The Generalized Reduced Gradient Method: A Reliable Tool for Optimal Design

1977 ◽  
Vol 99 (2) ◽  
pp. 394-400 ◽  
Author(s):  
G. A. Gabriele ◽  
K. M. Ragsdell
Keyword(s):  
Optimal Design ◽  
Gradient Method ◽  
Theoretical Development ◽  
Test Problems ◽  
Basic Algorithm ◽  
Reduced Gradient Method ◽  
Fortran Code ◽  
Reduced Gradient ◽  
Efficient Code ◽  
Generalized Reduced Gradient

This paper is a presentation of a method, called the Generalized Reduced Gradient Method, which has not received wide attention in the engineering design literature. Included is a theoretical development of the method, a description of the basic algorithm, and additional recommendations to produce an efficient code. A Fortran code employing this theory was written and tested on the Eason and Fenton [1] test problems, illustrating the method to be efficient and reliable.

Optimal Design of a Class of Welded Structures Based on Design for Latitude

1985 ◽  
Vol 107 (4) ◽  
pp. 482-487 ◽  
Author(s):  
E. Sandgren ◽  
G. Gim ◽  
K. M. Ragsdell
Keyword(s):  
Optimal Design ◽  
Objective Function ◽  
Gradient Method ◽  
Low Cost ◽  
Optimal Solution ◽  
Beam Structures ◽  
Welded Structures ◽  
Reduced Gradient Method ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

The minimization of the sensitivity of a design to variations in uncontrollable parameters is illustrated. The procedure is applied to the design of a class of welded beam structures which results in a low-cost design with minimal sensitivities. Dominant constraints are chosen which contain variations of the uncontrollable parameters. A dual objective function is formed and tradeoff curves are presented from which the optimal solution is selected. The minimization is carried out using the generalized reduced gradient method and other applications are presented.

Multi-objective traction optimization of vehicles in loose dry sand using the generalized reduced gradient method

2016 ◽  
Vol 64 ◽  
pp. 46-57 ◽  
Author(s):  
Joe D. Robinson ◽  
Farshid Vahedifard ◽  
Masoud Rais-Rohani ◽  
George L. Mason ◽  
Jody D. Priddy
Keyword(s):  
Gradient Method ◽  
Multi Objective ◽  
Reduced Gradient Method ◽  
Reduced Gradient ◽  
Dry Sand ◽  
Generalized Reduced Gradient

Functional Dependence and the Method of Alternate Formulations in Optimal Design

1992 ◽  
Vol 114 (4) ◽  
pp. 596-602
Author(s):  
C. R. Hammond ◽  
G. E. Johnson
Keyword(s):  
Optimal Design ◽  
Functional Dependence ◽  
Problem Formulation ◽  
System Model ◽  
Decision Variable ◽  
Reduced Gradient Method ◽  
State Variable ◽  
Mathematical Properties ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

In an earlier article in this journal we introduced the Method of Alternate Formulations (MAF). MAF is a nonnumerical approach to constrained optimal design implemented with symbolic mathematics. The MAF problem formulation is the same as is used by the generalized reduced gradient method. There are usually many ways to partition the design vector into decision variable and state variable components and so there are usually many different alternate formulations for the objective function and constraints. Each alternate formulation contains all of the information about the physical system. Yet all other mathematical properties (e.g., convexity, linearity, scaling, etc.) can change. It has been observed that some of the alternate formulations that should exist based strictly on the theory of combinations cannot be obtained. In this paper, we show that this phenomenon occurs whenever there is functional dependence in the system model. Several examples are used to show how functional dependence affects the search for the solution by MAF. Prediction of functional dependence at the outset informs the designer which formulations cannot exist. This allows the designer to concentrate effort (more productively) on other formulations of the problem.

Optimum Balancing of Three-Dimensional “RSSR” Mechanisms

1999 ◽  
Author(s):  
Tarcisio Antonio Hess Coelho ◽  
Valter Francisco Arruda Alves
Keyword(s):  
Dynamic Behavior ◽  
Gradient Method ◽  
Numerical Optimization ◽  
Three Dimensional ◽  
Physical Models ◽  
Line Position ◽  
Reduced Gradient Method ◽  
Optimum Configuration ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

Abstract The Generalized Reduced Gradient method of numerical optimization is applied in obtaining the reduction of moments and forces transmitted to the frame of a three-dimensional RSSR mechanism. Such a modification of dynamic behavior of the mechanism, or balancing, is achieved by the addition of counterweights attached to the moving links in an off-line position. The evaluation of the obtained optimum configuration is performed by comparing the measured vibration levels of the frame of physical models of the balanced and unbalanced mechanism.

Sign in / Sign up

Export Citation Format

Share Document