Physical programming - Effective optimization for computational design

Abstract

A new effective and computationally efficient approach for design optimization, hereby entitled physical programming, is developed. This new approach is intended to substantially reduce the computational intensity of large problems and to place the design process into a more flexible and natural framework. Knowledge of the desired attributes of the optimal design is judiciously exploited. For each attribute of interest to the designer (each criterion), regions are defined that delineate degrees of desirability: unacceptable, highly undesirable, undesirable, tolerable, desirable, and highly desirable. This approach completely eliminates the need for iterative weight setting, which is the object of the typical computational bottleneck in large design optimization problems. Two key advantages of physical programming are 1) once the designer's preferences are articulated, obtaining the corresponding optimal design is a noniterative process-in stark contrast to conventional weight-based methods and 2) it provides the means to reliably employ optimization with minimal prior knowledge thereof. The mathematical infrastructure that supports the physical programming design optimization framework is developed, and a numerical example provided. Physical programming is a new approach to realistic design optimization that may be appealing to the design engineer in an industrial setting.

A modified rotation strategy for directed search domain algorithm in multiobjective engineering optimization

“…Shrink the search domain. First, for each reference point M = (M 1 , ..., M n ) ∈ M, the following single optimization problem is formulated similar to the physical programming (Messac 1996;Messac and Mattson 2002):…”

“…In some cases, they can only capture part of the Pareto frontier (Marler and Arora 2004). The well-known classical MOO methods, which are able to approximate the whole Pareto frontier, include the Normal-Boundary Intersection (NBI) method (Dad and Dennis 1997;1998), the Normal constraint (NC) method (Messac et al 2003;Messac and Mattson 2004), the Physical Programming method (Messac 1996;Messac and Mattson 2002), and the Directed Search Domain (DSD) method (Utyuzhnikov et al 2009;Erfani and Utyuzhnikov 2011). All of these methods exploit the anchor points which are the minima of each objective in the objective space, as well as an aggregate objective function (AOF) (preference function).…”

Modeling and Multi-Objective Design Optimization of Quasi-Continuous High Magnetic Field Systems

“…According to the classification, a scoring system shown in Table 5 is established. The proposed system follows the 'ones vs others' criteria established by Messac [17].…”

2.1.1 Isoperformance: Analysis and Design of Complex Systems with Known or Desired Outcomes

“…Isoperformance, on the other hand, fixes the amount of performance at an acceptable level (NIB) and trades off the other objectives with respect to each other. This is similar in philosophy to Physical Programming, developed by Messac [1996] with the difference that in Physical Programming all objectives, LIB, NIB, and SIB, are mapped onto a unitless scale of goodness and combined together into an overall system utility. It is this unitless measure that is then optimized.…”

“…A number of researchers such as Taguchi, Cook [1997], and Messac [1996] have recognized that system requirements typically fall into one of three classes: "smaller-is-better" (SIB), "larger-is-better" (LIB), and "nominal-is-better" (NIB) (see Fig. 3).…”