Modeling relative importance of design criteria with a modified pareto preference

Engineering design problems are studied within a multicriteria optimization and decision-making framework. A methodology is developed that modifies the traditional Pareto preference to model designer's preferences reflected in the relative importance of criteria. The intent is to reduce the number of candidate designs to facilitate the selection of a preferred design. The versatility of this preference model allows it to be incorporated into the problem solution process either a priori, a posteriori, or iteratively, each offering different advantages. In the a priori approach, all Pareto efficient designs that do not satisfy the designer's preferences are never computed. In the a posteriori approach, a set of Pareto efficient designs is computed and then easily reduced based on the designer's preferences. Finally, the iterative approach offers the ability to adjust the designer's preferences by exploring their impact on the reduction of the Pareto efficient design set. The methodology is based on the concepts of convex cones and allowable tradeoff values between criteria. The theoretical foundation of the preference model is presented in the context of engineering design and the methodology is illustrated using a bi-criteria structural design problem and a tri-criteria vehicle dynamics design problem.