiting faculty member in various Institutes and Universities
like RCCIIT, Visva Bharati University, University of Calcutta,
Bardhaman University, West Bengal University of Technology
etc. He is a member of Board of Study of MCA, BCA of West
Bengal University and Technology. He has delivered numerous
lectures across India in the field of his research interest,
Network Security and Genetic Algorithms. He is an author/co-
author of several published articles in International Journals
and International Conferences. He has chaired an International
Conference technically supported by IEEE communication. He
has more than 20 research publications and currently Reviewer
and Member, Editorial Board in many conferences and journals
like International Journal of Data Modeling and Knowledge
Management, International Journal of Advanced Research in
Computer Science and Electronic Engineering.