Intra-set point generation and filtering in decision and criterion space

Abstract In various mathematical programming problems, especially in the area of multiple objective linear programming, the solution set generated by the model may often turn out to be a multidimensional subset of the feasible region rather than just a single point. Describing such solution sets to a decisionmaker can be difficult. In many cases, the only acceptable way to describe such a solution set is to do it by presenting the decision-maker with a finite number of representative points. The main purpose of this paper is to address techniques (that will be called intra-set point generation and filtering) that can be used to develop groups of representative solutions from a given set. Also, the paper outlines how the methods discussed can be coordinated with one another so as to form an interactive procedure. The interactive procedure can then be used to assist the decision-maker in locating his best solution in the set by looking at only a small finite number of representative solutions at each iteration. In order to demonstrate the usefulness of the intra-set point generation and filtering techniques, several illustrative applications have been provided.