Flexible, large scale digital computer program was designed for the solution of a wide range of multivariable parameter optimization problems. The program has the ability to solve constrained optimization problems involving up to one hundred parameters

Glatt, C. R.

Hague, D. S.

English

NASA Technical Reports Server

December 1968	 Brief 68-10453 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Computer Program for Parameter Optimization 
The problem: 
To develop multivariable search techniques for 
practicing engineers concerned with the optimization 
of nonlinear, parametrically-defined systems. 
The solution: 
A flexible, large scale digital computer program 
designed for the solution of a wide range of multi-
variable parameter optimization problems. 
How it's done: 
The program has the ability to solve constrained 
optimization problems involving up to one hundred 
parameters. Nine search techniques are available for 
problem solutions; they are: 
Sectioning—The local performance minima in a se-
quence of searches parallel to the coordinate axes 
are located; and hence, by repetition, the extremal 
of the multivariable function is located. 
Adaptive Creeping—This method is similar to sec-
tioning, but instead of finding the local minima 
parallel to the axes, this search merely introduces 
small perturbations in the minimizing direction. The 
size of these perturbations is determined adaptively 
by the search algorithm. 
Steepest-Descent—This method searches along a se-
quence of rays determined by the local direction in 
which performance decreases most rapidly for a 
given perturbation measure. Three perturbation 
measure options, together with the relevant weight-
ing matrices are available within the program. 
Quadratic Search—Except for the search directions, 
this method is similar to the steepest-descent method. 
The directions are aligned through the extrernals of 
a sequence of locally osculating second order sur-
faces (as opposed to the first order tangent planes 
employed in the steepest-descent search). 
Davidons Method—This method is a particular
form of the steepest-descent search. It progressively 
approaches the second-order quadratic search from 
information obtained by a sequence of first order 
steepest-descent searches. 
Random Point Search—The performance is evalu-
ated at a set of uniformly distributed random points 
in the parameter space in a Monte-Carlo-like manner. 
Random Ray Search—Small perturbations are intro- 
duced sequentially along a series of randomly di-
rected rays in the control space. 
Pattern—This method explores the linear ray de-
fined by the first and last point of a preceding 
search or search sequence. 
Magnification—This method searches the direction 
defined by a proportional change in all parameters. 
The searches may be employed separately or in any 
sequential combination. The optimization program 
may be rapidly coupled to a wide class of parameter 
optimization problems, including systems which have 
previously been synthesized as digital computer pro-
grams. 
Notes: 
I. This program is written in FORTRAN IV for use 
on the IBM 7094 or 360 computers. 
2. Inquiries should be directed to: 
COSMIC 
Computer Center 
University of Georgia 
Athens, Georgia 30601 
Reference: B68-10453 
Patent status: 
No patent action is contemplated by NASA. 
Source: C. R. Glatt 
of The Boeing Company 
under contract to 
Ames Research Center 
(ARC-10168) 
Category 06 
This document was prepared under the sponsorship of the National	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned rights.
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Computer program for parameter optimization

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