### Abstract

In this paper, we propose an improved genetic algorithm for the traveling salesman problem (TSP) by using the `visiting order restriction theorem'. The visiting order restriction theorem gives a necessary condition for the shortest tour of TSP on the Euclidean plane by using the convex hull. The convex hull for a set of points S on a plane is defined as the smallest convex polygon that encloses S. In our method, the initial tours are produced to satisfy the necessary condition of the theorem for the shortest path without increasing the computation time. The simulation results using 10 well-known benchmark problems show that our algorithm can find better tour with shorter time than Pal's algorithm.

Original language | English |
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Title of host publication | Proceedings of the IEEE International Conference on Systems, Man and Cybernetics |

Editors | Anon |

Publisher | IEEE |

Pages | 2279-2284 |

Number of pages | 6 |

Volume | 3 |

Publication status | Published - 1998 |

Externally published | Yes |

Event | Proceedings of the 1998 IEEE International Conference on Systems, Man, and Cybernetics. Part 3 (of 5) - San Diego, CA, USA Duration: Oct 11 1998 → Oct 14 1998 |

### Other

Other | Proceedings of the 1998 IEEE International Conference on Systems, Man, and Cybernetics. Part 3 (of 5) |
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City | San Diego, CA, USA |

Period | 10/11/98 → 10/14/98 |

### Fingerprint

### ASJC Scopus subject areas

- Hardware and Architecture
- Control and Systems Engineering

### Cite this

*Proceedings of the IEEE International Conference on Systems, Man and Cybernetics*(Vol. 3, pp. 2279-2284). IEEE.

**Improved genetic algorithm using the convex hull for traveling salesman problem.** / Takenaka, Yoichi; Funabiki, Nobuo.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE International Conference on Systems, Man and Cybernetics.*vol. 3, IEEE, pp. 2279-2284, Proceedings of the 1998 IEEE International Conference on Systems, Man, and Cybernetics. Part 3 (of 5), San Diego, CA, USA, 10/11/98.

}

TY - GEN

T1 - Improved genetic algorithm using the convex hull for traveling salesman problem

AU - Takenaka, Yoichi

AU - Funabiki, Nobuo

PY - 1998

Y1 - 1998

N2 - In this paper, we propose an improved genetic algorithm for the traveling salesman problem (TSP) by using the `visiting order restriction theorem'. The visiting order restriction theorem gives a necessary condition for the shortest tour of TSP on the Euclidean plane by using the convex hull. The convex hull for a set of points S on a plane is defined as the smallest convex polygon that encloses S. In our method, the initial tours are produced to satisfy the necessary condition of the theorem for the shortest path without increasing the computation time. The simulation results using 10 well-known benchmark problems show that our algorithm can find better tour with shorter time than Pal's algorithm.

AB - In this paper, we propose an improved genetic algorithm for the traveling salesman problem (TSP) by using the `visiting order restriction theorem'. The visiting order restriction theorem gives a necessary condition for the shortest tour of TSP on the Euclidean plane by using the convex hull. The convex hull for a set of points S on a plane is defined as the smallest convex polygon that encloses S. In our method, the initial tours are produced to satisfy the necessary condition of the theorem for the shortest path without increasing the computation time. The simulation results using 10 well-known benchmark problems show that our algorithm can find better tour with shorter time than Pal's algorithm.

UR - http://www.scopus.com/inward/record.url?scp=0032320002&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032320002&partnerID=8YFLogxK

M3 - Conference contribution

VL - 3

SP - 2279

EP - 2284

BT - Proceedings of the IEEE International Conference on Systems, Man and Cybernetics

A2 - Anon, null

PB - IEEE

ER -