ODS 2025 Milano

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 a set of requirements. This problem relates to the Team Composition Problem known in the literature. In the challenges, 11 players have to be selected among between 3,000 and 18,000 available players, which makes the problem highly combinatorial. The objectives of the problem we solve are to maximise 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 of the demands of this project is to provide solutions that cannot be improved manually by users 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 uses various operations research techniques, combining heuristics and exact methods.

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 we will show how Hexaly Optimizer internally leverages Branch-Cut-Price techniques to automatically solve this kind of problem, achieving near-optimal solutions within minutes on a standard laptop for mid-size problems. Here, “automatically” means out-of-the-box: no additional information or parameter tuning is required from the user.