Approximating the noninferior set in multiobjective linear programming problems

The aim of this paper is to develop algorithms for approximating the noninferior set in the objective space for multiobjective linear programming problems with three or more objectives. A geometrical measure of error is used in controlling the number of extreme points needed in generating an approximation of desired accuracy. In more specific terms, the error in the approximation is estimated by computing the deviation of a polytope containing the entire noninferior set (the upper bounding polytope) from a lower bounding polytope whose interior is known to be inferior. Extreme points are added to the approximation in an attempt to reduce the deviation between the two polytopes in as few computations as possible. The facets in the approximation of the noninferior set are obtained by computing the convex hull of the extreme points generated by the algorithm. Suitable tests are developed to determine those facets of the convex hull that belong to the approximation.