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Neural Network to solve Traveling Salesman Problem
Roadmap ,[object Object],[object Object],[object Object],[object Object],[object Object]
Background ,[object Object],[object Object],[object Object],[object Object]
Associative memory ,[object Object],[object Object],[object Object],[object Object],Original Degraded Reconstruction
Hopfield Network ,[object Object],[object Object],[object Object],[object Object]
Hopfield Network ,[object Object],[object Object],[object Object],[object Object]
Computation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Sgn(x) = +1  x>0 Sgn(x) = -1  x<0
Modes of operation ,[object Object],[object Object],[object Object],[object Object],[object Object]
Stability ,[object Object],[object Object],[object Object],[object Object],[object Object]
Procedure ,[object Object],[object Object],[object Object]
Weight learning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Multiple Vectors ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Energy ,[object Object],[object Object]
Energy function ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Continued… ,[object Object],[object Object],[object Object],[object Object],[object Object]
Applications of Hopfield Nets ,[object Object],[object Object],[object Object]
Traveling Salesman Problem ,[object Object]
Traveling Salesman Problem ,[object Object],[object Object],[object Object]
Hopfield Net for TSP ,[object Object],[object Object],[object Object],[object Object],σ kj  = 1 if city k is in position j σ kj  = 0 otherwise
Hopfield Net for TSP ,[object Object],[object Object]
Determination of Energy Function ,[object Object],[object Object],[object Object],[object Object],[object Object]
Energy Function (Contd..) ,[object Object],[object Object]
Energy Function (Contd..) ,[object Object],[object Object]
Energy Function (cont..) ,[object Object],[object Object],[object Object],[object Object]
Energy Function (cont..) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Weight Value ,[object Object],[object Object],[object Object],[object Object],[object Object]
Observation ,[object Object],[object Object],[object Object]
Observation (cont..) ,[object Object],[object Object],[object Object],[object Object]
Concurrent Neural Network  ,[object Object],[object Object],[object Object]
Objective Function ,[object Object],[object Object],[object Object]
Cont … ,[object Object],[object Object],[object Object],[object Object]
Solution ,[object Object],[object Object],[object Object],[object Object]
Minimization of energy function ,[object Object],[object Object],[object Object]
Minimization of energy function ,[object Object],[object Object],[object Object],[object Object]
Implementation ,[object Object],[object Object],[object Object]
Comparison – Hopfield vs Concurrent NN ,[object Object],[object Object],[object Object]
Comparison – SOM and Concurrent NN ,[object Object],[object Object],[object Object]
Result ,[object Object],[object Object],[object Object]
Shortest path generated Concurrent Neural Network (2127 km) Self Organizing Maps (1311km)
Behavior in terms of probability  Concurrent Neural Network Self Organizing Maps
Conclusion ,[object Object],[object Object],[object Object]
References ,[object Object],[object Object],[object Object]
References ,[object Object],[object Object],[object Object]
 
NP-complete NP-hard ,[object Object]
NP-complete NP-hard ,[object Object],[object Object],[object Object],[object Object]
Path lengths Concurrent Neural Network Self Organizing Maps

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Neural Network

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  • 39. Shortest path generated Concurrent Neural Network (2127 km) Self Organizing Maps (1311km)
  • 40. Behavior in terms of probability Concurrent Neural Network Self Organizing Maps
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  • 47. Path lengths Concurrent Neural Network Self Organizing Maps