travelling salesman problem an unfinished story
Post on 21-Dec-2015
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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 Comparisoncontinued...
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
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
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
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
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.