WB1 - Tutoriel Hexaly "Pleins feux sur les partenaires"

Mixed‑Integer Linear Programming (MILP) has been the dominant optimization framework in Operations Research for several decades. While it has proven extremely powerful, it is also well known that MILP formulations can become unwieldy when confronted with large‑scale, highly combinatorial, non‑convex, or structurally rich problems, particularly in application domains such as routing, scheduling, and packing.

Hexaly is an industrial optimization solver built around a hybrid, post‑MILP approach. Rather than relying primarily on linearization techniques and classical branch‑and‑bound‑centered workflows, it combines heuristic and exact methods and draws inspiration from multiple paradigms, including Mixed‑Integer Programming, Constraint Programming, Nonlinear Programming, and Black‑Box Optimization. A central design objective is modeling expressiveness and openness: enabling users to formulate problems closer to their natural combinatorial structure, while allowing diverse algorithmic components to interact in a complementary manner.

In this talk, I will present the guiding principles behind this approach, with a particular focus on discrete optimization problems where Hexaly currently demonstrates its strongest performance, such as large‑scale routing, scheduling, and packing. I will discuss how hybridization manifests not only at the algorithmic level, but also—crucially—within the modeling layer. Finally, I will provide a transparent overview of the solver’s current algorithmic status, supported by selected performance benchmarks.