  Feature selection is an intractable problem, therefore practical algorithms
often trade off the solution accuracy against the computation time. In this
paper, we propose a novel multi-stage feature selection framework utilizing
multiple levels of approximations, or surrogates. Such a framework allows for
using wrapper approaches in a much more computationally efficient way,
significantly increasing the quality of feature selection solutions achievable,
especially on large datasets. We design and evaluate a Surrogate-Assisted
Genetic Algorithm (SAGA) which utilizes this concept to guide the evolutionary
search during the early phase of exploration. SAGA only switches to evaluating
the original function at the final exploitation phase.
  We prove that the run-time upper bound of SAGA surrogate-assisted stage is at
worse equal to the wrapper GA, and it scales better for induction algorithms of
high order of complexity in number of instances. We demonstrate, using 14
datasets from the UCI ML repository, that in practice SAGA significantly
reduces the computation time compared to a baseline wrapper Genetic Algorithm
(GA), while converging to solutions of significantly higher accuracy. Our
experiments show that SAGA can arrive at near-optimal solutions three times
faster than a wrapper GA, on average. We also showcase the importance of
evolution control approach designed to prevent surrogates from misleading the
evolutionary search towards false optima.
