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Travelling Salesman Problem

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.

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Travelling Salesman Problem

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  1. Travelling Salesman Problem an unfinished story...

  2. Contents • Description of the problem • History • Sample Algorithms • Performance Comparison • TSP with Parallel Computing • Conclusion

  3. Description of the Problem Givena number of cities and the costs of travelling fromany city to anyother city, whatis the least-cost round-trip route thatvisitseach city exactly once and thenreturns to the starting city?

  4. 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.

  5. Sample Algorithms • Constructive Heuristics • Nearest Neighbour (Greedy) • Insertion Heuristics • 2-OPT • 3-OPT • Genetic Algoritms • Simulated Annealing • Neural Network

  6. Performance Comparison

  7. Performance Comparison continued...

  8. TSP with Parallel Computing Time (sec.) NP

  9. TSP with Parallel Computing

  10. TSP with Parallel Computing

  11. TSP with Parallel Computing

  12. 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.

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