ODS 2025 Milano

Hexaly is a new kind of global optimization solver. Hexaly APIs unify modeling concepts from mixed-linear programming, nonlinear programming, and constraint programming. Its modeling interface is nonlinear and set-oriented. It also supports user-coded functions, thus enabling black-box optimization and, more particularly, simulation optimization. Under the hood, Hexaly combines various exact and heuristic optimization methods: spatial branch-and-bound, simplex methods, interior-point methods, automatic Dantzig-Wolfe reformulation, column and row generation, propagation methods, local search, population-based methods, and surrogate modeling techniques for black-box optimization. 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.

We will illustrate these new modeling concepts on vehicle routing problems (among others) and show how Hexaly internally leverages Branch-Cut-Price techniques to automatically solve these problems, achieving near-optimal solutions within minutes on a standard laptop for large-scale problems. Here, “automatically” means out-of-the-box: no additional information or parameter tuning is required from the user.

FC Squad Building Challenge is a game mode of a famous football video game. This mode offers challenges to complete. A challenge consists of building a team of players that respects requirements. This problem relates to the Team Composition Problem known in the literature. In the challenges, 11 players must be selected among 18,000 available players, making the problem highly combinatorial. The objectives of the problem we solve are to maximize the number of priority players selected (if the user has set some priority players) and to minimize the total price of the team. Each player has several characteristics: a club, a nationality, a league, a quality (Bronze, Silver, or Gold), a rating, a price, and a set of preferred positions.

Two decisions are thus to be considered in this problem: a Boolean and an integer decision for each player. The boolean indicates if the player is selected for the team, and the integer indicates his position in the team. The requirements to fulfil can be constraints on the possible players to choose (for example, a minimum quality required). The team can also have some overall requirements, such as a maximum number of selected players from the same club. One key point is to provide solutions that users cannot manually improve in a very short computation time, less than 10 seconds.

This presentation is about modeling and solving this problem with Hexaly, a mathematical optimization solver that combines exact and heuristic optimization methods.