A pseudo-genetic algorithm suited to compositional data

Genetic algorithms can solve least-squares problems where local minima may trap more traditional methods. Although genetic algorithms are applicable to compositional as well as noncompositional data, the standard implementation treats compositional data awkwardly. A need to decode, renormalize, then reincode the fitted parameters to regain a composition is not only computationally costly, but may thwart convergence. A modification to the genetic algorithm, described here, adapts the tools of reproduction, crossover, and mutation to compositional data. The modification consists of replacing crossover with a linear mixture of two parents and replacing mutation with a linear mixture of one of the members of the breeding population and a randomly generated individual. By using continuously evolving populations, rather than discrete generations, reproduction is no longer required. As a test of this new approach, a mixture of four Gaussian functions with given means and variances are deconvolved to recover their mixing proportions.