Channel Assignment using Chaotic Simulated Annealing Enhanced Hopfield Neural Network

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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
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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).

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Cells and Interference

• Divide the region to smaller sub-regions (cells).
• You have the whole frequency range for each cell.

The Problem of Interference
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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.
• NP-Hard!

N21 (Cells number)
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Example
cells
channels
Demands
Compatibility matrix (shows the severity of the
interference)
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Example
cells
channels
Demands
Compatibility matrix (shows the severity of the
interference)
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Combinatorial Optimization Problem
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Combinatorial Optimization Problem(Samples)

• Traveling Salesman Problem
• VLSI Connection Optimization
• Job Scheduling
• Postal Delivery
• Car Sequencing
• Channel Assignment Problem

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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

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Hopfield N.N. for COP
Lyapunov function
Hopfield NN minimizes this Lyapunov function.
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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

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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

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The Network Dynamics
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Hopfield N.N. Formulation of Channel Assignment
Problem
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Experiments
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Experiments
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Experiments
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Conclusions

• Hopfield NN with chaotic injected noise and
  forcing constraints as external inputs can solve
  COP very well.

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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 networks state information to change the
  amount of chaotic noise injected to the network
  adaptively (progress estimator)
• Hardware implementation