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Estatística
Título: STRONG LOWER BOUNDS FOR THE CVRP VIA COLUMN AND CUT
Autor: MARCELO MALTA RODRIGUES MARTINS
Colaborador(es): MARCUS VINICIUS SOLEDADE POGGI DE ARAGAO - Orientador
RAFAEL MARTINELLI PINTO - Coorientador
Catalogação: 11/JAN/2017 Língua(s): ENGLISH - UNITED STATES
Tipo: TEXT Subtipo: THESIS
Notas: [pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio.
[en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio.
Referência(s): [pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=28669&idi=1
[en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=28669&idi=2
DOI: https://doi.org/10.17771/PUCRio.acad.28669
Resumo:
The Capacitated Vehicle Routing Problem (CVRP) is the seminal version of the vehicle routing problem, a classical problem in Operational Research. Introduced by Dantzig e Ramser, the CVRP generalizes the Traveling Salesman Problem (TSP) and the Bin Packing Problem (BPP). In addition, routing problems arise in several real world applications, often in the context of reducing costs, polluent emissions or energy within transportation activities. In fact, the cost with transportation can be roughly estimated to represent 5 per cent to 20 per cent of the overall cost of a delivered product. This means that any saving in routing can be much relevant. The CVRP is stated as follows: given a set of n plus 1 locations - a depot and n customers - the distances between every pair of locations, integer demands associated with each customer, and a vehicle capacity, we are interested in determining the set of routes that start at the depot, visits each customer exactly once and returns to the depot. The total distance traveled by the routes should be minimized and the sum of the demands of customers on each route should not exceed the vehicle capacity. This work considers that the number of available vehicles is given. State of the art algorithms for finding and proving optimal solutions for the CVRP compute their lower bounds through column generation and improving it by adding cutting planes. The columns generated may be elementary routes, where customers are visited only once, or relaxations such as q-routes and the more recent ng-routes, which differ on how they allow repeating customers along the routes. Cuts may be classified as robust, those that are defined over arc variables, and non-robust (or strong), those that are defined over the column generation master problem variables. The term robust used above refers to how adding the cut modifies the efficiency of solving the pricing problem. Besides the description above, the most efficient exact algorithms for the CVRP use too many elements turning its replication a hard long task. The objective of this work is to determine how good can be lower bounds computed by a column generation algorithm on ng-routes using only capacity cuts and a family of strong cuts, the limited memory subset row cuts. We assess the leverage achieved with the consideration of this kind of strong cuts and its combination with others techniques like Decremental Space State Relaxation (DSSR), Completion Bounds, ng-Routes and Capacity Cuts over a Set Partitioning formulation of the problem. Extensive computational experiments are presented along with an analysis of the results obtained.
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