solving traveling salesman problem with hopfield net

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Solving Traveling salesman Problem with Hopfield Net Aiming Lu

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Solving Traveling salesman Problem with Hopfield Net. Aiming Lu. Traveling Salesman Problem. - PowerPoint PPT Presentation

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Page 1: Solving Traveling salesman Problem with Hopfield Net

Solving Traveling salesman Problem with Hopfield Net

Aiming Lu

Page 2: Solving Traveling salesman Problem with Hopfield Net

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.

Page 3: Solving Traveling salesman Problem with Hopfield Net

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.

Page 4: Solving Traveling salesman Problem with Hopfield Net

Energy Function

4

1,1,,,

2

3

,

2

,,

1

,,

22

22

E

x yx iiyiyixyx

E

x iix

E

i x xyiyix

E

x i ijjxix

vvvdD

NvC

vvB

vvA

E

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

Page 5: Solving Traveling salesman Problem with Hopfield Net

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)

yiyiyxy

x jxj

ij xyyixjxi

VVdDNVC

VBVAu

),()( 1,1,

dtduxi

Vxi=(1+tanh(uxi/u0)

Page 6: Solving Traveling salesman Problem with Hopfield Net

Result