An Evolutionary Algorithm With Applications to Statistics
Mary C. Meyer · Journal of Computational and Graphical Statistics · 2003
Evolutionary algorithms are used to find maxima of functions. Their claim to fame is an ability to find a global maximum in the presence of local maxima. The computations do not require derivatives or convexity, but still may be fairly computationally intensive in larger dimensions. This article presents a new type of evolutionary algorithm that works well in many dimensions, with the added advantage that linear equality constraints are implemented in a natural way. Bounds on the coordinates of the solution are also easy to implement. Several examples are presented and the new algorithm is compared with standard versions of evolutionary algorithms. The first group consists of functions in one or two dimensions, chosen to be difficult to maximize by gradient or simplex-based methods. The second set of examples are from statistics problems that are known to be computationally difficult. The first is least absolute deviations nonlinear regression with bootstrapped confidence bounds on the mean response, the second is smoothed nonparametric unimodal density estimation requiring both a linear equality constraint and linear inequality constraints. The Fortran subroutine is available for the user.