APPROXIMATING THE NONINFERIOR SET IN MULTIOBJECTIVE LINEAR-PROGRAMMING PROBLEMS

The aim of this paper is to develop algorithms for approximating the n oninferior set in the objective space for multiobjective linear progra mming problems with three or more objectives. A geometrical measure of error is used in controlling the number of extreme points needed in g enerating an approximation of desired accuracy. In more specific terms , the error in the approximation is estimated by computing the deviati on of a polytope containing the entire noninferior set (the upper boun ding polytope) from a lower bounding polytope whose interior is known to be inferior. Extreme points are added to the approximation in an at tempt to reduce the deviation between the two polytopes in as few comp utations as possible. The facets in the approximation of the noninferi or 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.