Title: Mathematical modelling and nature-inspired metaheuristics for solving the football team selection problem

Authors: Soukaina Laabadi; Mohamed Nezar Abourraja

Addresses: Laboratory of applied Mathematics, ENS of Casablanca, Hassan II University, Casablanca, Morocco ' AIRA Laboratory, Smart Factory and Robotics, Hassan I University, Settat, Morocco

Abstract: The football team selection (FTS) problem consists of selecting performant players from a squad under given constraints to form an optimal team. Many relevant solutions have been developed; however, the literature review revealed that metaheuristic-based solutions are scarce despite their well-known effectiveness in solving selection problems. To fill this gap, first, this paper develops a 0/1 linear programming model incorporating financial limitations, age considerations, and injury status as constraints. Second, to solve it, CPLEX optimisation tool and two nature-inspired algorithms are employed, namely the binary particle swarm optimisation (BPSO) and genetic algorithms (GAs). Then, experiments are conducted using data from the 2022 FIFA World Cup, specifically focusing on the big four. The results demonstrate that both BPSO and GAs yield promising outcomes that outperform those of CPLEX, closely aligning with real-world data, particularly when considering team performance as a key factor in achieving victory. The proposed approaches offer valuable insights into optimising FTS; ultimately it can be generalised to other multi-player sports.

Keywords: football; player selection; team formation; 0/1 linear programming; genetic algorithms; binary particle swarm optimisation; BPSO.

DOI: 10.1504/IJAOM.2025.148396

International Journal of Advanced Operations Management, 2025 Vol.16 No.3, pp.261 - 285

Received: 26 Jun 2024
Accepted: 15 May 2025
Published online: 03 Sep 2025 *

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