Mathematical and pragmatic perspectives of physical programming

Physical programming (PP) is an emerging multiobjective and design optimiza tion method that has been applied successfully in diverse areas of engineer ing and operations research. The application of PP calls for the designer t o express preferences by defining ranges of differing degrees of desirabili ty for each design metric. Although this approach works well in practice, i t has never been shown that the resulting optimal solution is not unduly se nsitive to these numerical range definitions. PP is shown to be numerically well conditioned, and its sensitivity to designer input (with respect to o ptimal solution) is compared with that of other popular methods. The import ant proof is provided that all solutions obtained through PP are Pareto opt imal and the notion of Pareto optimality is extended to one of pragmatic im plication. The important notion of P dominance that extends the concept of Pareto optimality beyond the cases minimize and maximize is introduced. P d ominance is shown to lead to the important concept of generalized Pareto op timality. Numerical results are provided that illustrate the favorable nume rical properties of physical programming.