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1
CHAPTER
ONE
1
BASIC CONCEPTS
11 INTRODUCTION
The concept of optimization is basic to much of what we do in our daily
lives. The desire to run a faster race, win a debate, or increase corporate
profit implies a desire to do or be the best in some sense. In engineering, we
wish to produce the “best quality of life possible with the resources avail
able.” Thus in “designing” new products, we must use design tools which
provide the desired results in a timely and economical fashion. Numerical
optimization is one of the tools at our disposal.
In studying design optimization, it is important to distinguish between
analysis and design. Analysis is the process of determining the response of a
specified system to its environment. For example, the calculation of stresses
in a structure that result from applied loads is referred to here as analysis.
Design, on the other hand, is used to mean the actual process of defining the
system. For example, structural design entails defining the sizes and loca
tions of members necessary to support a prescribed set of loads. Clearly,
analysis is a subproblem in the design process because this is how we eval
uate the adequacy of the design.
Much of the design task in engineering is quantifiable, and so we are
able to use the computer to analyze alternative designs rapidly. The purpose
of numerical optimization is to aid us in rationally searching for the best
design to meet our needs.
While the emphasis here is on design, it should be noted that these
methods can often be used for analysis as well. Nonlinear structural analysis
is an example where optimization can be used to solve a nonlinear energy
minimization problem.
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NUMERICAL OPTIMIZATION TECHNIQUES FOR ENGINEERING DESIGN
Although we may not always think of it this way, design can be defined
as the process of finding the minimum or maximum of some parameter
which may be called the objective function. For the design to be acceptable,
it must also satisfy a certain set of specified requirements called constraints.
That is, we wish to find the constrained minimum or maximum of the objec
tive function. For example, assume we wish to design an internalcombus
tion engine. The design objective could be to maximize combustion
efficiency. The engine may be required to provide a specified power output
with an upper limit on the amount of harmful pollutants which can be emit
ted into the atmosphere. The power requirements and pollution restrictions
are therefore constraints on the design.
Various methods can be used to achieve the design goal. One approach
might be through experimentation where many engines are built and tested.
The engine providing maximum economy while satisfying the constraints
on the design would then be chosen for production. Clearly this is a very
expensive approach with little assurance of obtaining a true optimum
design. A second approach might be to define the design process analyti
cally and then to obtain the solution using differential calculus or the calcu
lus of variations. While this is certainly an attractive procedure, it is seldom
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 Spring '08
 PETERIFJU

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