Influence diagrams with multiple objectives and tradeoff analysis

Influence diagrams have been important models for decision problems because of their ability to both model a problem rigorously at its mathematical level and depict its high-level structure graphically. Once the structure and numerical details of an influence diagram have been specified, it can be evaluated to determine the optimal decision policy. However, when evaluating multiple objectives, in the past this determination was based on the assumption that utility functions that commensurate the objectives are available. This paper extends the structure and solution algorithm for influence diagrams to allow for the inclusion of noncommensurate objectives using multiobjective tradeoff analysis instead of utility theory. This eliminates the need to specify any preference information before the influence diagram is solved. The proposed multiobjective-based methodology is also useful for decision makers who either do not want to accept the assumptions of utility theory for a particular problem, or are confronted with a problem in which it is neither practical nor viable to construct a utility function. Additionally, this paper establishes the relationship between multiobjective influence diagrams and multiobjective decision trees. This relationship is important because it allows a decisionmaker to utilize the advantages of both representations. An example problem is presented to introduce both the extended multiobjective influence diagram methodology and the relationship linking multiobjective decision trees to multiobjective influence diagrams.