The parameter configuration problem consists of finding a parameter configuration that provides the most effective performance by a given algorithm. This paper addresses this problem for MILP solvers through a new multi-phase tuner based on the iterated local search metaheuristic. The goal is to find near-optimal, if not optimal, configuration(s) for efficiently solving large-scale industrial optimization problems. Instead of tuning in the entire configuration space induced by the set of parameters, the proposed tuner focuses on a small pool of parameters that is enhanced dynamically with new promising ones. Furthermore, it uses statistical learning to benefit from the dynamically accumulated information to forbid less promising parameter combinations. A computational study on a widely used commercial CPLEX solver with instances from the MIPLIB library and a real large-scale optimization problem highlights the promising potential of the tuner.