Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 695087, 10 pages
Research Article

A Novel Ranking Method Based on Subjective Probability Theory for Evolutionary Multiobjective Optimization

Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB, Canada T2N 1N4

Received 10 March 2011; Revised 30 June 2011; Accepted 21 July 2011

Academic Editor: Yuri Vladimirovich Mikhlin

Copyright © 2011 Shuang Wei and Henry Leung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Most of the engineering problems are modeled as evolutionary multiobjective optimization problems, but they always ask for only one best solution, not a set of Pareto optimal solutions. The decision maker's subjective information plays an important role in choosing the best solution from several Pareto optimal solutions. Generally, the decision-making processing is implemented after Pareto optimality. In this paper, we attempted to incorporate the decider's subjective sense with Pareto optimality for chromosomes ranking. A new ranking method based on subjective probability theory was thus proposed in order to explore and comprehend the true nature of the chromosomes on the Pareto optimal front. The properties of the ranking rule were proven, and its transitivity was presented as well. Simulation results compared the performance of the proposed ranking approach with the Pareto-based ranking method for two multiobjective optimization cases, which demonstrated the effectiveness of the new ranking approach.