Jean-Philippe Dubus

IJCAI Conference 2009 Conference Paper

• Jean-Philippe Dubus
• Christophe Gonzales
• Patrice Perny

This paper deals with multiobjective optimization in the context of multiattribute utility theory. The alternatives (feasible solutions) 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. Due to decomposability, utility vectors attached to solutions can be compiled into a graphical structure closely related to junction trees, the so-called GAI net. We first show how the structure of the GAI net can be used to determine efficiently the exact set of Paretooptimal solutions in a product set and provide numerical tests on random instances. Since the exact determination of the Pareto set is intractable in worst case, we propose a near admissible algorithm with performance guarantee, exploiting the GAI structure to approximate the set of Pareto optimal solutions. We present numerical experimentations, showing that both utility decomposition and approximation significantly improve resolution times in multiobjective search problems.

IJCAI Conference 2009 Conference Paper

• Jean-Philippe Dubus
• Christophe Gonzales
• Patrice Perny

This paper deals with Decision-Making in the context of multiattribute utility theory and, more precisely, with the problem of efficiently determining the best alternative w. r. t. an agent’s preferences (choice problem). We assume that alternatives are elements of a product set of attributes and that the agent’s preferences are represented by a generalized additive decomposable (GAI) utility on this set. Such a function allows an efficient representation of interactions between attributes while preserving some decomposability of the model. GAI utilities can be compiled into graphical structures called GAI networks that can be exploited to solve choice problems using collect/distribute schemes essentially similar to those used in Bayesian networks. In this paper, rather than directly using this scheme on the GAI network for determining the most preferred alternative, we propose to work with another GAI function, acting as an upper-bound on utility values and enhancing the model’s decomposability. This method still provides the exact optimal solution but speeds up significantly the search. It proves to be particularly useful when dealing with choice and ranking under constraints and within collective Decision-Making, where GAI nets tend to have a large size. We present an efficient algorithm for determining this new GAI function and provide experimental results highlighting the practical efficiency of our procedure.