Integrated Ant Colony Optimization and Mixed Integer Linear Programming for Multi-objective Railway Timetabling

This paper presents an algorithmic framework for automatic railway timetabling, developed within the project “Tools for mathematical optimization of strategic railway timetable models” funded by the Norwegian Railway Directorate (Jernbanedirektoratet). It describes the algorithmic core of the developed tool, called Automatic Timetabler with Multiple Objectives. The framework integrates a Multi-Objective Ant Colony Optimization (MOACO) algorithm and a Mixed Integer Linear Programming (MILP) formulation. MOACO performs a fast-but-coarse exploration of the solution space, populating and maintaining an approximated Pareto optimal set of timetables. The timetables generated by MOACO are refined by the MILP formulation, exploring a neighborhood of the input solution and returning feasible, high-quality timetables. The tool is assessed on case studies driven from real practice in Norway.