Keyword: Matheuristics


A column-generation-based matheuristic for periodic and symmetric train timetabling with integrated passenger routing

Bernardo Martin-Iradi*, Stefan Ropke

In this study, the periodic train timetabling problem is formulated using a time-space graph formulation that exploits the properties of a symmetric timetable. Three solution methods are proposed and compared where solutions are built by what we define as a dive-and-cut-and-price procedure. An LP relaxed version of the problem with a subset of constraints is solved using column generation where each column corresponds to the train paths of a line. Violated constraints are added by separation and a heuristic process is applied to help to find integer solutions. The passenger travel time is computed based on a solution timetable and Benders’ optimality cuts are generated allowing the method to integrate the routing of the passengers. We propose two large neighborhood search methods where the solution is iteratively destroyed and repaired into a new one and one random iterative method. The problem is tested on the morning rush hour period of the Regional and InterCity train network of Zealand, Denmark. The solution approaches show robust performance in a variety of scenarios, being able to find good quality solutions in terms of travel time and path length relatively fast. The inclusion of the proposed Benders’ cuts provide stronger relaxations to the problem. In addition, the graph formulation covers different real-life constraints and has the potential to easily be extended to accommodate more constraints.

European Journal of Operational Research / 2022
Go to paper

Matheuristics for slot planning of container vessel bays

Korach, Aleksandra; Brouer, Berit Dangaard; Jensen, Rune Møller

Stowage planning is an NP-hard combinatorial problem concerned with loading a container vessel in a given port, such that a number of constraints regarding the physical layout of the vessel and its seaworthiness are satisfied, and a number of objectives with regard to the quality of the placement are optimized. State-of-the-art methods decompose the problem into phases, the latter of which, known as slot planning, involves loading the containers into slots of a bay. This article presents an efficient matheuristic for the slot planning problem. Matheuristics are algorithms using mathematical programming techniques within a heuristic framework. The method finds solutions for 96% of 236 instances based on real stowage plans, 90% of them optimally, with an average optimality gap of 4.34% given a limit of one second per instance. This is an improvement over the results provided by previous works.

European Journal of Operational Research, Volume 282 / 2020
Go to paper