MULTICRITERIA OPTIMIZATION: A GENERAL CHARACTERIZATION OF EFFICIENT SOLUTIONS*

In the context of deterministic multicriteria maximization, a Pareto optimal, nondominated, or efficient solution is a feasible solution for which an increase in value of any one criterion can only be achieved at the expense of a decrease in value of at least one other criterion. Without restrictions of convexity or continuity, it is shown that a solution is efficient if and only if it solves an optimization problem that bounds the various criteria values from below and maximizes a strictly increasing function of these several criteria values. Also included are discussions of previous work concerned with generating or characterizing the set of efficient solutions, and of the interactive approach for resolving multicriteria optimization problems. The final section argues that the paper's main result should not actually be used to generate the set of efficient solutions, relates this result to Simon's theory of satisficing, and then indicates why and how it can be used as the basis for interactive procedures with desirable characteristics.