1. Solving Traveling salesman Problem with Hopfield Net
Aiming Lu

2. Traveling Salesman Problem
Given a finite number of cities along with the cost of travel between each pair of them, find the cheapest way of visiting all the cities and returning to your starting point. Every city can only be visited only once.

3. Apply Hopfield net to TSP
Use an n by n matrix to represent a tour. Vxi – x-th city as the i-th stop.
The problem is to construct an energy function that can be used to find a stable state of the network that expresses the cheapest valid city tours.

4. Energy Function E1: Row inhibition, favor only 1 city in a row
E2:Col inhibition, favor only 1 city in a col
E3: Global inhibition, favor the state that all cities are present
E4:Distance inhibition, favor minimum distance of the tour
A,B,C,D,N: are constants

5. Learning Procedure Initiation
Cities distance
uxi(0) = u00 + ((rand-1)/10.*u0)
Repeat iteration until stop criterion is satisfied: uxi(t+1) = uxi(t) + t(duxi/dt)
Vxi=(1+tanh(uxi/u0)

6. Result