Real Parameter Optimization In this chapter we will be studying the problem of finding optima in functions of the form 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 pre-dates 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 m-tuples of numbers to a single parameter to be optimized, is a natural Collections: Mathematics