travelling salesman problem an unfinished story

12
Travelling Salesman Problem an unfinished story...

Post on 21-Dec-2015

227 views

Category:

Documents


8 download

TRANSCRIPT

Page 1: Travelling Salesman Problem an unfinished story

Travelling Salesman Problem

an unfinished story...

Page 2: Travelling Salesman Problem an unfinished story

Contents

• Description of the problem

• History

• Sample Algorithms

• Performance Comparison

• TSP with Parallel Computing

• Conclusion

Page 3: Travelling Salesman Problem an unfinished story

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?

Page 4: Travelling Salesman Problem an unfinished story

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.

Page 5: Travelling Salesman Problem an unfinished story

Sample Algorithms

• Constructive Heuristics

– Nearest Neighbour (Greedy)

– Insertion Heuristics

• 2-OPT

• 3-OPT

• Genetic Algoritms

• Simulated Annealing

• Neural Network

Page 6: Travelling Salesman Problem an unfinished story

Performance Comparison

Page 7: Travelling Salesman Problem an unfinished story

Performance Comparisoncontinued...

Page 8: Travelling Salesman Problem an unfinished story

TSP with Parallel

Computing

1 2 5 100.00

2.00

4.00

6.00

8.00

10.00

12.00

NC = 100

100 Cities

Time (sec.)

NP

Page 9: Travelling Salesman Problem an unfinished story

TSP with Parallel

Computing

1 2 5 100.00

2.00

4.00

6.00

8.00

10.00

12.00

3.10 3.19

6.83

10.47

200 Cities

200 Cities

Number of Processors

Tim

e

Page 10: Travelling Salesman Problem an unfinished story

TSP with Parallel

Computing

1 2 5 100.00

5.00

10.00

15.00

20.00

25.00

30.00

500 Cities

Number of Processors

Tim

e

Page 11: Travelling Salesman Problem an unfinished story

TSP with Parallel

Computing

1 2 5 100.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

700 Cities

Number of Processors

Tim

e

Page 12: Travelling Salesman Problem an unfinished story

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.