Speeding up the optimal method of Drezner for the \(p\)-centre problem in the plane.

*(English)*Zbl 1394.90383Summary: This paper revisits an early but interesting optimal algorithm first proposed by Drezner to solve the continuous \(p\)-centre problem. The original algorithm is reexamined and efficient neighbourhood reductions which are mathematically supported are proposed to improve its overall computational performance. The revised algorithm yields a considerably high reduction in computational time reaching, in some cases, a decrease of 96%. This new algorithm is now able to find proven optimal solutions for large data sets with over 1300 demand points and various values of \(p\) for the first time.

##### MSC:

90B80 | Discrete location and assignment |

90B85 | Continuous location |

90C59 | Approximation methods and heuristics in mathematical programming |

90C60 | Abstract computational complexity for mathematical programming problems |

##### Software:

TSPLIB
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\textit{B. Callaghan} et al., Eur. J. Oper. Res. 257, No. 3, 722--734 (2017; Zbl 1394.90383)

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