In this paper, we study novel variants of the well‐known two‐echelon vehicle routing problem in which a truck works on the first echelon to transport parcels and a fleet of drones to intermediate depots while in the second echelon, the drones are used to deliver parcels from intermediate depots to customers. The objective is to minimize the completion time instead of the transportation cost as in classical two‐echelon vehicle routing problems. Depending on the context, a drone can be launched from the truck at an intermediate depot once (single‐trip drone) or several times (multiple‐trip drone). Mixed‐integer linear programming models are first proposed to formulate mathematically the problems and solve to optimality small‐sized instances. To handle larger instances, a metaheuristic based on the idea of greedy randomized adaptive search procedure is introduced. The main novel feature of our metaheuristic lies in the design of initial solution construction and local search operators, which can cover all the decision layers of the problems and run in scriptOfalse(1false)$\mathcal{O}(1)$ using additional data structures. Experimental results obtained on instances of different contexts are reported and analyzed.
This paper deals with the Traveling Salesman Problem with Multi-Visit Drone (TSP-MVD) in which a truck works in collaboration with a drone that can serve up to q > 1 customers consecutively during each sortie. We propose a Mixed Integer Linear Programming (MILP) formulation and a metaheuristic based on Iterated Local Search to solve the problem. Benchmark instances collected from the literature of the special case with q = 1 are used to test the performance of our algorithms. The obtained results show that our MILP model can solve a number of instances to optimality. This is the first time optimal solutions for these instances are reported. Our ILS performs better other algorithms in terms of both solution quality and running time on several class of instances. The numerical results obtained by testing the methods on new randomly generated instances show again the effectiveness of the methods as well as the positive impact of using the multi-visit drone.
The Vehicle Routing Problem with Roaming Delivery Locations (VRPRDL) is a variant of the Vehicle Routing Problem (VRP) in which a customer can be present at many locations during a working day and a time window is associated with each location. The objective is to find a set of routes such that (i) the total traveling cost is minimized, (ii) only one location of each customer is visited within its time window, and (iii) all capacity constraints are satisfied. To solve the problem, we introduce a hybrid genetic algorithm which relies on problem-tailored solution representation, mutation, local search operators, as well as a set covering component exploring routes found during the search to find better solutions. We also propose a new split procedure which based on dynamic programming to evaluate the fitness of chromosomes. Experiments conducted on the benchmark instances clearly show that our proposed algorithm outperforms existing approaches in terms of stability and solution quality. We also improve 49 best known solutions of the literature.
In this paper, we study novel variants of the well-known twoechelon vehicle routing problem in which a truck works on the first echelon to transport parcels and a fleet of drones to intermediate depots while in the second echelon, the drones are used to deliver parcels from intermediate depots to customers. The objective is to minimize the completion time instead of the transportation cost as in classical 2-echelon vehicle routing problems. Depending on the context, a drone can be launched from the truck at an intermediate depot once (single trip drone) or several times (multiple trip drone). Mixed Integer Linear Programming (MILP) models are first proposed to formulate mathematically the problems and solve to optimality small-size instances. To handle larger instances, a metaheuristic based on the idea of Greedy Randomized Adaptive Search Procedure (GRASP) is introduced. Experimental results obtained on instances of different contexts are reported and analyzed.
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