International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
A Heuristic Approach to Cell to Switch Assignment
Anil Goyal*1, Rita Mahajan#2, Deepak Bagai#3
*1
E&EC Department, PEC University of Technology,
Chandigarh -160012, India
#2
Assistant Professor, E&EC Department, PEC University of Technology,
Chandigarh -160012, India
#3
Associate Professor, E&EC Department, PEC University of Technology,
Chandigarh -160012, India
Abstract—In this paper, we consider a problem of network design
of personal communication services (PCS). The problem is to
assign cells to the switches of a PCS network in an efficient
manner. We consider two types of costs. First is the cost of handoffs
between cells. Second is the cost of cabling between a cell site and
its associated switch. There is constraint on the problem by the call
volume handling capacity of switch. This paper describes Firefly
Algorithm with Heuristic Method and proposes a possible way it to
solve the problem of assignment of cells of a geographical area to
the available number of switches based on the minimization of total
cost for the assignment.
involves the consumption of resources while maintaining
communication link between two users [3].
Keywords–– CSA, Firefly Algorithm, Heuristics Approach, Particle
Swarm Optimization.
I. INTRODUCTION
Since the last few decades, the significant advancement in
the field of mobile communication systems has taken place.
Despite this significant improvement in the area of Personal
Communication Services, the issues regarding the assignment of
cells to switches in order to minimize the handoff cost and
cabling costs in a reasonable time is still challenging [1].
The handoff caused by a subscriber movement from one
cell to another cell, involves both i.e. the modification of the
location of the user in the database of companyand also the
execution of a fairly complicated protocol between switches
Switch1 and Switch2 as shown in Fig.1. The handoff cost
between cell A and cell B is less because it involves only
Switch1 and also the handoff is simple while handoff between
cell A and cell C is complex and the handoff cost is also more as
it involves two switches i.e. Switch1 and Switch2 Therefore,
there are two types of handoffs, first involves one switch and the
second involves two switches. Intuitively, the cells among
which the handoff frequency is high should be assigned to the
same switch as far as possible to reduce the cost of handoffs [2]
as shown in Fig 1. But the call handling capacity of each switch
is limited that however, acts as a constraint. Cabling cost
ISSN: 2231-5381
Fig1. Handoff from B to C is more expansive than B to A
This paper presents idea to solve the problem of assignment of
cells to switches using Firefly Algorithm given In 2008, byXinShe Yang [4] along with Heuristics method used by Bhaskar
Sengupta in 1995 [2].
II. PROBLEM FORMULATION
The problem of assignment of cells to switches was first
introduced by Arif Merchant and Bhaskar Sengupta [2] in 1995.
All the cells in a particular region are assigned to the available
number of switches in order to minimize the total cost which is
the sum of cabling cost and handoff cost maintaining two
constraints.
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
The problem is constrained by following two facts:
1) Each cell must be assigned to exactly one switch.
2) Each switch has some limited capacity and assignment of
cells must be done in such a way so that the total load on the
switch should not exceed the capacity of the switch.
III. MATHEMATICAL MODELING
The terms used in formulating the mathematical expressions
are given as [1].
• Let no. of cells be ‘n’ and no. of switches be ‘m’
• hij – handoff cost between cell i and cell j
• cik – cabling cost between cell i and switch k
• dij – distance between cell i and switch (MSC) j
• Mk – call handling capacity of switch k
• λi - No of communication in cell i
• Y ij – 1 if cell I and j are assigned to same switch and 0
otherwise.
• X ik – 1 if cell I is assigned to switch k and 0 otherwise.
For all cases, the range of i, j and k are defined as:
1≤ ≤ , 1≤ ≤ , 1≤ ≤
A. Formulation of Constraints
1) We should assign one cell to one switch only
= 1,1 ≤ ≤
2. Total Handoff Cost: We consider two types of handoffs, first
that involves one switch and second which involves two
switches. The handoff occurring between cells belong to the
same switch consume much less network resources than what
occurs between cells that belong to two different switches.
ℎ (1 −
3. Total Cost: So our objective is to minimize the total cost
which can be formed by the addition of Handoff and Cabling
cost. The objective function thus formed is given as under:
( )
,1 ≤
( )
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) … ( )
V. IMPLEMENTATION OF FIREFLY ALGORITHM
ALONGWITH HEURISTIC METHOD
≤
… ( )
1. Total Cabling Cost: This is formulated as a function of
distance between base station and switch and number of calls
that a cell can handle per unit time [5]. ( ) is the cost of
cabling per kilometre which is also modelled as a function of the
number of calls that a cell ‘i’ can handles as:
+
ℎ (1 −
… ( )
B. Formulation of Cost Function
=
+
IV. EXISTING METHODOLOGY
There are various methods available for assigning cell to
switches like, heuristic approaches, like Genetic Algorithm [6]
[7], Ant Colony Optimization [8] and Particle Swarm
Optimization [9], Firefly Algorithm [10] have been developed
for this kind of problem.
In this paper Firefly Algorithm [4] alongwith the
Heuristic Method [1] is implemented and results are compared
with the Particle Swarm Optimization as used in [9].
2) Each switch has some capacity
≤
) … ( )
A. Firefly Algorithm
Firefly algorithm is developed by Xin-She Yang [5] in 2008
and as used by Apoorva Sharma [10] in 2012 which is inspired
by the mutual attraction of fireflies based on the absorption of
light and distance between two fireflies. Algorithm assumes that
position of each firefly is fixed in the space and a firefly moves
towards a light source that produces more power than it.
Firefly algorithm idealizes some of the characteristics of the
firefly behavior. Three rules are followed by them. They are
mentioned as under:
… ( ) 1) 1) All the fireflies are of same sex.
= 1,2, … … ( )
2) A firefly brighter than other firefly attracts that firefly
towards itself; strength of the attractiveness is proportional
to the firefly’s brightness andafter some distance the
brightness attenuates; the brightest firefly moves randomly.
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
3) The quality of solution determines brightness of every firefly;
in most of the cases, it can be proportional to the objective
function.
B. Heuristic Method
Heuristic Method is used to find out the best initial
solution as given in [3] and we assign this best solution to one
firefly and all other p-1 fireflies are assigned random values.
The various values of constants used are as follows:
 Randomness, α=1
 Absorption coefficient, β=1
 Brightness at source,γ=1
The various parameters used for the initialization of problem
are:
 handoff cost between two cells= 0 to 21 per hour
 constant A used in cabling cost=1
 constant B used in cabling cost=0.001
C. Algorithm
TABLE I
COMPARISON TABLE
The steps for implementation of algorithm are as follows:
Step 1




Step 2


Step 3

Step 4

Step 5




Initialize the number of cells (n), switches (m) and
number of fireflies (p) in the solution space.
Initialize p-1 fireflies randomly and assign the initial
best solution to one firefly as obtained by the Heuristic
Method.
The position of cells and switches is assigned randomly
in the search space.
Calculate the distance between each cell and switch.
Generate the assigned matrix (xij) for each firefly where
each particle is between 0 and 1.
The row and column of matrix represents switches and
cell respectively.
Gets the solution matrixusing the assigned matrix by
making the largest value of each column to 1 and all
other are set to 0.
Total cost is calculated based on this solution matrix.
The brightest firefly is foundon the basis of this new
cost which has the minimum cost for the assignment.
Based on the attractiveness of best firefly, update the
position of all other firefliesand also on the basis of
distance and randomness of fireflies.
The position of best firefly is updated randomly.
Repeat step 3 to 5 until we get the desired results.
VI. EXPERIMENTS AND RESULTS
To test the effectiveness of the method suggested above
for the cell assignment problem, we conduct a number of
experiments. MATLAB code is used to perform the experiments
for various cases of cells and switches for firefly algorithm.
Also we assume that the cells lie on a hexagonal grid of roughly
equal dimensions in 2 dimensions. Various comparison results
are shown in Table I.
ISSN: 2231-5381
No of
Switches,
No. of cells
Cabling
2, 25
126
1857
Total cost Total cost
by FA +
by PSO
Heuristic
Method
1983
2177
2, 50
308
7823
8131
9070
2, 100
522
33422
33944
35339
2, 150
834
74814
75648
79461
2, 200
1017
133730
134747
140670
2, 250
1434
2137700
2139134
2201330
3, 25
149
2131
2280
2989
3, 50
304
10714
11018
11436
3, 100
708
45060
45768
46553
3, 150
737
95789
96526
105210
3, 200
1154
178400
179554
187100
3, 250
1734
280480
282214
291850
5, 25
135
2408
2543
3710
5, 50
293
12723
13016
13936
5, 100
563
53340
53903
56452
5, 150
860
120870
121730
126100
5, 200
1135
216590
217725
224530
5, 250
1448
342720
344168
352100
10, 25
115
3414
3529
3980
10, 50
286
14889
15175
15538
10, 100
629
60949
61578
62940
10, 150
823
139320
140143
142990
10, 200
1127
248670
249797
253440
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cost
Handoff
cost
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International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue5- May 2013
A.
1460
388520
389980
394120
Cost Comparison Graphs
FOR 2 SWITCHES
2500000
T
O
T
A
L
2000000
1500000
Total cost by FA
+ Heuristic
Method
1000000
C
O
S
T
500000
FOR 5 SWITCHES
400000
T 350000
O
T 300000
A 250000
L 200000
150000
C
100000
O
50000
S
T
0
Total cost by
PSO
0
2, 25
COMBINATION OF CELLS AND SWITCHES
(SWITCH, CELL)
O
T
A
L
300000
250000
200000
Total cost by FA
+ Heuristic
Method
150000
C
O
S
T
100000
FOR 10 SWITCHES
450000
T 400000
O 350000
T
300000
A
L 250000
200000
150000
C
100000
O
50000
S
0
T
Total cost by
PSO
50000
0
3, 25 3, 3,
100 200
COMBINATION OF CELLS AND SWITCHES
(SWITCH,CELL)
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Total cost by FA +
Heuristic Method
Total cost by PSO
10, 25
10, 50
10, 100
10, 150
10, 200
10, 250
350000
T
Total cost by PSO
COMBINATION OF CELLS AND SWITCHES
(SWITCH,CELL)
2,
2,
100 200
FOR 3 SWITCHES
Total cost by FA +
Heuristic Method
5, 25
5, 50
5, 100
5, 150
5, 200
5, 250
10, 250
Combination of Cells and Switches
(Switch,Cell)
VII. CONCLUSION
From the experiments performed we can conclude that
firefly algorithm along with Heuristics Method can be
implemented successfully for the assignment of cells to the
switches. As we increase the number of fireflies the probability
of finding the minimum cost and in less number of iterations is
increased. The time required by CPU is less in case of firefly
algorithm and Heuristic Approach is less as compared to PSO.
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1.
VIII. REFERENCES
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3.
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