Fundamental Principle of Probability-Based Multi-objective Optimization and Applications

The inherent shortcomings of previously proposed multi-objective optimization methods are employing “additive” algorithm for the normalized evaluation index and weighting factor, which implies to take the form of “union” in the spirit of set theory. In fact, for the evaluation of “simultaneous optimization of multi-performance utility index”, the form of “intersection” in set theory and “joint probability” in probability theory should be more suitable for the problem. The viewpoint of system theory is consistent with this understanding as well. In this chapter, the new idea of preferable probability is introduced to reflect the degree of preference of the candidate’s utility in the selection of multi-objective optimization in viewpoint of system theory; all the utility indexes of candidate schemes are divided into two types, i.e., the beneficial type and the unbeneficial type for the selection of the schemes; each utility index of the candidate scheme contributes a partial preferable probability quantitatively, and the overall/total preferable probability of a candidate scheme is the product of all partial preferable probabilities in the spirit of probability theory, which thus transfers the multi-objective optimization problem into an overall (integrated) single-objective optimization issue naturally. The total preferable probability is the uniquely decisive indicator in the competitive selection process. In addition, examples of applications in material selection and some other businesses in broader and more general fields are given, and the results show the effectiveness of the new methodology.