A simple algorithm for optimization and model fitting: AGA (asexual genetic algorithm)

Abstract

Context. Mathematical optimization can be used as a computational tool to obtain the optimal solution to a given problem in a systematic and efficient way. For example, in twice-differentiable functions and problems with no constraints, the optimization consists of finding the points where the gradient of the objective function is zero and using the Hessian matrix to classify the type of each point. Sometimes, however it is impossible to compute these derivatives and other type of techniques must be employed such as the steepest descent/ascent method and more sophisticated methods such as those based on the evolutionary algorithms.Aims. We present a simple algorithm based on the idea of genetic algorithms (GA) for optimization. We refer to this algorithm as AGA (asexual genetic algorithm) and apply it to two kinds of problems: the maximization of a function where classical methods fail and model fitting in astronomy. For the latter case, we minimize the chi-square function to estimate the parameters in two examples: the orbits of exoplanets by taking a set of radial velocity data, and the spectral energy distribution (SED) observed towards a YSO (Young Stellar Object).Methods. The algorithm AGA may also be called genetic, although it differs from standard genetic algorithms in two main aspects: a) the initial population is not encoded; and b) the new generations are constructed by asexual reproduction.Results. Applying our algorithm in optimizing some complicated functions, we find the global maxima within a few iterations. For model fitting to the orbits of exoplanets and the SED of a YSO, we estimate the parameters and their associated errors.