1. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network 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

2. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network 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).

3. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Cells and Interference Divide the region to smaller sub- regions (cells). You have the whole frequency range for each cell. The Problem of Interference

4. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network 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! N=21 (Cells number)

5. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Example cells channels Demands Compatibility matrix (shows the severity of the interference)

6. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Example cells channels Demands Compatibility matrix (shows the severity of the interference)

7. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Combinatorial Optimization Problem

8. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Combinatorial Optimization Problem (Samples) Traveling Salesman Problem –VLSI Connection Optimization Job Scheduling –Postal Delivery –Car Sequencing Channel Assignment Problem

9. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network 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

10. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Hopfield N.N. for COP Lyapunov function Hopfield NN minimizes this Lyapunov function.

11. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network 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

12. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Example of Trapping in a Local Minimum

13. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network 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

14. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network The Network Dynamics

15. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Hopfield N.N. Formulation of Channel Assignment Problem

16. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Experiments

17. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Experiments

18. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Experiments

19. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network Conclusions Hopfield NN with chaotic injected noise and forcing constraints as external inputs can solve COP very well.

20. Channel Assignment using Chaotic Simulated Annealing Enhanced Neural Network 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