Abstract: This paper introduces the Surrogate-assisted Multi-objective Grey Wolf Optimizer (SMOGWO) as a novel methodology for addressing the complex problem of empty-heavy train allocation, with a focus on line utilization balance. By integrating surrogate models to approximate the objective functions, SMOGWO significantly improves the efficiency and accuracy of the optimization process. The effectiveness of this approach is evaluated using the CEC2009 multi-objective test function suite, where SMOGWO achieves a superiority rate of 76.67% compared to other leading multi-objective algorithms. Furthermore, the practical applicability of SMOGWO is demonstrated through a case study on empty and heavy train allocation, which validates its ability to balance line capacity, minimize transportation costs, and optimize the technical combination of heavy trains. The research highlights SMOGWO’s potential as a robust solution for optimization challenges in railway transportation, offering valuable contributions toward enhancing operational efficiency and promoting sustainable development in the sector.

Key words: Surrogate-assisted model, Grey wolf optimizer, Multi-objective optimization, Empty-heavy train allocation