Size Limited Iterative Method: A Hybridized Heuristic for Train Unit Scheduling Optimization

In this research is presented an hybrid approach based on heuris- tics for solving large instances for the Train Unit Scheduling Optimization (TUSO). TUSO has been modelled as an IntegerMulti-Commodity Flow Problem (IMCF) lay on a Directed Acyclic Graph (DAG), and solved by Integer Linear Programming (ILP). This method proceeds in a way to iteratively improve the quality of one or more given feasible solutions by solving reduced instances of the original problem where only a subset of the arcs in the DAG are heuristically chosen to be optimised. Our approach is designed for reducing the original DAG into a much smaller size, but still retaining all the essential arcs for the optimal solution as much as possible. The capabilities of this frame-work for train unit scheduling optimization are tested by real-world cases and compared with the results from running the ILP solver alone for the original full problem instance and with the manual solutions for each dataset