7. VRP with Time Windows

Cordeau, Jean‐François; Desaulniers, Guy; Desrosiers, Jacques; Solomon, Marius M.; Soumis, François

doi:10.1137/1.9780898718515.ch7

Cited by 221 publications

(128 citation statements)

References 67 publications

(135 reference statements)

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“…Cordeau et al [5] review a number of different approaches, and the recent surveys by Bräysy and Gendreau [6,7] provide a complete list of studies utilizing a number of heuristics and a comparison of the results obtained. Although numerous metaheuristic methods have been proposed, this paper concentrates on those using evolutionary computation methods, since they have a natural approach for dealing with multi-objective problems, and have been successful in many practical situations [8].…”

Section: Introductionmentioning

confidence: 99%

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

García-Nájera

Bullinaria

2011

Computers & Operations Research

154

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The Vehicle Routing Problem with Time Windows is a complex combinatorial problem with many real-world applications in transportation and distribution logistics. Its main objective is to find the lowest distance set of routes to deliver goods, using a fleet of identical vehicles with restricted capacity, to customers with service time windows. However, there are other objectives, and having a range of solutions representing the trade-offs between objectives is crucial for many applications. Although previous research has used evolutionary methods for solving this problem, it has rarely concentrated on the optimization of more than one objective, and hardly ever explicitly considered the diversity of solutions. This paper proposes and analyzes a novel multi-objective evolutionary algorithm, which incorporates methods for measuring the similarity of solutions, to solve the multi-objective problem. The algorithm is applied to a standard benchmark problem set, showing that when the similarity measure is used appropriately, the diversity and quality of solutions is higher than when it is not used, and the algorithm achieves highly competitive results compared with previously published studies and those from a popular evolutionary multi-objective optimizer.

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Section: Introductionmentioning

confidence: 99%

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

García-Nájera

Bullinaria

2011

Computers & Operations Research

154

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“…For the case when P = P, (45) is equivalent to the original problem (BLP), but when P P the value of the optimal solution to (45) is only an upper bound on that of the optimal solution to the original problem. The set conv{x p | p ∈ P} contains an optimal solution to (BLPConv), but the set {x p | p ∈ P}, which is used in (45), does not necessarily contain an optimal solution to (BLP) [42].…”

Section: B2 Binary Programmentioning

confidence: 99%

“…This could be adapted to hVRP, but a di erent ow formulation than (12) would then have to be used. In [45] the authors state that being aware of the connection between the ow formulation and the set partitioning formulation is important to help construct e cient branching and cutting strategies compatible with the column generation approach in order to obtain integer solutions [45, p. 169]. …”

Section: B2 Binary Programmentioning

confidence: 99%

Modeling and Solving Vehicle Routing Problems with Many Available Vehicle Types

Barman

Lindroth

Strömberg

2015

Springer Proceedings in Mathematics &Amp; Statistics

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In this thesis, models have been formulated and mathematical optimization methods developed for the heterogeneous vehicle routing problem with a very large set of available vehicle types, called many-hVRP. This is an extension of the standard heterogeneous vehicle routing problem (hVRP), in which typically fairly small sets of vehicle types are considered.Two mathematical models based on standard models for the hVRP have been formulated for the many-hVRP. Column generation and dynamic programming have been applied to both these models, following a successful algorithm for the hVRP. Benders' decomposition algorithm has also been applied to one of the models. In addition to the standard cost structure, where the cost of a pair of a vehicle and a route is determined by the length of the route and the vehicle type, we have studied costs that depend also on the load of the vehicle along the route. These load dependent costs were easily incorporated into the models, and other extensions could be similarly incorporated.By using a standard set of test instances (with between three and six vehicle types in each instance) we have been able to compare our implementation with published results for hVRP. For many-hVRP, we have extended these instances to include larger sets of vehicle types (with between 91 and 381 vehicle types in each instance). The results show that the algorithms implemented for the two models nd optimal solutions in a similar amount of time, but Benders' algorithm at times takes much longer to verify optimality. However, some other properties of Benders' algorithm suggests that it may constitute a good basis for a heuristic, when instances with even larger sets of vehicle types are used.

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“…O subproblema k ∈ V será o seguinte problema de caminho mínimo com restrições de tempo e capacidade (Cordeau et al (2000)):…”

Section: Problema De Roteamento De Veículos Com Janelas De Tempounclassified

“…Tais ferramentas permitem que problemas inerentemente complexos também possam ser resolvidos em tempo computacional aceitável, através da utilização de técnicas combinadas como, por exemplo, o Método de Geração de Colunas aplicado a problemas de Programação Inteira. Baseado no trabalho de Dantzig & Wolfe (1960), a primeira aplicação prática desta técnica foi na determinação de padrões de corte unidimensionais (Gilmore & Gomory (1961), (1963)) e, desde então, seu uso difundiu-se de forma intensa (Cook & Rich (1999), Cordeau et al (2000), Day & Ryan (1977), Desrochers & Soumis (1989), Desrochers et al (1992), Lorena & Senne (2002), Neame (1999), Savelsbergh (1997), , Valério de Carvalho (1996), Vance (1993) e Vance et al (1994)). …”

Section: Introductionunclassified

A relaxação Lagrangeana/surrogate e o método de geração de colunas: novos limitantes e novas colunas

2003

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* Corresponding author / autor para quem as correspondências devem ser encaminhadas Recebido em 02/2002, aceito em 11/2002 após 1 revisão ResumoOs métodos de geração de colunas e o de decomposição de Dantzig-Wolfe ficaram conhecidos como métodos eficientes para o tratamento de problemas de programação linear com grande número de variáveis. Um problema mestre restrito é identificado e novas colunas são geradas através de um subproblema. Também é bem conhecido que estes métodos sofrem de problemas de estabilização. Para amenizar estes problemas, as variáveis duais tem sido controladas de várias maneiras, em geral, restringindo sua norma para evitar grandes variações. A relaxação Lagrangeana/surrogate foi proposta recentemente para estabilização de métodos subgradientes. Considera-se neste trabalho a combinação do método de geração de colunas e a relaxação Lagrangeana/surrogate como uma proposta de estabilização. Alguns resultados computacionais são apresentados para problemas de p-medianas e várias aplicações são sugeridas. Algumas questões em aberto são levantadas para futura pesquisa.Palavras-chave: métodos de estabilização, relaxação Lagrangeana/surrogate, geração de colunas. AbstractColumn generation and Dantzig-Wolfe decomposition are very successful methods for large-scale linear programming problems. It is also well known the instability of the overall process. Stabilizing methods work constraining the norm of the dual vector arising from restricted masters. This work shows how to combine the Lagrangean/surrogate relaxation and column generation aiming a stabilized method.

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7. VRP with Time Windows

Cited by 221 publications

References 67 publications

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

Modeling and Solving Vehicle Routing Problems with Many Available Vehicle Types

A relaxação Lagrangeana/surrogate e o método de geração de colunas: novos limitantes e novas colunas

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