Modelling and Optimization of a Non-Constrained Multi-objective Problem having Multiple Utility Functions using Bayesian Theory

One of the multi-objective optimization methods makes use of the utility function for the objective functions. Utility function creating the most satisfaction answers for decision makers (DMs) by considering the priorities of the DMs; in an available studies; there are only one utility function for each objective function. But due to practical situation in different decision making environments in an industry or trade lead each goal has multiple utility functions. This paper presents a model of multi- objective problem in which each of the objective function has multiple utility function applying Bayesian theory. This model allows DMs to calculate the probability of these utilities using conditional probability in conditions of uncertainty. In addition, examples are given to illustrate the usefulness of this model