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

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.