Decision making with multiple objectives using GAI networks

This paper deals with preference representation on combinatorial domains and preference-based recommendation in the context of multicriteria or multiagent decision making. The alternatives of the decision problem are seen as elements of a product set of attributes and preferences over solutions are represented by generalized additive decomposable (GAI) utility functions modeling individual preferences or criteria. Thanks to decomposability, utility vectors attached to solutions can be compiled into a graphical structure closely related to junction trees, the so-called GAI network. Using this structure, we present preference-based search algorithms for multicriteria or multiagent decision making. Although such models are often non-decomposable over attributes, we actually show that GAI networks are still useful to determine the most preferred alternatives provided preferences are compatible with Pareto dominance. We first present two algorithms for the determination of Pareto-optimal elements. Then the second of these algorithms is adapted so as to directly focus on the preferred solutions. We also provide results of numerical tests showing the practical efficiency of our procedures in various contexts such as compromise search and fair optimization in multicriteria or multiagent problems.