An interactive integrated multiobjective optimization approach for quasiconcave / quasiconvex utility functions

Abstract

In this paper, a new interactive, integrated approach for solving multiobjective optimization problems is presented. The approach is general in that it handles two broad classes of implicit utility functions: quasiconcave and quasiconvex. The first step is to use preference comparison-based tests to determine the class of utility function that is consistent with the Decision Maker (DM's) underlying preferences with respect to a sample of nondominated alternatives. Then one of the imbedded algorithms that is appropriate for the selected utility function is used. In the case of quasiconcave utility, a modified Geoffrion-Dyer-Feinberg algorithm [7] is applied. It projects the gradient-based improvement direction on the nondominated frontier and provides an interactive termination criterion. The quasiconvex utility-based algorithms chosen depends on the structure of the feasible set. The demands upon the DM are kept to a minimum in the sense that only paired comparisons of alternatives and trade-off evaluations are elicited by all the algorithms. An example is presented for the quasiconcave utility-based algorithm.