MCDM Location Problems

Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods

“…In fact, in many situations more than one objective has to be taken into account, thus leading to multiobjective location problems. See [37] for a survey of the most representative multicriteria location problems considered in the literature.…”

“…Unfortunately, as pointed out in [40], for the majority of multiobjective optimization problems, it is not easy to obtain such a description, since the efficient set includes typically a very large number or infinite number of points. The methods proposed in the literature with that purpose are specialized either for particular problems (for instance, in [37] it is shown how to obtain the whole efficient set of some location problems) or for a particular class of multiobjective problems (for instance, the multiobjective simplex methods for the linear case [18]). To the extent of our knowledge, only two general methods (see [13,15]) have been proposed in the literature with that purpose for the general nonlinear biobjective problem (1).…”

The Weighted Fuzzy Barycenter

“…In a more formalized point of view, the problem handled belongs to the optimal location problem frame (Hakimi, 1964;Nickel & Puerto, 2005) and more precisely can be defined as the 1-facility optimal discrete location problem for a set of discrete demand points in a continuous space (Labbé, Peeters, & Thisse, 1995;Shan, 2005). In this field of the operations research, most studies deal with three wellknown metrics from the Lp-norm family: the k-median, that models the L1-norm (minimizing the sum of Euclidian distances), the kcenter, that models the L ∞ -norm (minimizing the maximum distance) and, between those, the gravity center, that models the L2-norm (minimizing the sum of the squared Euclidean distances).…”