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**A thermodynamically motivated simulation procedure for combinatorial optimization problems.**
*(English)*
Zbl 0541.90070

Summary: Exchange algorithms are an important class of heuristics for hard combinatorial optimization problems as, e.g., salesman problems or quadratic assignment problems. In Kirkpatrick’s and Cerny’s exchange algorithms for the travelling salesman problem and placement problem they propose to perform an exchange not only if the objective function value decreases by this exchange, but also in certain cases if the objective function value increases. An exchange increasing the objective function value is performed stochastically depending on the size of the increment.

Computational tests with quadratic assignment problems revealed an excellent behaviour in such an approach. Suboptimal solutions differing 1-2% from the best known solutions are obtained by a simple program in short time. By starting this program several times with different starting values all known minimal objective function values were reached. Thus this approach is well suited also for smaller computers and leads in short time to acceptable solutions.

Computational tests with quadratic assignment problems revealed an excellent behaviour in such an approach. Suboptimal solutions differing 1-2% from the best known solutions are obtained by a simple program in short time. By starting this program several times with different starting values all known minimal objective function values were reached. Thus this approach is well suited also for smaller computers and leads in short time to acceptable solutions.

### MSC:

90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |

90C10 | Integer programming |

65K05 | Numerical mathematical programming methods |

68Q25 | Analysis of algorithms and problem complexity |

### Keywords:

simulation; combinatorial optimization; heuristics; quadratic assignment; exchange algorithms; Computational tests
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\textit{R. E. Burkard} and \textit{F. Rendl}, Eur. J. Oper. Res. 17, 169--174 (1984; Zbl 0541.90070)

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### References:

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[8] | Nugent, C. E.; Vollmann, T. E.; Ruml, J., An experimental comparison of techniques for the assignment of facilities to locations, J. Operations Res., 16, 150-173 (1968) |

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