Screening alternatives in multiple criteria subset selection

New techniques are presented to reduce the number of feasible alternatives in certain multiple criteria subset selection problems, thereby making it less difficult to find a good subset. The class of m-best alternatives problems is defined and the relation between dominance and potential optimality explored in the context of this class. A program is proposed to identify whether an individually dominated alternative can belong to an optimal subset satisfying certain pre-specified constraints. The extension of the proposed method to multi-objective knapsack problems is considered. Two examples illustrate the screening procedures for m-best alternatives problems and multi-objective knapsack problems.