Cone contraction method with visual interaction for multiple-objective non-linear programs

We describe an interactive procedure, implemented on a PC, for solving multiple-objective non-linear programming (MONP) problems. The procedure is composed of two stages. The first stage consists of modelling decision maker's (DM's) preferences using a fuzzy outranking relation in a sample of non-dominated points. The relation is then translated into a preference cone defining a subset of non-dominated points of greatest interest to the DM. In the second stage the subset of non-dominated points generated by the cone is scanned interactively. A graphical interface enables a visual interaction. The DM can either reduce directly the subset of non-dominated points to be scanned or retract to the first stage and give finer preference information which results in contraction of the cone and reduction of the subset of non-dominated points scanned in the second stage. Description of the procedure is followed by presentation of its application to a didactic MONP problem.