Introduction

Abstract

Since the First International Conference on Multiple Criteria Decision Making, held at the University of South Carolina in 1972 (Cochrane and Zeleny (eds.) 1973), it has been increasingly recognized that most of the real-world decision-making problems usually involve multiple, noncommensurable, and conflicting objectives which should be considered simultaneously. One of the major systems-analytic multiobjective approaches to decision-making under constraints is multiobjective optimization as a generalization of traditional single-objective optimization. For such multiobjective optimization problems, it is significant to realize that multiple objectives are often noncommensurable and cannot be combined into a single objective. Moreover, the objectives usually conflict with each other and any improvement of one objective can be achieved only at the expense of another. With this observation, in multiobjective optimization, the notion of Pareto optimality or efficiency has been introduced instead of the optimality concept for single-objective optimization. However, decisions with Pareto optimality or efficiency are not uniquely determined; the final decision must be selected from among the set of Pareto optimal or efficient solutions. Consequently, the aim in solving multiobjective optimization problems is to derive a compromise or satisficing† solution of a decision maker (DM) which is also Pareto optimal based on subjective value judgments (see, for example, Chankong and Haimes 1983a; Cohon 1978; Goicoechea, Hansen and Duckstein 1982; Grauer, Lewandowski, and Wierzbicki (eds.) 1982; Grauer and Wierzbicki (eds.) 1984; Haimes, Hall, and Freedman 1975; Hwang and Masud 1979; Nijkamp 1979; Seo and Sakawa 1988; Steuer 1986; Zeleny 1982).