Train Operation Optimisation for Maximising Regenerative Braking Energy Utilisation Based on Dynamic Coalition Formation Game

Regenerative braking energy (RBE) generated during train braking can directly supply traction trains. Maximising RBE utilisation requires forming optimal train coalitions. A key challenge lies in dynamically determining optimal coalitions under switching train regimes. This paper proposes a dynamic coalition formation game to identify optimal coalitions for maximising RBE utilisation. First, multiple speed profiles with different inter-station journey times are generated as candidate operating strategies. Given a selected speed profile combination, the coalition formation game dynamically identifies coalitions of braking and traction trains and evaluates their RBE utilisation through a designed utility function. A coalition matching rate is introduced to guide adaptive coalition expansion and reduce candidate coalition evaluations. The obtained coalition utilities are integrated into an adaptive particle swarm optimisation (APSO) fitness function, which iteratively searches for the optimal profiles. Based on real-life metro data, the results show that the proposed approach improves RBE utilisation by over 10% compared to the scheduled timetable under both off-peak and peak scenarios. Coalition formation involving three and four trains demonstrates the effectiveness of the dynamic coalition formation game in adaptively expanding and reforming. Moreover, APSO demonstrates superior performance compared with standard PSO, genetic algorithm and differential evolution.