The multi-depot heterogeneous VRP with backhauls: formulation and a hybrid VNS with GRAMPS meta-heuristic approach

In this paper, we investigate the Multi-Depot Heterogeneous VRP with Backhauls. Though problem is a generalisation of three existing routing problems, first time combined investigated. A mathematical formulation presented followed by some tightening. powerful and novel hybridisation Variable Neighbourhood Search (VNS) Greedy Randomized Adaptive Memory Programming proposed. As there are no instances available for bench-marking evaluation purposes, generated data sets combining those from vehicle problems. The proposed meta-heuristic obtains number optimal solutions small yields about $$13\%$$ gap lower bounds compared to nearly $$40\%$$ $$20\%$$ average values our CPLEX implementation VNS without hybridisation, respectively.