Pareto analysis in multiobjective optimization using the collinearity theorem and scaling method

This paper presents a method to predict the relative objective weighting scheme necessary to cause arbitrary members of a Pareto solution set to become optimal. First, a polynomial description of the Pareto set is constructed utilizing simulation and high performance computing. Then, using geometric relationships between the member of the Pareto set in question, the location of the utopia point and the polynomial coefficients, the weighting of the performance metrics which causes a particular member of the Pareto set to become optimal is determined. The use of this technique, termed the scaling method, is examined via using a sample problem from the field of vehicle dynamics optimization. The scaling method is based on the collinearity theorem which is also presented in the paper.