Channel Assignment using Chaotic Simulated
Annealing Enhanced Hopfield Neural
Network
Amir massoud Farahmand (a,b)
Mohammad Javad Yazdanpanah (b)
a) Department of Computing Science, University of Alberta
b) Department of Electrical and Computer Engineering, University of Tehran
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Your Big Company
Suppose that you have a mobile communication
company and want you to earn money as much as
possible.
You want to service to your costumers in a large
geographical space, e.g. Vancouver.
You need to assign a unique frequency channel to each
costumer (e.g. 870.12MHz to 870.14MHz).
The problem is that you only have a limited frequency
range (e.g. 869MHz - 894MHz for downlink in
Canada).
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Cells and Interference
Divide the region to smaller subregions (cells).
You have the whole frequency
range for each cell.
The Problem of Interference
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Channel Assignment Problem
•
•
•
Channel assignment problem is a
common problem in cellular
telecommunication.
Resources: frequency channels and
cells.
Sources of Interference:
–
Interference between adjacent cells
•
–
•
•
Dominant for frequency-close
channels.
Interference between two frequency
channels in the same cell.
Goal: assign channels in order to
maximize the utilization of the
network while minimizing the
interference.
This problem is a instance of a
combinatorial optimization problem.
–
N=21 (Cells number)
NP-Hard!
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Example
cells
channels
N 4
M  10
Demands

DT  1 1 1 3
Compatibility matrix
(shows the severity of the
interference)
5

4
C 
0

0

4 0 0

5 0 1
0 5 2

1 2 5 
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Example
cells
channels
N 4
M  11
Demands
DT  1 1 1 3
Compatibility matrix
(shows the severity of the
interference)
5

4
C 
0

0

4 0 0

5 0 1
0 5 2

1 2 5 
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Combinatorial Optimization
Problem
min F(X ) 
X
N
M
N
M
N
M
min  X i, j Q(i, j,p,q)X p, q  C(i, j)X i, j
X
i 1 j 1
p1 q1
i 1 j 1
 X  D i  1,...,N
i
 j i, j
subject to
 X i, j  1 i  1,...,M
 i
X i, j  0,1
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Combinatorial Optimization Problem
(Samples)
• Traveling Salesman Problem
– VLSI Connection Optimization
• Job Scheduling
– Postal Delivery
– Car Sequencing
• Channel Assignment Problem
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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How to Solve a COP?
• Search all space?!
– Infeasible for large problems.
• Approximately solve it
– Different heuristics
– Meta-heuristics
•
•
•
•
Simulated Annealing
Tabu Search
Evolutionary Computation Methods
Hopfield Neural Networks
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Hopfield N.N. for COP


ui (t  1)   
 w ij x j  Ii 

 j

xi (t)  f ui (t) 
1
1 e ui (t ) / 
Lyapunov function
EHop(t)  
1
wij xi (t)xj (t)   I i xi (t)


2 i j
i
min F(X ) 
X
N
M
N
M
N
M
min  X i, j Q(i, j,p,q)X p, q  C(i, j)X i, j
X
i 1 j 1
p1 q1
i 1 j 1
 X  D i  1,...,N
i
 j i, j
subject to
 X i, j  1 i  1,...,M
 i
X i, j  0,1
Hopfield NN minimizes this Lyapunov function.
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Hopfield N.N. for COP
Difficulties
• Infeasible solutions
– Solutions that do not
satisfy constraints
• Energy function is
strictly decreasing
– Local minima
dilemma
Solutions
• Hill-Climbing
methods to escape
from local minima
– Simulated Annealing
noise
– Chaotic noise
• Forcing constraints
– Force lying in
constraint plane
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Example of Trapping in a Local Minimum
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Main Idea
• Inject chaotic noise to enhance the
searching capability of the network
– Decay the noise gradually
– Reset the noise to its full power several
times
• Force constraints explicitly
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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The Network Dynamics


ui (t  1)   
 w ij x j  Ii 
 i (t)
 j

1
x i (t)  f ui (t) 
1 eui (t )/
1
i (t)  zi (t)  h
0.9
0.8
a(t 1)  1 a(t) a0
1
*
h  z  1
a0
0.7
Amplitude
z i (t 1)  a(t)z i (t)1 z i (t)
0.6
0.5
0.4
0.3
0.2
0.1
0
100
200
300
400
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
500
Time
600
700
800
900
1000
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Hopfield N.N. Formulation of
Channel Assignment Problem
N
M
N
M
1
min   X i, j   Cip X p,q
2 i1 j1
p1 q1
subject to :
X
i, j
 Dk
k  1,...,N
j
X i, j  0,1
Wijpq  ipjq(dcsc ) 1 ip jqCip ip 1 jq
I i  Di  1
I Eij
M


 Di   X ik 


k 1
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Experiments
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QuickTime™ and a
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Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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TIFF (Uncompre ssed ) decomp resso r
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Experiments
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Experiments
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Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Conclusions
• Hopfield NN with chaotic injected noise
and forcing constraints as external
inputs can solve COP very well.
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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Suggestions for Further
Research
• Applying this method to other COP
• Investigating the effect of parameters to the
quality of solutions
– Is it robust to parameters method?
• Comparing with other chaotification methods
• Use network’s state information to change the
amount of chaotic noise injected to the
network adaptively (progress estimator)
• Hardware implementation
Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network
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