Optimizing Travel Time and Regenerative Energy for Periodic Timetables

2026-05-04

AI Summary

This study addresses the bi-objective optimization of passenger travel time and regenerative braking energy recovery in periodic train timetabling. The authors propose a novel PESP-Passenger-Energy model that, for the first time, integrates both objectives within a unified periodic event scheduling framework, revealing their combinatorial structure and identifying polynomially solvable special cases. Leveraging graph-theoretic techniques—specifically matching and Hamiltonian path methods—the paper analyzes computational complexity in single-station networks, proving NP-hardness even for single-objective variants while demonstrating efficient solvability under certain conditions. The model’s efficacy is validated through two real-world case studies, and the resulting Pareto frontiers offer both theoretical insights and practical tools for designing energy-efficient and service-oriented train schedules.

Abstract

Regenerating braking energy is one major pathway to make rail traffic energy-efficient. It is therefore desirable to design timetables that exploit this feature. However, timetables that allow to regenerate energy are often bad for the passengers. We hence formulate and analyze a bicriteria optimization problem (PESP-Passenger-Energy) to find periodic railway timetables that maximize the regenerated energy in terms of the brake-traction overlap time and minimize the travel time of the passengers. Our model extends the Periodic Event Scheduling Problem (PESP) and offers a rich combinatorial theory. We investigate its computational complexity on one-station networks, building on matchings and Hamiltonian paths. Besides showing its NP-hardness even for a single objective, we identify several polynomial-time solvable special cases. Finally, we provide two case studies, underlining the practicability of our model, and analyzing the Pareto front.

Problem

• periodic timetabling
• regenerative energy
• travel time
• bicriteria optimization
• railway scheduling

Innovation

• Periodic Event Scheduling Problem
• Regenerative Braking Energy
• Bicriteria Optimization
• Brake-Traction Overlap
• Pareto Front