Sustainable Efficiency Optimization for Synchronously Integrated Urban Rail Transit: SIMILP—A Hybrid Enhanced Approach Balancing Economy, Safety, and Capacity

Abstract Integrated urban rail transit (IUR) systems are vital for the resilience of global megacities; however, integrating heterogeneous networks presents profound challenges due to technical disparities to operational paralysis. This paper proposes a sustainable efficiency assessment framework utilizing a synchronous integration mixed-integer linear programming (SIMILP) model to reconcile economic revenue with technical safety constraints, effectively addressing limitations of traditional MILP models in managing nonlinear technical compatibility. We established a multi-criteria compatibility matrix, $${\text{Kf}}_{\text{s}\text{o}\text{e}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Kf</mml:mtext> <mml:mtext>soe</mml:mtext> </mml:msub> </mml:math> , by quantifying safety integrity levels (SIL), grades of automation (GoA), and type of alignment (TOA) through a geometric mean methodology. A Hybrid Quadratic Programming (QP) model, augmented by a Penalty Function and executed via SIMILP model, was developed to optimize operational frequencies ( $${X}_{\text{o}\text{p}\text{t}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>X</mml:mi> <mml:mtext>opt</mml:mtext> </mml:msub> </mml:math> ) across ten distinct rail modes, including Metro (MS, MX), Commuter Rail (CS, CC), and Light Rail (LL). The study identifies a “Technical Gold Standard” in the MS-CS corridor (100% compatibility) while revealing “Technical Valleys” (efficiency &lt; 30%) in lines such as MX due to safety-risk thresholds. Comparative analysis reveals that while conventional cost-minimization models lead to service shutdowns for branch lines, our SIMILP-based Enhanced Hybrid model restores 100% connectivity with an MX line capacity reaching 45 trips/h. To achieve sustainability, the model accepts a 39.28% increase in net operating costs, reviving frequencies from 0 to 27 trips/h for low-revenue corridors while anchoring capacity of decisive lines. This research proves that synchronous integration urban rail transit (SIUR) is a transition, providing a scalable tool to harmonize technical rigor with socioeconomic welfare, ensuring the high performance of assets is not compromised by system components .