  Multi-model inference covers a wide range of modern statistical applications
such as variable selection, model confidence set, model averaging and variable
importance. The performance of multi-model inference depends on the
availability of candidate models, whose quality has been rarely studied in
literature. In this paper, we study genetic algorithm (GA) in order to obtain
high-quality candidate models. Inspired by the process of natural selection, GA
performs genetic operations such as selection, crossover and mutation
iteratively to update a collection of potential solutions (models) until
convergence. The convergence properties are studied based on the Markov chain
theory and used to design an adaptive termination criterion that vastly reduces
the computational cost. In addition, a new schema theory is established to
characterize how the current model set is improved through evolutionary
process. Extensive numerical experiments are carried out to verify our theory
and demonstrate the empirical power of GA, and new findings are obtained for
two real data examples.
