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Solving Min-Max Capacitated Vehicle Routing Problem by Local Search

Son Van Nguyen, Dung Quang Pham, Trung Quoc Bui, Hoang Thanh Nguyen

Abstract


Vehicle routing is a class of combinatorial optimization problems in transportation and logistics. Min-max capacitated vehicle routing is a problem of this class in which the length of the longest route must be minimized. This paper investigates local search approach for solving the min-max capacitated vehicle routing problem with different neighborhood structures. We also propose a combined function instead of the objective function itself for controlling the local search. Experimental results on different datasets show the efficiency of our proposed algorithms compared to previous techniques.

Keywords


vehicle routing; local search; min-max vehicle routing; combinatorial optimization

References


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keywords = "Multi-neighborhood",

keywords = "Cooperative search",

keywords = "Solution pool ",

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keywords = "Routing",

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keywords = "Metaheuristic ",

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}

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keywords = "Multi-depot",

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keywords = "Lower bound",

keywords = "Heuristic ",

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}

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author = {Luca Maria Gambardella and Éric Taillard and Giovanni Agazzi},

title = {MACS-VRPTW: A Multiple Colony System For Vehicle Routing Problems With Time Windows},

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year = {1999},

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publisher = {McGraw-Hill}

}

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title = "A branch-and-price algorithm for the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows ",

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year = "2010",

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url = "http://www.sciencedirect.com/science/article/pii/S0377221710001700",

author = "Gabriel Gutiérrez-Jarpa and Guy Desaulniers and Gilbert Laporte and Vladimir Marianov",

keywords = "Transportation",

keywords = "Vehicle routing",

keywords = "Deliveries and selective pickups",

keywords = "Time windows",

keywords = "Branch-and-price",

keywords = "Shortest paths with resources ",

abstract = "In the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows, the set of customers is the union of delivery customers and pickup customers. A fleet of identical capacitated vehicles based at the depot must perform all deliveries and profitable pickups while respecting time windows. The objective is to minimize routing costs, minus the revenue associated with the pickups. Five variants of the problem are considered according to the order imposed on deliveries and pickups. An exact branch-and-price algorithm is developed for the problem. Computational results are reported for instances containing up to 100 customers. "

}

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author = "Michel Gendreau and François Guertin and Jean-Yves Potvin and René Séguin",

keywords = "Vehicle dispatching",

keywords = "Real-time",

keywords = "Tabu search",

keywords = "Neighborhood",

keywords = "Ejection chains",

keywords = "Parallel computing ",

abstract = "This paper proposes neighborhood search heuristics to optimize the planned routes of vehicles in a context where new requests, with a pick-up and a delivery location, occur in real-time. Within this framework, new solutions are explored through a neighborhood structure based on ejection chains. Numerical results show the benefits of these procedures in a real-time context. The impact of a master–slave parallelization scheme, using an increasing number of processors, is also investigated. "

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},

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}

,

abstract = { The paper is concerned with the optimum routing of a fleet of gasoline delivery trucks between a bulk terminal and a large number of service stations supplied by the terminal. The shortest routes between any two points in the system are given and a demand for one or several products is specified for a number of stations within the distribution system. It is desired to find a way to assign stations to trucks in such a manner that station demands are satisfied and total mileage covered by the fleet is a minimum A procedure based on a linear programming formulation is given for obtaining a near optimal solution. The calculations may be readily performed by hand or by an automatic digital computing machine. No practical applications of the method have been made as yet. A number of trial problems have been calculated, however. }

}

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title = "The vehicle routing problem: A taxonomic review ",

journal = "Computers & Industrial Engineering ",

volume = "57",

number = "4",

pages = "1472 - 1483",

year = "2009",

note = "",

issn = "0360-8352",

doi = "http://dx.doi.org/10.1016/j.cie.2009.05.009",

url = "http://www.sciencedirect.com/science/article/pii/S0360835209001405",

author = "Burak Eksioglu and Arif Volkan Vural and Arnold Reisman",

keywords = "Routing",

keywords = "Vehicle routing",

keywords = "VRP",

keywords = "Taxonomy",

keywords = "Classification ",

abstract = "This paper presents a methodology for classifying the literature of the Vehicle Routing Problem (VRP). {VRP} as a field of study and practice is defined quite broadly. It is considered to encompass all of the managerial, physical, geographical, and informational considerations as well as the theoretic disciplines impacting this ever emerging-field. Over its lifespan the {VRP} literature has become quite disjointed and disparate. Keeping track of its development has become difficult because its subject matter transcends several academic disciplines and professions that range from algorithm design to traffic management. Consequently, this paper defines VRP’s domain in its entirety, accomplishes an all-encompassing taxonomy for the {VRP} literature, and delineates all of VRP’s facets in a parsimonious and discriminating manner. Sample articles chosen for their disparity are classified to illustrate the descriptive power and parsimony of the taxonomy. Moreover, all previously published {VRP} taxonomies are shown to be relatively myopic; that is, they are subsumed by what is herein presented. Because the {VRP} literature encompasses esoteric and highly theoretical articles at one extremum and descriptions of actual applications at the other, the article sampling includes the entire range of the {VRP} literature. "

}

@article{groer2010,

title = "A library of local search heuristics for the vehicle

routing problem",

journal = "Math. Prog. Comp.",

volume = "",

number = "2",

pages = "79 - 101",

year = "2010",

note = "",

issn = "",

doi = "",

url = "",

author = "C. Groer and B. Golden and E. Wasil",

keywords = "",

keywords = "",

keywords = "",

keywords = "",

keywords = "",

abstract = ""

}


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Journal of Computer Science and Cybernetics ISSN: 1813-9663

Published by Vietnam Academy of Science and Technology