Weighting factor extensions for finite multiple objective vector minimization problems

Abstract This paper develops two procedures for finding the efficient set of finite action multiple-objective problems. The first gives an exact characterization of the efficient set in terms of the weighted q -th-powers of the objective functions, for a fixed q , and gives a lower bound for q . The second gives an exact characterization of the efficient set in the t -th-order minima of the weighted objective functions. Some consideration is given to problems whose feasible action sets correspond to the vertices of certain polytopes and connectedness conjectures are given for which no counterexamples have yet been found.