Abstract
An existing family of genetic algorithms, which were designed with discrete and binary variables in mind, has been extended in this paper to handle truly continuous variables. Its close relationships with Monte Carlo methods, the simplex method, simulated annealing and other direct, i.e. Derivative-free global optimization algorithms creates a really versatile tool for various difficult optimization tasks. The main area of its application should be the reconstruction of unknown, continuous, and possibly smooth, distributions of various physical quantities derived from the experimental data. Among them might be: grain-size distribution for particulate magnetic materials derived from isothermal magnetization curves, distribution of relaxation times derived from luminescence experiments or chemical kinetics (inverse Laplace transform), and other large-scale numerically hard problems. One such problem, namely solving for the grain-size distribution for particulate magnetic materials, is presented as a working example and treated in detail. Applications of this algorithm should be stable deconvolution of various spectra with a variable window and non-parametric curve smoothing with a non-smooth objective function.