Euclidean centers: Computation, properties and a MOLP application

The question of centers addresses the issue of how to inscribe an object within a region defined by a set of constraints. More than one centering approach can be defined which leads to a different inscribed object and a different derivation procedure for both the object as well as its center. When attempting to inscribe the largest sphere within the constraints polytope the problem is defined as one of finding the Euclidean center of that polytope. We address in this paper various issues associated with the derivation of the Euclidean center and illustrate one application of this center to multiple-objective linear programming (MOLP) problems. c © 2007 Elsevier Ltd. All rights reserved.