Cluster Analysis of Separation of “Independent Objective” for Probability-Based Multi-objective Optimization

In the evaluation of the probability-based multi-objective optimization, the need of “independent response” of the multi-objective is necessary, and the “independent response” is analogical as an “independent event” from the respect of probability theory. This is a novel approach with brand new concept of “preferable probability.” The novel methodology can be used in many fields, including material selection, programming problem, energy planning, operation research, etc. In this chapter, the separation of an “independent objective” from “multiple objectives” is discussed by utilizing cluster analysis. The results show that using linear correlation coefficient to distinguish the “similarity” of performances is a rational method, which thus can be used to supply appropriate objective classification for the probability-based multi-objective optimization.