Genetic Algorithms

Abstract

Consider an optimization problem where we want to find the maximum of a continuous function y = f(x),x = (x ₁,…, x _n ), for x ∈ D, where D is a subset of R ⁿ. We may first try calculus methods where we solve the system of equations ∂ f /∂x_i = 0, 1 ≤ i ≤ n, inside D,for all the critical points (the candidates for max or min) But this is an n × n system of non-linear (in general) equations to solve simultaneously for all solutions in D. This is, in general, a difficult problem to solve. But we will also have to look on the boundary of D, assuming that D is a closed subset of R ⁿ, for the max. This procedure only applies to functions f which are continuously differentiable in D.