Multiobjective Optimization using GAI Models

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 Pareto-optimal 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.