Physical programming - A mathematical perspective

Abstract

Physical programming (PP) is a new 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 his/her preferences by defining ranges of differing degrees of desirability for each design metric. Although this approach works well in practice, it had never been shown that the optimal solution is not unduly sensitive to these numerical range definitions. This paper shows that PP is indeed numerically well conditioned, and also compares its sensitivity to designer input (with respect to optimal solution) with that of other popular methods. This paper also provides the important proof that all solutions obtained through PP are Pareto optimal, and extends the notion of Pareto optimality to one of pragmatic implication. This paper introduces the important notion of P-Dominance that extends the concept of Pareto optimality beyond the cases minimize and maximize. We show that P-Dominance leads to the important concept of Generalized Pareto Optimal@. Numerical results arc provided, which illustrate the favorable numerical properties of physical programming.