An Overview of Techniques for Solving Multiobjective Mathematical Programs

Multiobjective mathematical programming has been one of the fastest growing areas of OR/MS during the last 15 years. This paper presents: some reasons for the rapidly growing increase in interest in multiobjective mathematical programming, a discussion of the advantages and disadvantages of the three general approaches (articulation of the decision maker's preference structure over the multiple objectives prior to, during, or after the optimization) towards multiobjective mathematical programming, a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming, and a discussion of important areas for further research. The overview concentrates on those techniques which require an articulation of the decision maker's preference structure either during or after the optimization, since these are the areas where most of the recent research has been conducted. It differs from previous overviews in that, in addition to the timing of the elicited preference information, the techniques are also classified according to the types of decision variables contained in the model (i.e., only continuous decision variables, or at least some discrete decision variables). In addition, the types of preference information (e.g., a ranking of outcomes) required of the various techniques are also discussed.