Chapter 1
General Introduction
Sooner or later, every scientist or engineer runs into the problem of having to
find the “best” solution some set of decisions can give. Usually, the variables
governing such problems are related to one another in a rather complicated way,
and finding the “best” combination of them can seem intractable. Normally, the
relations b etween these decision variables can be translated into so-called ob-
jective functions, and the value of each of these functions can be interpreted as
a measure of the quality that particular combination of the decision variables
give to a particular aspect of the solution.
As such, N-dimensional optimization problems with m individual objective
functions can be stated generally as
find ” min ”F (x) =
f
1
(x)
f
2
(x)
.
.
.
f
m
(x)
subject to
G(x) < 0
H(x) = 0
lb ≤ x ≤ ub,
where
x = [x
1
, x
2
, . . . , x
N
] ,
and f
1
(x) through f
m
(x) indicate the individual objective functions. In al-
most all practical cases, finding good solutions is not a problem, but finding the
best solution is much more difficult. Moreover, for most problems encountered
in practice, the objective functions f
1
(x) through f
m
(x) are highly nonlinear,
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