, Volume 51, Issue 3, pp 1275-1295

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

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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.

J. Jiang was supported by NUAA Research FundingNO.190.
X. Yuan was supported by NSFC Grant 10701055 and 70732003, and an FRG grant from HKBU.