 
Summary: Chapter 3
Real Parameter Optimization
In this chapter we will be studying the problem of finding optima in functions of the form
f(x1, x2, . . . , xn) that take a vector or array of n real parameters to a single real value. There
are easy and hard examples and part of the chapter is a discussion of when a problem merits
the use of evolutionary computation and when it might not. Finding the maximum of
f(x) = 4  2x  x2
(3.1)
does not even require calculus. It could have been solve in Babylon in 2000 B.C., millennia
before the invention of calculus. Someone who is up on their calculus will simply glance at
the equation and say "the maximum occurs at x = 1 and has a value of y = 5. Solving
such an equation with evolutionary computation would be a bit comic.
Real parameter optimization is one of the earliest applications of evolutionary compu
tation. Evolution strategies were originally designed to optimize parameters that described
an airfoil and also has had substantial success at designing nozzles that convert hot water
into steam efficiently. Real parameter optimization also substantially predates evolutionary
computation; it is one of the original applications of the differential calculus with roots in
the geometry of the third century B.C. and modern treatments credited to Isaac Newton and
Gottfried Leibniz in the seventeenth century. The natural representation from the calculus,
as functions mapping mtuples of numbers to a single parameter to be optimized, is a natural
