Research on Comparision between Deterministic Method and Uncertain Method for Solving Uncertain Multiobjective Programming

Abstract

Since there are often few or no samples and asymmetry information in the problems, uncertainty theory is introduced to study uncertain multi-objective programming (UMP), which cannot be solved by probability theory. Generally speaking, there are two types of methods for solving the UMP problem: in deterministic method, using the numerical characteristics of an uncertain variable, the UMP problem is transformed into a deterministic multiobjective programming, and then solved by the weighting method and ideal point method; in the uncertain method, the UMP problem is transformed into an uncertain single-objective programming, and then is solved by the evaluation criteria of the uncertain variables. The theoretical analysis and the data results for numerical examples solved by the AC algorithm designed in the paper show that the two types of methods are obviously different. Further, using this comparison, the essential difference between the two methods is whether the uncertainty relation between objective functions sholud be considered. Therefore, when the uncertainty relation is closely related, the uncertain method is more appropriate; otherwise, the deterministic method should be chosen.

Keywords

• uncertainty theory
• uncertain multiobjective programming
• asymmetry
• deterministic method
• AC algorithm