Solving Traveling salesman Problem with Hopfield Net

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Presentation transcript:

Solving Traveling salesman Problem with Hopfield Net Aiming Lu

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.

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.

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

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)

Result