  Variable selection is recognized as one of the most critical steps in
statistical modeling. The problems encountered in engineering and social
sciences are commonly characterized by over-abundance of explanatory variables,
non-linearities and unknown interdependencies between the regressors. An added
difficulty is that the analysts may have little or no prior knowledge on the
relative importance of the variables. To provide a robust method for model
selection, this paper introduces the Multi-objective Genetic Algorithm for
Variable Selection (MOGA-VS) that provides the user with an optimal set of
regression models for a given data-set. The algorithm considers the regression
problem as a two objective task, and explores the Pareto-optimal (best subset)
models by preferring those models over the other which have less number of
regression coefficients and better goodness of fit. The model exploration can
be performed based on in-sample or generalization error minimization. The model
selection is proposed to be performed in two steps. First, we generate the
frontier of Pareto-optimal regression models by eliminating the dominated
models without any user intervention. Second, a decision making process is
executed which allows the user to choose the most preferred model using
visualisations and simple metrics. The method has been evaluated on a recently
published real dataset on Communities and Crime within United States.
