A fundamental question in the field of approximation algorithms, for a given problem instance, is the selection of the best (or a suitable) algorithm with regard to some performance criteria. A practical strategy for facing this problem is the application of machine learning techniques. However, limited support has been given in the literature to the case of more than one performance criteria, which is the natural scenario for approximation algorithms. We propose multidimensional Bayesian network (mBN) classifiers as a relatively simple, yet well-principled, approach for helping to solve this problem. Precisely, we relax the algorithm selection decision problem into the elucidation of the nondominated subset of algorithms, which contains the best. This formulation can be used in different ways to elucidate the main problem, each of which can be tackled with an mBN classifier. Namely, we deal with two of them: the prediction of the whole nondominated set and whether an algorithm is nondominated or not. We illustrate the feasibility of the approach for real-life scenarios with a case study in the context of Search Based Software Test Data Generation (SBSTDG). A set of five SBSTDG generators is considered and the aim is to assist a hypothetical test engineer in elucidating good generators to fulfil the branch testing of a given programme.