In order to align with the varying demands of market over time and the developmental needs of the railway, there has been a significant increase in the frequency and scale of adjustments to the train diagram. The old and new alternate passenger train diagram represents a dynamic operational plan that synergizes the operation of trains with the utilization of rolling stock during alternate periods. This paper introduces an integrated cooperative optimization time–space network for the new and old alternate train diagrams. It treats the utilization of rolling stock during alternate periods and resolution of conflicts between the old and new routes as a unified description of the optimization problem for the operation paths of passenger train stock in the spatio-temporal network of alternate periods. Building upon this, we set the objective as the cost of rolling stock utilization during alternate periods, with rolling stock utilization rules and train running intervals as constraints. And then we establish a comprehensive cooperative optimization 0–1 integer planning model and design a Lagrangian heuristic algorithm.