The LBS-Discrete Interactive Procedure for Multiple-Criteria Analysis of Decision Problems

An interactive procedure, called LBS-Discrete (Light Beam Search), for multiple-criteria analysis of decision problems with an explicitly given set of alternatives is presented. An alternative is defined as a non-dominated point in the space of criteria. The set of alternatives is assumed to be finite and relatively large. The procedure is an extension of the Light Beam Search method for linear and non-linear multiple-objective programming (Jaszkiewicz and Slowinski, 1992b) to the discrete case. While existing interactive procedures may involve the decision maker (DM) in too difficult comparisons of the candidates for the best compromise alternative, the LBS-Discrete procedure tries to overcome this inconvenience. It supports both learning about the problem and successive improvement of the current point. At the decision phase of the procedure, a sample of non-dominated points, composed of the current point and a number of alternative proposals, is presented to the DM. In order to ensure a relatively easy evaluation of the sample by the DM, it is generated in a way taking into account a preference information of intra- and inter-criteria type given by the DM with respect to the current point. The local preference model has the form of an outranking relation and defines a subregion of the non-dominated set. The sample presented to the DM comes from this subregion. The procedure can be compared to projecting a focused beam of light from a spotlight at the reference point onto the non-dominated set; the highlighted subregion changes when either the reference point or the point of interest in the non-dominated set are changed. This explains the name LBS-Discrete. Finally, a microcomputer implementation of the LBS-Discrete with an important graphical interface is characterized and its application to an agricultural problem is presented.