Mathematical and Pragmatic Perspectives of Physical Programming

Abstract

Physical programming (PP) is an emerging multiobjective and design optimizationmethod 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 de ning 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 de nitions. 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 pragmaticimplication.The important notion of P dominancethat 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.

The optimization control research of the master /slave on the internet-based tele-operation robot system

“…The advantages of it are [9,10]: After confirming the designer's preferences, the optimal design that agrees with it can be obtained. Compared with the traditional method which set the weighting coefficient of the object back and force, it can reduce the burden of the compute greatly.…”

A method for generating a well-distributed Pareto set in nonlinear multiobjective optimization

“…The optimization is based on minimization of an aggregate preference function determined by the preference functions (class functions) with the preferences set a priori. The notion of the generalized Pareto optimal solution is introduced in the PP-based method [20] on the basis of the PP class functions. To provide a well-distributed Pareto set, the off-set strategy is introduced in the PP-based algorithm in [18].…”

“…To avoid this limitation the notion of a generalized Pareto optimal solution is introduced in [20]. The correspondence between the standard and generalized Pareto optimal solutions is provided in [24].…”

Robustness-based design optimization under data uncertainty

“…Other methods include goal programming (Zou and Mahadevan, 2006), compromise decision support problem Mistree, 1993, 1995;Chen et al, 1996), compromise programming (CP) (Zalney, 1973;Zhang, 2003;Chen et al, 1999) and physical programming (Messac, 1996;Messac et al, 2001;Messac and Ismail-Yahaya, 2002;Chen et al, 2000). Each of these methods has its own advantages and limitations.…”