Modeling and Optimizing of a Non-constrained MultiObjective Problem having Multiple Utility Functions Using the Bayesian Theory

One of the multi-objective optimization methods makes use of the utility function for the objective functions. A utility function induces the most satisfactory solution for a decision maker (DM) by considering DM’s priorities. In existing studies, there are only one utility function for each objective function. But due to practical situations in different decision making environments in an industry or a trade, each goal may have multiple utility functions. Here, we present a multi- objective model in which each objective function has multiple utility functions applying Bayesian theory. The model allows the DM to calculate the probability of the utilities using conditional probability in conditions of certainty. Examples are worked through to illustrate the usefulness of the proposed model.