A Barzilai‐Borwein‐based heuristic algorithm for locating multiple facilities with regional demand

A Barzilai‐Borwein‐based heuristic algorithm for locating multiple facilities with regional demand

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Article ID: iaor20122502
Volume: 51
Issue: 3
Start Page Number: 1275
End Page Number: 1295
Publication Date: Apr 2012
Journal: Computational Optimization and Applications
Authors: ,
Keywords: combinatorial optimization, gradient methods, facilities
Abstract:

We are interested in locations of multiple facilities in the plane with the aim of minimizing the sum of weighted distance between these facilities and regional customers, where the distance between a facility and a regional customer is evaluated by the farthest distance from this facility to the demand region. By applying the well‐known location‐allocation heuristic, the main task for solving such a problem turns out to solve a number of constrained Weber problems (CWPs). This paper focuses on the computational contribution in this topic by developing a variant of the classical Barzilai‐Borwein (BB) gradient method to solve the reduced CWPs. Consequently, a hybrid Cooper type method is developed to solve the problem under consideration. Preliminary numerical results are reported to verify the evident effectiveness of the new method.

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