Abstract
In this paper, we investigate the Multi-Depot Heterogeneous VRP with Backhauls. Though the problem is a generalisation of three existing routing problems, this is the first time this combined routing problem is investigated. A mathematical formulation is first presented followed by some tightening. A powerful and novel hybridisation of Variable Neighbourhood Search (VNS) with the Greedy Randomized Adaptive Memory Programming Search is proposed. As there are no problem instances available for bench-marking and evaluation purposes, we generated data sets by combining those from existing vehicle routing problems. The proposed meta-heuristic obtains a number of optimal solutions for small instances and yields about \(13\%\) gap from the lower bounds compared to nearly \(40\%\) and \(20\%\) average gap values for our CPLEX implementation and the VNS without hybridisation, respectively.
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Acknowledgements
The authors acknowledge the support of the Scientific and Technological Research Council of Turkey (TÜBİTAK), Grant Number 1001 - 213M438. The authors are also grateful to both referees whose invaluable comments have improved the content as well as the presentation of the paper.
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Kocatürk, F., Tütüncü, G.Y. & Salhi, S. The multi-depot heterogeneous VRP with backhauls: formulation and a hybrid VNS with GRAMPS meta-heuristic approach. Ann Oper Res 307, 277–302 (2021). https://doi.org/10.1007/s10479-021-04137-6
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DOI: https://doi.org/10.1007/s10479-021-04137-6