Global maximization of UTA functions in multi-objective optimization

The UTAs (UTilité Additives) type methods for constructing nondecreasing additive utility functions were first proposed by Jacquet-Lagrèze and Siskos in 1982 for handling decision problems of multicriteria ranking. In this article, by UTA functions, we mean functions which are constructed by the UTA type methods. Our purpose is to propose an algorithm for globally maximizing UTA functions of a class of linear/convex multiple objective programming problems. The algorithm is established based on a branch and bound scheme, in which the branching procedure is performed by a so-called I-rectangular bisection in the objective (outcome) space, and the bounding procedure by some convex or linear programs. Preliminary computational experiments show that this algorithm can work well for the case where the number of objective functions in the multiple objective optimization problem under consideration is much smaller than the number of variables.