ON COMPUTING OBJECTIVE FUNCTION VALUES IN MULTIPLE-OBJECTIVE QUADRATIC-LINEAR PROGRAMMING

In this paper, we will consider the computation of objective function values when a nondominated frontier is searched in multiple objective quadratic-linear programming (MOQLP). Reference directions and weighte d-sums constitute a methodological basis for the search. This idea lea ds to a parametric linear complementarity model formulation. A critica l task of making a search procedure efficient, is to compute the chang es in quadratic and linear objective functions efficiently when a sear ch direction is changed or a basis change is performed, Those changes in objective functions can be computed by a so-called direct or indire ct method. The direct method is a straightforward one and based on the use of unit changes in basic decision variables. Instead, the indirec t method utilizes some other basic variables of the model. We will int roduce the indirect method and make theoretical and empirical comparis ons between the methods. Based on the comparisons, we point out that t he indirect method is clearly much more efficient than the direct one. (C) 1998 Elsevier Science B.V.