A Branch-and-Cut based Pricer for the Capacitated Vehicle Routing Problem

openIl Capacitated Vehicle Routing Problem, abbreviato come CVRP, è un problema di ottimizzazione combinatoria d'instradamento nel quale, un insieme geograficamente sparso di clienti con richieste note deve essere servito da una flotta di veicoli stazionati in una struttura centrale. Negli ultimi due decenni, tecniche di Column generation incorporate all'interno di frameworks branch-price-and-cut sono state infatti l'approccio stato dell'arte dominante per la costruzione di algoritmi esatti per il CVRP. Il pricer, un componente critico nella column generation, deve risolvere il Pricing Problem (PP) che richiede la risoluzione di un Elementary Shortest Path Problem with Resource Constraints (ESPPRC) in una rete di costo ridotto. Pochi sforzi scientifici sono stati dedicati allo studio di approcci branch-and-cut per affrontare il PP. L'ESPPRC è stato tradizionalmente rilassato e risolto attraverso algoritmi di programmazione dinamica. Questo approccio, tuttavia, ha due principali svantaggi. Per cominciare, peggiora i dual bounds ottenuti. Inoltre, il tempo di esecuzione diminuisce all'aumentare della lunghezza dei percorsi generati. Per valutare la performance dei loro contributi, la comunità di ricerca operativa ha tradizionalmente utilizzato una serie d'istanze di test storiche e artificiali. Tuttavia, queste istanze di benchmark non catturano le caratteristiche chiave dei moderni problemi di distribuzione del mondo reale, che sono tipicamente caratterizzati da lunghi percorsi. In questa tesi sviluppiamo uno schema basato su un approccio branch-and-cut per risolvere il pricing problem. Studiamo il comportamento e l'efficacia della nostra implementazione nel produrre percorsi più lunghi comparandola con soluzioni all'avanguardia basate su programmazione dinamica. I nostri risultati suggeriscono che gli approcci branch-and-cut possono supplementare il tradizionale algoritmo di etichettatura, indicando che ulteriore ricerca in quest'area possa portare benefici ai risolutori CVRP.The Capacitated Vehicle Routing Problem, CVRP for short, is a combinatorial optimization routing problem in which, a geographically dispersed set of customers with known demands must be served by a fleet of vehicles stationed at a central facility. Column generation techniques embedded within branch-price-and-cut frameworks have been the de facto state-of-the-art dominant approach for building exact algorithms for the CVRP over the last two decades. The pricer, a critical component in column generation, must solve the Pricing Problem (PP), which asks for an Elementary Shortest Path Problem with Resource Constraints (ESPPRC) in a reduced-cost network. Little scientific efforts have been dedicated to studying branch-and-cut based approaches for tackling the PP. The ESPPRC has been traditionally relaxed and solved through dynamic programming algorithms. This approach, however, has two major drawbacks. For starters, it worsens the obtained dual bounds. Furthermore, the running time degrades as the length of the generated routes increases. To evaluate the performance of their contributions, the operations research community has traditionally used a set of historical and artificial test instances. However, these benchmark instances do not capture the key characteristics of modern real-world distribution problems, which are usually characterized by longer routes. In this thesis, we develop a scheme based on a branch-and-cut approach for solving the pricing problem. We study the behavior and effectiveness of our implementation in producing longer routes by comparing it with state-of-the-art solutions based on dynamic programming. Our results suggest that branch-and-cut approaches may supplement the traditional labeling algorithm, indicating that further research in this area may bring benefits to CVRP solvers

A Guided Neighborhood Search Applied to the Split Delivery Vehicle Routing Problem

The classic vehicle routing problem considers the distribution of goods to geographically scattered customers from a central depot using a homogeneous fleet of vehicles with finite capacity. Each customer has a known demand and can be visited by exactly one vehicle. Each vehicle services the assigned customers in such a way that all customers are fully supplied and the total service does not exceed the vehicle capacity. In the split delivery vehicle routing problem, a customer can be visited by more than one vehicle, i.e., a customer demand can be split between various vehicles. Allowing split deliveries has been proven to potentially reduce the operational costs of the fleet. This study efficiently solves the split delivery vehicle routing problem using three new approaches. In the first approach, the problem is solved in two stages. During the first stage, an initial solution is found by means of a greedy approach that can produce high quality solutions comparable to those obtained with existing sophisticated approaches. The greedy approach is based on a novel concept called the route angle control measure that helps to produce spatially thin routes and avoids crossing routes. In the second stage, this constructive approach is extended to an iterative approach using adaptive memory concepts, and then a variable neighborhood descent process is added to improve the solution obtained. A new solution diversification scheme is presented in the second approach based on concentric rings centered at the depot that partitions the original problem. The resulting sub-problems are then solved using the greedy approach with route angle control measures. Different ring settings produce varied partitions and thus different solutions to the original problem are obtained and improved via a variable neighborhood descent. The third approach is a learning procedure based on a set or population of solutions. Those solutions are used to find attractive attributes and construct new solutions within a tabu search framework. As the search progresses, the existing population evolves, better solutions are included in it whereas bad solutions are removed from it. The initial set is constructed using the greedy approach with the route angle control measure whereas new solutions are created using an adaptation of the well known savings algorithm of Clarke and Wright (1964) and improved by means of an enhanced version of the variable neighborhood descent process. The proposed approaches are tested on benchmark instances and results are compared with existing implementations

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Técnicas de clustering aplicadas a la resolución de problemas de optimización combinatoria con restricciones espaciales y temporales

En esta investigación se aborda la resolución de la familia de problemas denominada problemas de planificación de asistentes de atención domiciliaria, conocida por sus siglas en inglés HCSP (Home Care Scheduling Problem). La importancia en la resolución de esta familia de problemas ha ido en aumento durante los últimos años, importancia que también se ha visto reflejada en el mundo académico con un creciente número de publicaciones tal y como reflejan dos recientes revisiones sobre estado del arte Fikar y Hirsch (2017); Cisse et al. (2017). Este interés está motivado principalmente por dos factores, a saber, el envejecimiento de nuestra población y la necesidad de buscar alternativas más eficientes en la prestación de servicios de atención domiciliaria. El envejecimiento progresivo de nuestra población, es quizás uno de los retos más importantes que deberemos afrontar como sociedad, reto que ha sido señalado por diversos organismos tanto europeos como internacionales (World Health Organization, 2015). En dicho contexto demográfico, y con una creciente demanda de peticiones de asistencia domiciliaria, las empresas prestadoras de servicios de atención domiciliaria deben buscar formas más eficientes y alternativas de satisfacer la creciente demanda, preservando la calidad del servicio y garantizando unos servicios de atención domiciliaria de calidad y sostenibles para nuestros mayores. Esta investigación se centra en la resolución de un problema real y de fácil transferencia a la industria, reportado por la compañía EULEN. Dicha compañía presta servicios de atención domiciliaria en la Comunidad de Madrid y debe atender anualmente alrededor de 1.5 millones de servicios, lo que se traduce en 2.1 millones de horas de trabajo, no incluyendo estas cifras las ineficiencias inherentes a la prestación de servicios, como son los desplazamientos y los tiempos de espera incurridos por los asistentes. El problema es abordado semanalmente, debiendo atender a 13.344 servicios cada semana. Estos servicios a su vez están formados por tareas, que deben prestarse a una hora concreta y en una localización particular. De estos servicios, el 80% debe ser atendido de lunes a viernes en horario matinal (07:00 a 14:30) con lo que alrededor de 10.700 servicios deben ser planificados y asignados a la vez. El tamaño del problema abordado, el cual está un orden de magnitud por encima de los abordados en el estado del arte, junto con la imposibilidad de dividir el problema en instancias más pequeñas ha requerido el diseño e implementación de técnicas específicas, a fin de poderlo resolver en un tiempo y con un coste que posibilite la operativa diaria de la compañía prestadora de servicio. El problema se aborda desde la perspectiva del clustering, consistiendo su resolución en la agrupación de servicios dentro de grupos de servicios o clústers, los cuales conformarán el horario de trabajo de cada asistente de atención domiciliaria. La utilización de dicha perspectiva presenta varios desafíos que han sido resueltos a lo largo de la presente investigación, entre ellas destacan: el inusual tamaño de las instancias a resolver, las restricciones a respetar que contemplan aspectos espaciales y temporales, así como la necesidad de definir un concepto de similitud o distancia entre. Dicho concepto de similitud es definido a fin de tener en cuenta las componentes espaciales y temporales del problema. Una vez definido, el problema se aborda con tres técnicas novedosas: la primera de ellas es un método de clustering jerárquico inspirabasada en colonias de hormigas Dorigo y Gambardella (1997) y se denominan ACS-HCSP y IACS-HCSP. Todas las técnicas son evaluadas experimentalmente de un modo exhaustivo, con un total de 96 configuraciones distintas adaptadas a diferentes entornos. En primer lugar, se comparan las técnicas propuestas entre sí a fin de determinar su rendimiento, tanto como en calidad como en tiempo de ejecución, realizándose los pertinentes análisis de significación estadística. Una vez determinada las técnicas que tienen un mejor rendimiento se pasa a comparar de modo exhaustivo las técnicas ACS-HCSP y IACS-HCSP a fin de determinar si las modificaciones propuestas para la técnica IACS-HCSP producen mejoras significativas, obteniéndose un resultado positivo. Finalmente y con el objetivo de comparar las técnicas propuestas con técnicas existentes en el estado del arte, las técnicas propuestas son comparadas con las heurísticas propuestas por Quintana et al. (2017) y con la solución actual de la compañía, obteniendo la técnica IACS-HCSP mejores resultados y permitiendo un ahorro económico estimado de 3.7 millones de euros anuales. Palabras clave: Clustering, metaheurísticas, problemas de optimización combinatoria, optimización basada en colonias de hormigas, problemas de planificación de asistentes de atención domiciliaria.do en el método de Ward (1963), mientras que las dos aproximaciones restantes se basan en la metaheurística conocida como optimización basada en colonias de hormigas Dorigo y Gambardella (1997) y se denominan ACS-HCSP y IACS-HCSP. Todas las técnicas son evaluadas experimentalmente de un modo exhaustivo, con un total de 96 configuraciones distintas adaptadas a diferentes entornos. En primer lugar, se comparan las técnicas propuestas entre sí a fin de determinar su rendimiento, tanto como en calidad como en tiempo de ejecución, realizándose los pertinentes análisis de significación estadística. Una vez determinada las técnicas que tienen un mejor rendimiento se pasa a comparar de modo exhaustivo las técnicas ACS-HCSP y IACS-HCSP a fin de determinar si las modificaciones propuestas para la técnica IACS-HCSP producen mejoras significativas, obteniéndose un resultado positivo. Finalmente y con el objetivo de comparar las técnicas propuestas con técnicas existentes en el estado del arte, las técnicas propuestas son comparadas con las heurísticas propuestas por Quintana et al. (2017) y con la solución actual de la compañía, obteniendo la técnica IACS-HCSP mejores resultados y permitiendo un ahorro económico estimado de 3.7 millones de euros anuales.This research addresses the resolution of the family of problems called Home Care Scheduling Problem (HCSP) problems. The importance of solving this family of problems has been increasing in recent years, an importance that has also been reflected in the academic world with a growing number of publications Fikar y Hirsch (2017); Cisse et al. (2017). This interest is motivated mainly by two factors, namely, the ageing of our population and the need to seek more efficient alternatives in the provision of home care services. The progressive ageing of our population is perhaps one of the most important challenges that we will face as a society, a challenge that has been identified both by European and international bodies World Health Organization (2015). In this demographic context, and with the growing demand for home-based care requests, home-based care service providers must look for more efficient and alternative ways to meet the growing demand, while preserving the quality of service and ensuring quality and sustainable home-based care services for our elderly. This research addresses a real and easily transferable problem to the industry, faced by the company EULEN. The company provides home care services in the Community of Madrid and must provide around 1.5 million services per year, which amounts 2.1 million working hours, not including the inefficiencies inherent in the provision of services, such as travel and waiting times incurred by caregivers. The problem is addressed on a weekly basis, with 13344 services to be scheduled to each week. These services in turn consist of tasks, which must be provided at a specific time and at a particular location. Of these services, 80 percent must be provided Monday through Friday in morning shift (07:00 to 14:30) so that about 10,700 services must be planned and assigned at the same time. The size of the problem addressed is one order of magnitude higher than those addressed in the state of the art, along with the impossibility of dividing the problem into smaller instances has required the design and implementation of specific techniques for its resolution. The problem is tackled from the perspective of clustering, consisting of resolving it by grouping services into groups of services or clusters, which will confom the timetable of each assistant. The main difficulty of tackling the problem from the perspective of clustering, in addition to its unusual size, are its restrictions and the concept of similarity or distance between clusters. This concept is defined to take into account the spatial and temporal components of the problem. Once defined, the problem is tackled with three novel techniques: the first is a hierarchical clustering method inspired by the Ward Ward (1963) method, while the other two approaches are based on the metaheuristics Ant Colony Optimization proposed by (Dorigo y Gambardella, 1997) and are called ACS-HCSP and IACS-HCSP. All techniques are evaluated experimentally in a comprehensive manner, with a total of 96 different configurations adapted to different environments. First, the proposed techniques are compared with each other in order to determine their performance, both in terms of quality and execution time, and the relevant analyses of statistical significance are carried out. Once the techniques with the best performance have been determined, a comprehensive comparison of the ACS-HCSP and IACS-HCSP techniques is made to determine whether the proposed modifications to the IACS-HCSP technique produce significant improvements, with a positive result. Finally, and with the aim of comparing the techniques proposed with existing state-of-the-art techniques, the proposed techniques are compared with the heuristic techniques proposed by Quintana et al. (2017) and with the company’s current solution, obtaining the IACS-HCSP technique with better results and allowing an estimated economic yearly saving of 3.7 million euros. Keywords: Clustering, metaherustics, combinatorial optimization problems, ant colony optimization, home care scheduling problems.Programa Oficial de Doctorado en Ciencia y Tecnología InformáticaPresidente: Inés María Galván León.- Secretario: Francisco Luna Valero.- Vocal: Diego Pérez Liéban

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282