The Light Beam Search Over a Non-dominated Surface of a Multiple-objective Programming Problem

An interactive procedure for multiple-objective analysis of linear and non-linear programs is presented. At the decision phase of the procedure, a sample of points, composed of the current point and a number of alternative proposals, is presented to the decision maker (DM). The sample is constructed to ensure a relatively easy evaluation of the sample by the DM. To this end an outranking relation is used as a local preference model in a neighbourhood of the current point. The outranking relation is used to define a sub-region of the non-dominated set the sample presented to the DM comes from. The DM has two possibilities, or degrees of freedom, to move from one sub-region to another which better fits his/her preferences. The first possibility consists in specifying a new reference point which is then projected onto the non-dominated set in order to find a better non-dominated point. The second possibility consists in shifting the current point to a selected point from the sub-region. In both cases, a new sub-region is defined around the updated current point. This technique can be compared to projecting a focused beam of light from a spotlight at the reference point onto the non-dominated set; the highlighted sub-region changes when either the reference point or the point of interest in the non-dominated set are changed.