Inferring Parameters of a Relational System of Preferences from Assignment Examples using an Evolutionary Algorithm

Abstract

Most evolutionary multi-objective algorithms perform poorly in many-objective problems. They normally do not make selective pressure towards the Region of Interest (RoI), the privileged zone in the Pareto frontier that contains solutions important to a DM. Several works have proved that a priori incorporation of preferences improves convergence towards the RoI. The work of (Fernandez, E. Lopez, F. Lopez, & Coello Coello, 2011) uses a binary fuzzy outranking relational system to map many-objective problems into a tri-objective optimization problem that searches the RoI; however, it requires the elicitation of many preference parameters, a very hard task. The use of an indirect elicitation approach overcomes such situation by allowing the parameter inference from a battery of examples. Even though the relational system of Fernandez et al. (2011) is based on binary relations, it is more convenient to elicit its parameters from assignment examples. In this sense, this paper proposes an evolutionary-based indirect parameter elicitation method that uses preference information embedded in assignment examples, and it offers an analysis of their impact in a priori incorporation of DM’s preferences. Results show, through an extensive computer experiment over random test sets, that the method estimates properly the model parameter’s values.