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GBSSS: The generalized big square small square method for planar single- facility location. (English) Zbl 0760.90067
Summary: Big Square Small Square is a geometrical branch-and-bound algorithm, devised by P. Hansen, D. Peeters, D. Richard and J.-F. Thisse [Oper. Res. 33, 1251-1265 (1985; Zbl 0582.90027)], for the solution of constrained planar minisum single-facility location problems with \(L_ p\) norms and continuous non-decreasing costfunctions. The method basically works by splitting the studied planar region into squares, and either rejecting or further processing these squares by the evaluation of a lower bound. We present a modified version of this algorithm aimed at correcting a small failure to converge, accelerating the calculations, minimising the information to be stored, and, most importantly, determining a region of near-optimality. Furthermore the method is applicable to any planar single-facility problem with distances measured by mixed norms and as an objective any continuous function of the distances. This includes nearly all the models which have been proposed in the literature.

MSC:
90B85 Continuous location
90-08 Computational methods for problems pertaining to operations research and mathematical programming
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