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Rail transit optimization comprises the mathematical modeling and solution of operational planning problems in railway and urban metro systems, including line planning, train timetabling, rolling stock circulation, crew scheduling, and stop-skipping patterns ^[1]. The train timetabling problem determines the scheduled departure and arrival times of each train at each station, subject to safety constraints such as minimum headways, station track capacities, block-section occupancy rules, and speed restrictions, and it is typically formulated as a mixed-integer or multi-commodity flow model on a time-space network that represents each train path as a flow of units through nodes ^[2]. The objective function commonly balances long-term operational cost against service quality, minimizing fleet size, net energy consumption, or passenger waiting and in-vehicle travel time while satisfying time-dependent origin-destination travel demand; integrated approaches simultaneously optimize timetables, stop plans, and rolling stock assignments to account for the tight coupling between these interrelated operational planning decisions ^[3].