Abstract:To address system load imbalance and insufficient coordination in the integrated operation of suburban railways and urban rail transit, a multi-type train formation operation plan based on two-dimensional “section-network” comprehensive load balancing is proposed, aiming to coordinate local section and overall network loads. A multi-objective optimization model is established to minimize passenger travel cost and enterprise operating cost while maximizing load balancing, subject to constraints such as through-train turnaround capacity and available vehicles. An adaptive variable neighborhood sparrow search algorithm, integrating variable neighborhood search and hierarchical disturbance strategies, is developed to solve the model. A case study shows that, compared with plans involving integrated operation with short formations, long formations, and transfer-based multi-type formations, the proposed plan significantly reduces passenger and enterprise costs and enhances section-network load balancing. Compared with the standard sparrow search algorithm and particle swarm optimization, the proposed algorithm improves solution quality by 3.37% and 6.98%, respectively, with higher computational efficiency. The results provide a methodological reference for optimizing train scheduling in multi-system integrated rail transit operations.