Mathematical and Pragmatic Perspectives of Physical Programming

Abstract

Physical programming (PP) is an emerging multiobjective and design optimization method that has been applied successfully in diverse areas of engineering and operations research. The application of PP calls for the designer to express preferences by defining ranges of differing degrees of desirability for each design metric. Although this approach works well in practice, it has never been shown that the resulting optimal solution is not unduly sensitive to these numerical range definitions. PP is shown to be numerically well conditioned, and its sensitivity to designer input (with respect to optimal solution) is compared with that of other popular methods. The important proof is provided that all solutions obtained through PP are Pareto optimal and the notion of Pareto optimality is extended to one of pragmatic implication. The important notion of P dominance that extends the concept of Pareto optimality beyond the cases minimize and maximize is introduced. P dominance is shown to lead to the important concept of generalized Pareto optimality. Numerical results are provided that illustrate the favorable numerical properties of physical programming.