Travelling Salesman Problem

strangerwineΤεχνίτη Νοημοσύνη και Ρομποτική

19 Οκτ 2013 (πριν από 3 χρόνια και 8 μήνες)

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Travelling Salesman Problem

an unfinished story...

Contents


Description of the problem


History


Sample Algorithms


Performance Comparison


TSP with Parallel Computing


Conclusion

Description of the Problem






Given

a

number

of

cities

and

the

costs

of

travelling

from

any

city

to

any

other

city,

what

is

the

least
-
cost

round
-
trip

route

that

visits

each

city

exactly

once

and

then

returns

to

the

starting

city?


History



The

origins

of

the

travelling

salesman

problem

are

unclear
.

A

handbook

for

travelling

salesmen

from

1832

mentions

the

problem

and

includes

example

tours

through

Germany

and

Switzerland,

but

contains

no

mathematical

treatment
.

Sample Algorithms


Constructive Heuristics


Nearest Neighbour (Greedy)


Insertion Heuristics


2
-
OPT


3
-
OPT


Genetic Algoritms


Simulated Annealing


Neural Network

Performance Comparison

Performance Comparison

continued...

TSP with Parallel Computing

0.00
2.00
4.00
6.00
8.00
10.00
12.00
1
2
5
10
NC = 100

100 Cities
Time (sec.)

N
P

TSP with Parallel Computing

3.10

3.19

6.83

10.47

0.00
2.00
4.00
6.00
8.00
10.00
12.00
1
2
5
10
Time

Number of Processors

200 Cities

200 Cities
TSP with Parallel Computing

0.00
5.00
10.00
15.00
20.00
25.00
30.00
1
2
5
10
Time

Number of Processors

500 Cities
TSP with Parallel Computing

0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
1
2
5
10
Time

Number of Processors

700 Cities
Conclusion


For small
-
size TSP (n < 50), improved greedy
2
-
opt algorithm is recommended.


For medium
-
size TSP ( 50 < n < 100), improved
2
-
opt algorithm and neural network are
recommended for their optimality and
efficiency.


For large
-
size problem (100 < n < 500), the
improved genetic algorithm is recommended.


For any problem
-
size, if the computational
time is not a constraint, the improved neural
network is always recommended.