Heuristic Solution Approaches to the Solid Assignment Problem

The 3-dimensional assignment problem, also known as the Solid Assignment Problem (SAP), is a challenging problem in combinatorial optimisation. While the ordinary or 2-dimensional assignment problem is in the P-class, SAP which is an extension of it, is NP-hard. SAP is the problem of allocating n jobs to n machines in n factories such that exactly one job is allocated to one machine in one factory. The objective is to minimise the total cost of getting these n jobs done. The problem is commonly solved using exact methods of integer programming such as Branch-and-Bound B&B. As it is intractable, only approximate solutions are found in reasonable time for large instances. Here, we suggest a number of approximate solution approaches, one of them the Diagonals Method (DM), relies on the Kuhn-Tucker Munkres algorithm, also known as the Hungarian Assignment Method. The approach was discussed, hybridised, presented and compared with other heuristic approaches such as the Average Method, the Addition Method, the Multiplication Method and the Genetic Algorithm. Moreover, a special case of SAP which involves Monge-type matrices is also considered. We have shown that in this case DM finds the exact solution efficiently. We sought to provide illustrations of the models and approaches presented whenever appropriate. Extensive experimental results are included and discussed. The thesis ends with a conclusions and some suggestions for further work on the same and related topics

Optimization of Electric Scooter Rebalancing Tour through Mathematical programming

openThe pursuit of Sustainable Development Goal 11 (SDG11), striving to create inclusive, resilient, and sustainable urban environments, has become a global priority. One of SDG11’s key objectives is to ensure safe, affordable, accessible, and sustainable transport systems for all. In response to this imperative, the concept of electric scooter (e-scooter) sharing has gained remarkable popularity. This innovative model allows users to access e-scooters on demand, providing a personalized last-mile solution that complements public transportation and has the potential to reduce private car ownership and greenhouse gas emissions. As e-scooters take on an increasingly pivotal role in urban mobility, the efficient management of their distri- bution and charging presents a critical challenge. One of the key problems in this sharing system is to ensure that e-scooter is not over-saturated and under-utilized. This thesis embarks on a comprehensive exploration of the com- plexities surrounding this challenge and proposes solutions to enhance the integration of e-scooter sharing into everyday urban life. The core idea revolves around conducting a night tour operation that allow operator to drop full-charge e-scooter, but also swap the battery of the low charged unit to re-balance the e-scooter distribution. Within this thesis, two mathematical programming formulations are presented in order to plan ahead the route and suggested actions at each station during the night tour. The first model, adapted from previous literature work on bike sharing systems rebalancing, provides a benchmark and introduces readers to the night rebalancing tour problem. The second model represents an original improved version, allowing night tour operators to swap only the battery rather than the whole e-scooter unit during operations. Both models confront the challenge of managing exponential growth in constraints and size of the solution space as the number of stations increases. In response, tailor-made branch-and-cut algorithms are developed to efficiently solve this problem. This scalable framework offers the potential to manage extensive e-scooter fleets and station networks within the city, enabling companies to enhance their operations, foster citizen trust, and establish e-scooter sharing systems as a dependable choice for daily last-mile transportation. This thesis aims to make the topic accessible and easily understandable, inviting broader participation and contributions to research in this vital field.The pursuit of Sustainable Development Goal 11 (SDG11), striving to create inclusive, resilient, and sustainable urban environments, has become a global priority. One of SDG11’s key objectives is to ensure safe, affordable, accessible, and sustainable transport systems for all. In response to this imperative, the concept of electric scooter (e-scooter) sharing has gained remarkable popularity. This innovative model allows users to access e-scooters on demand, providing a personalized last-mile solution that complements public transportation and has the potential to reduce private car ownership and greenhouse gas emissions. As e-scooters take on an increasingly pivotal role in urban mobility, the efficient management of their distri- bution and charging presents a critical challenge. One of the key problems in this sharing system is to ensure that e-scooter is not over-saturated and under-utilized. This thesis embarks on a comprehensive exploration of the com- plexities surrounding this challenge and proposes solutions to enhance the integration of e-scooter sharing into everyday urban life. The core idea revolves around conducting a night tour operation that allow operator to drop full-charge e-scooter, but also swap the battery of the low charged unit to re-balance the e-scooter distribution. Within this thesis, two mathematical programming formulations are presented in order to plan ahead the route and suggested actions at each station during the night tour. The first model, adapted from previous literature work on bike sharing systems rebalancing, provides a benchmark and introduces readers to the night rebalancing tour problem. The second model represents an original improved version, allowing night tour operators to swap only the battery rather than the whole e-scooter unit during operations. Both models confront the challenge of managing exponential growth in constraints and size of the solution space as the number of stations increases. In response, tailor-made branch-and-cut algorithms are developed to efficiently solve this problem. This scalable framework offers the potential to manage extensive e-scooter fleets and station networks within the city, enabling companies to enhance their operations, foster citizen trust, and establish e-scooter sharing systems as a dependable choice for daily last-mile transportation. This thesis aims to make the topic accessible and easily understandable, inviting broader participation and contributions to research in this vital field

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum