2025 INFORMS Annual Meeting Atlanta

Hexaly is a new type of global optimization solver. Its modeling interface is nonlinear and set-oriented. It also supports user-coded functions, enabling seamless integration of simulation with optimization or machine learning with optimization. The Hexaly API unifies modeling concepts from mixed-integer programming, nonlinear programming, and constraint programming. Under the hood, Hexaly combines various exact and heuristic optimization methods: spatial branch-and-bound, simplex methods, interior-point methods, propagation, automatic branch-cut-price, local search, and surrogate modeling.

Hexaly stands out from traditional solvers like Gurobi, CPLEX, and OR-Tools by delivering super-fast solutions to problems such as routing, sequencing, scheduling, packing, clustering, matching, assignment, and location. For example, Hexaly provides solutions that are close to the best-known results in the literature for vehicle routing problems with thousands of points and scheduling problems with millions of tasks, achieving this in just one minute of runtime on a basic computer.

In addition to the Optimizer, Hexaly offers an innovative platform called Hexaly Studio, designed to prototype, develop, and deploy optimization applications quickly in a low-code fashion. This web-based platform is also well-suited for educational purposes; like all other Hexaly products, it is free for faculty and students.

Hexaly is a model-and-run solver that integrates heuristics and exact methods. A set-based modeling formalism was introduced to simplify the modeling of some combinatorial problems, like routing or packing problems. For instance, in a routing problem, list variables can be used to model the sequence of visits made by each truck. These decision variables are well suited for a heuristic search but are much more challenging to integrate into a mathematical programming approach to compute lower bounds. A direct MILP reformulation introduces a quadratic number of binary decisions with several big M constraints, leading to poor scalability and bounds. Hexaly automatically detects such structures in a user model and reformulates them in an extended MILP model to compute lower bounds parallel to a heuristic search. This model is solved efficiently using the literature’s state-of-the-art branch-and-cut-and-price techniques and column elimination algorithms. This talk will present the general approach, the algorithms used for the resolution, and some benchmarks on the classical vehicle routing and packing problems.