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**Using simulated annealing to solve routing and location problems.**
*(English)*
Zbl 0593.90054

Summary: In recent papers by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi [“Optimization by simulated annealing”, IBM T. J. Watson Research Centre, Yorktown Hights, NY (1982); Science 220, 671–680 (1983; Zbl 1225.90162)] an analogy between the statistical mechanics of large multivariate physical systems and combinatorial optimization has been presented and used to develop a general strategy for solving discrete optimization problems. The method relies on probabilistically accepting intermediate increases in the objective function through a set of user-controlled parameters. It is argued that by taking such controlled uphill steps, from time to time, a high quality solution can eventually be found in a moderate amount of computer time. In this paper, we implement this idea, apply it to the traveling salesman problem and the p-median location problem, and test the approach extensively.

### MSC:

90C10 | Integer programming |

65K05 | Numerical mathematical programming methods |

68Q25 | Analysis of algorithms and problem complexity |

90B05 | Inventory, storage, reservoirs |

### Keywords:

simulated annealing; statistical mechanics of large multivariate physical systems; combinatorial optimization; controlled uphill steps; traveling salesman; p-median location### Citations:

Zbl 1225.90162
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\textit{B. L. Golden} and \textit{C. C. Skiscim}, Nav. Res. Logist. Q. 33, 261--279 (1986; Zbl 0593.90054)

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.