Forward and Line-Based Cycle Bases for Periodic Timetabling

Abstract The optimization of periodic timetables is an indispensable planning task in public transport. Although the event scheduling problem (PESP) provides elegant mathematical formulation timetabling that led to many insights for primal heuristics, it notoriously hard solve optimality. One reason standard mixed-integer linear programming formulations, relaxations are weak, and integer variables pure technical nature general do not correlate with objective value. While first has been addressed by developing several families cutting planes, we focus on second aspect. We discuss integral forward cycle bases as a concept compute improved dual bounds PESP instances. To this end, develop theory digraphs. Specifically application timetabling, devise generic procedure construct line-based event-activity networks give simple recipe basis such networks. Finally, analyze 16 railway instances benchmark library PESPlib, match them structure, use better 14 out