Multi-train trajectory optimisation to maximise rail network energy efficiency under travel-time constraints

Optimising the trajectories of multiple interacting trains to maximise energy efficiency is a difficult, but highly desirable, problem to solve. A bespoke genetic algorithm has been developed for the multi-train trajectory optimisation problem and used to seek a near-optimal set of control point distances for multiple trains, such that a weighted sum of the time and energy objectives is minimised. Genetic operators tailored to the problem are developed including a new mutation operation and the insertion and deletion pairs of control points during the reproduction process. Compared with published results, the new GA was shown to increase the quality of solutions found by an average of 27.6% and increase consistency by a factor of 28. This allows more precise control over the relative priority given to achieving time targets or increasing energy efficiency

A Mixed Integer Programming Model to Minimize Fuel Consumption in Freight Train Operation

Fuel consumption is among the most important criteria in train operations. Considerable efforts have been made to identify optimal speed for enhanced fuel economy. The train speed control is achieved through switching the power notches, which sets constant level of fuel supply to the engine in a typical diesel-electric locomotive. A global optimal speed, however, cannot be considered appropriate due to the localized variations in the track gradient and curvature, apart from the variations in the load. An efficient train operation also requires the train completes its journey within a given travel time. This study aims at determining optimal train speeds to minimize the total fuel consumption in completing the journey, while considering the local variations in the track geometry and other properties. A nonlinear mixed integer programming model is formulated to solve the considered problem using an off-the-shelf optimization software package. A multiphase-steps improved method is proposed for solving the considered problem more effectively. Numerical examples are presented to illustrate the developed model and solution method