A Branch-and-price Algorithm for the Multi-Vehicle Covering Tour Problem

doi:10.1016/j.endm.2013.10.010

Electronic Notes in Discrete Mathematics

Volume 44, 5 November 2013, Pages 61-66

https://doi.org/10.1016/j.endm.2013.10.010 Get rights and content

Abstract

In this paper, we propose a Branch-and-price (BP) algorithm and a Column Generation Heuristic (CGH) for the Multi-Vehicle Covering Tour Problem (m-CTP). Specific dominance and extension pruning rules are introduced to accelerate the resolution of the pricing problems. To the best of our knowledge, this is the first work dedicated to the exact resolution of m-CTP. The algorithm managed to solve about 30% of the instances in our test bed, within a 4 hour CPU time limit. Our preliminary computational experiments suggest that both the lower bounds provided by the formulation behind BP and the CGH upper bounds are of good quality.

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Heuristics for the multi-vehicle covering tour problem
Computers & Operations Research
(2000)

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Exact methods for mono-objective and Bi-Objective Multi-Vehicle Covering Tour Problems
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Otherwise, constraints (3) are necessary unless a solution can visit a service point without serving it. Some papers in the literature keep such constraints (Ha et al., 2013; Hachicha et al., 2000; Lopes et al., 2013) whereas some others do not (Artigues et al., 2018; Jozefowiez, 2014). We keep the constraints as we do not wish to make hypothesis on the instances and design a generic algorithm.
The Multi-vehicle Covering Tour Problem and the Bi-Objective Multi-vehicle Covering Tour Problem have been studied for more than thirty years. Both problems have several practical applications in industry. In this paper, we propose an effective exact method for the Multi-vehicle Covering Tour Problem based on column generation techniques. The effectiveness of the exact method is owed to tailored dominance rules and completion bounds. To validate our approach, we conducted extensive computational experiments on instances from literature. The comparison with state-of-the-art methods shows the effectiveness of the proposed method. In particular, seven open instances are closed to optimality for the first time, and the best lower bounds of the six open instances are improved. The exact method for the Multi-vehicle Covering Tour Problem is also embedded in a ϵ-constraint exact method to solve its bi-objective counterpart. Computational results show that the lower bound set provided by this bi-objective exact method is stronger than those provided by the state-of-the-art method from the literature.
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The authors proposed a mathematical formulation and three heuristic algorithms for the introduced problem. Moreover, Lopes et al. (2013) developed a branch-and-price algorithm for this problem. Finally, branch-and-cut and metaheuristic algorithms were proposed by Bostel et al. (Hà et al., 2013).
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¹: Alexandre Salles da Cunha is partially funded by CNPq grants 305423/2012-6, 477863/2010-8 and FAPEMIG grant PRONEX APQ-01201-09

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A Branch-and-price Algorithm for the Multi-Vehicle Covering Tour Problem

Abstract

Computers & Operations Research