K-Prototype Clustering Assisted Hybrid Heuristic Approach for Train Unit Scheduling

This paper presents a K-Prototype assisted hybrid heuristic approach called SLIM+KP for solving large instances of the Train Unit Scheduling Optimization (TUSO) problem. TUSO is modelled as an Integer Multi-commodity Flow Problem (IMCFP) based on a Directed Acyclic Graph (DAG). When the problem size goes large, the exact solver is unable to solve it in reasonable time. Our method uses hybrid heuristics by iteratively solving reduced instances of the original problem where only a subset of the arcs in the DAG are heuristically chosen to be optimised by the same exact solver. K-Prototype is a clustering method for partitioning. It is an improvement of K-Means and K-Modes to handle clustering with the mixed data types. Our approach is designed such that the arcs of the DAG are clustered by K-prototype and each time only a small fraction of the arcs are selected to form the reduced instances. The capabilities of this framework were tested by real-world cases from UK train operating companies and compared with the results from running an exact integer solver. Preliminary results indicate the proposed methodology achieves the same optimal solutions as the exact solver for small instances but within shorter time, and yields good solutions for instances that were intractable for the exact solver.