Disaggregation in Bundle Methods: Application to the Train Timetabling Problem

TL;DR

This paper compares standard and new disaggregate bundle methods for solving dual problems in train timetabling, demonstrating that the disaggregate approach converges faster in realistic scenarios.

Contribution

Introduction of a novel disaggregate bundle method and comparison with the standard aggregate method for train timetabling optimization.

Findings

Disaggregate method converges faster than aggregate method.

Both methods effectively solve large-scale train timetabling problems.

Numerical tests on realistic scenarios validate the efficiency of the disaggregate approach.

Abstract

Bundle methods are often used to solve dual problems that arise from Lagrangian relaxations of large scale optimization problems. An example of such problems is the train timetabling problem. This paper focuses on solving a dual problem that arises from Lagrangian relaxation of a train timetabling optimization program. The dual problem is solved using bundle methods. We formulate and compare the performances of two different bundle methods: the aggregate method, which is a standard method, and a new, disaggregate, method which is proposed here. The two methods were tested on realistic train timetabling scenarios from the Iron Ore railway line. The numerical results show that the new disaggregate approach generally yields faster convergence than the standard aggregate approach.