Combining Gradient Information and Primitive Directions for High-Performance Mixed-Integer Optimization

Abstract: In this paper we consider bound-constrained mixed-integer optimization problems where the objective function is differentiable w.r.t.\ the continuous variables for every configuration of the integer variables. We mainly suggest to exploit derivative information when possible in these scenarios: concretely, we propose an algorithmic framework that carries out local optimization steps, alternating searches along gradient-based and primitive directions. The algorithm is shown to match the convergence properties of a derivative-free counterpart. Most importantly, the results of thorough computational experiments show that the proposed method clearly outperforms not only the derivative-free approach but also the main alternatives available from the literature to be used in the considered setting, both in terms of efficiency and effectiveness.