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

TL;DR

This paper introduces a novel optimization framework that combines gradient information and primitive directions for bound-constrained mixed-integer problems, demonstrating superior efficiency and effectiveness over existing methods.

Contribution

It proposes a new algorithmic approach that integrates derivative-based and primitive directions, matching convergence rates of derivative-free methods while outperforming them in practice.

Findings

Outperforms existing derivative-free methods in efficiency

Achieves better effectiveness in solution quality

Matches convergence properties of derivative-free algorithms

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.