A Lagrangian heuristic algorithm for a real-world train timetabling problem

A Lagrangian heuristic algorithm for a real-world train timetabling problem

The train timetabling problem (TTP) aims at determining an optimal timetable for a set of trains which does not violate track capacities and satisfies some operational constraints. In this paper, we describe the design of a train timetabling system that takes into account several additional constraints that arise in real-world applications. In particular, we address the following issues: • Manu...

Solution of Real-World Train Timetabling Problems

Approaches to a real-world train timetabling problem in a railway node

We consider the Train Timetabling Problem (TTP) in a railway node (i.e. a set of stations in an urban area interconnected by tracks), which calls for determining the best schedule for a given set of trains during a given time horizon, while satisfying several track operational constraints. In particular, we consider the context of a highly congested railway node in which different Train Operato...

A Lagrangian Decomposition Algorithm for Robust Green Transportation Location Problem

In this paper, a green transportation location problem is considered with uncertain demand parameter. Increasing robustness influences the number of trucks for sending goods and products, caused consequently, increase the air pollution. In this paper, two green approaches are introduced which demand is the main uncertain parameter in both. These approaches are addressed to provide a trade-off b...

A Lagrangian Heuristic for Robustness, with an Application to Train Timetabling

Finding robust yet efficient solutions to optimization problems is a major practical issue that received large attention in recent years. Starting with stochastic programming, many of the approaches to robustness lead to a significant change in the problem formulation with respect to the non-robust (nominal) case. Besides requiring a much larger computational effort, this often results into maj...