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A hyperbolic smoothing approach to the Multisource Weber problem

JOURNAL OF GLOBAL OPTIMIZATION 2014年第1期60卷 49-58页

作者： Xavier, Vinicius L. Frana, Felipe M. G. Xavier, Adilson E. Lima, Priscila M. V. Univ Fed Rio de Janeiro PESC COPPE Rio De Janeiro Brazil Univ Fed Rio de Janeiro iNCE Rio De Janeiro Brazil

The Multisource Weber problem, also known as the continuous location-allocation problem, or as the Fermat-Weber problem, is considered here. A particular case of the Multisource Weber problem is the minimum sum-of-distances clustering problem, also known as the continuous -median problem. The mathematical modelling of this problem leads to a formulation which, in addition to its intrinsic bi-level nature, is strongly nondifferentiable. Moreover, it has a large number of local minimizers, so it is a typical global optimization problem. In order to overcome the intrinsic difficulties of the problem, the so called Hyperbolic Smoothing methodology, which follows a smoothing strategy using a special differentiable class function, is adopted. The final solution is obtained by solving a sequence of low dimension differentiable unconstrained optimization sub-problems which gradually approaches the original problem. For the purpose of illustrating both the reliability and the efficiency of the method, a set of computational experiments making use of traditional test problems described in the literature was performed. Apart from consistently presenting better results when compared to related approaches, the novel technique introduced here was able to deal with instances never tackled before in the context of the Multisource Weber problem.

关键词： Multisource Weber problem min-sum-distances clustering problem Nondifferentiable programming

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A hyperbolic smoothing approach to the Multisource Weber problem

A hyperbolic smoothing approach to the Multisource Weber pro...

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25th European Conference on Operational Research (EURO)

作者： Xavier, Vinicius L. Frana, Felipe M. G. Xavier, Adilson E. Lima, Priscila M. V. Univ Fed Rio de Janeiro PESC COPPE Rio De Janeiro Brazil Univ Fed Rio de Janeiro iNCE Rio De Janeiro Brazil

关键词： Multisource Weber problem min-sum-distances clustering problem Nondifferentiable programming

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