A comparison of two reference point methods in multiple objective mathematical programming

When making decisions with multiple criteria, a decision maker often thinks in terms of an aspiration point or levels of achievement for the criteria. In multiple objective mathematical programming, solution methods based on aspiration points can generate nondominated solutions using a variety of scalarizing functions. These reference point solution methods commonly use a scalarizing function that reaches down from the ideal solution, in a direction specified by the aspiration point. Conversely, a similar scalarizing function can push out from the nadir point toward a specified aspiration point. These scalarizing functions are similar in structure but diametrically opposed in their reference points. In this paper we examine how these approaches behave from a technical point of view and conduct an experiment to understand better the human behaviour of users of these approaches. Insights we gain on the evenness of dispersion are relevant when attempting to construct a representation of the nondominated set. Further, the technical characteristics of the two formulations' solutions, combined with behavioural tendencies, allow us to comment on the implications for their use in interactive multiple objective methods.