The Multiple Trip Vehicle Routing Problem with Backhauls: Formulation and a Two-Level Variable Neighbourhood Search

Abstract

Ιν τηισ παπερ α νεω ςΡΠ ϖαριαντ τηε Μυλτιπλε Τριπ ςεηιχλε Ρουτινγ Προβλεm ωιτη Βαχκηαυλσ (ΜΤ−ςΡΠΒ) ισ ινϖεστιγατεδ. Τηε χλασσιχαλ ΜΤ−ςΡΠ mοδελ ισ εξτενδεδ βψ ινχλυδινγ τηε βαχκηαυλινγ ασπεχτ. Αν ΙΛΠ φορmυλατιον οφ τηε ΜΤ−ςΡΠΒ ισ φιρστ πρεσεντεδ ανδ ΧΠΛΕΞ ρεσυλτσ φορ σmαλλ ανδ mεδιυm σιζε ινστανχεσ αρε ρεπορτεδ. Φορ λαργε ινστανχεσ οφ τηε ΜΤ−ςΡΠΒ α Τωο−Λεϖελ ςΝΣ αλγοριτηm ισ δεϖελοπεδ. Το γαιν α χοντινυουσ βαλανχεδ ιντενσιφιχατιον ανδ διϖερσιφιχατιον δυρινγ τηε σεαρχη προχεσσ ςΝΣ ισ εmβεδδεδ ωιτη τηε σεθυεντιαλ ςΝD ανδ α mυλτι−λαψερ λοχαλ σεαρχη αππροαχη. Τηε αλγοριτηm ισ τεστεδ ον α σετ οφ νεω ΜΤ−ςΡΠΒ δατα ινστανχεσ ωηιχη ωε γενερατεδ. Ιντερεστινγ χοmπυτατιοναλ ρεσυλτσ αρε πρεσεντεδ. Τηε Τωο− Λεϖελ ςΝΣ προδυχεδ εξχελλεντ ρεσυλτσ ωηεν τεστεδ ον τηε σπεχιαλ ϖαριαντ οφ τηε ςΡΠΒ.

A biased‐randomized metaheuristic for the vehicle routing problem with clustered and mixed backhauls

“…Even better results have been also obtained for the TV instances, with an average gap of 0.00% in 15 s. At this point, it is worthy to remember that the best‐known solutions are provided by different algorithms in the literature, which means that our approach seems to be quite competitive when compared against each individual algorithm. To confirm this statement, we have directly compared the performance of our algorithm against the performance of the following state‐of‐the‐art metaheuristics: the tabu search (BTS) from Brandão , the large neighborhood search (LNS) from Ropke and Pisinger , the reactive‐adaptive memory programming search (RTS‐AMP) from Wassan , the multiant colony system from Gajpal and Abad , the route promise algorithm (RPA) from Zachariadis and Kiranoudis , the multiattribute general purpose algorithm (UHGS) from Vidal et al , the iterated local search (ILS‐1000) from Cuervo et al and the Two‐Level VNS algorithm from Wassan et al . For the GJB instances, Figure shows a multiple box‐plot graph comparing the gaps provided by each of the considered metaheuristics with respect to the BKS (as usual in these type of graphs, the central boxes represent the values between the first and third quartiles of the data distribution, while outliers are marked with a star symbol).…”

“…One of the main characteristic of their approach is the statistical analysis of the algorithm components, which allows them to obtain very competitive results in terms of solution quality and computing times. Wassan et al introduced a new variant called Multiple Trip Vehicle Routing Problem with Backhauls and solve large instances using a two‐level Variable Neighborhood Search algorithm. From a practical point of view, the VRPB is also considered into the field of reverse logistics and green logistics.…”

Hybrid Genetic Algorithms and Simulated Annealing for Multi-trip Vehicle Routing Problem with Time Windows

“…Vehicles that have finished visiting the customer node must return to the initial depot within the predefined time windows depot [17]. Multi-Trip Vehicle Routing Problem (MT-VRP) is one of the development of classic VRP problems in which a vehicle travels on multiple routes within a certain time frame [18]. The MT-VRP is a special vehicle route issue where each vehicle can serve more than one trip where each trip starts from the depot, passes several customers and ends up in the depot and the total customer demand should not exceed capacity [19].…”

Variable neighborhood search based approaches to a vehicle scheduling problem in agriculture

“…The multiple trip VRP with backhauls is considered by Wassan et al. (). The authors proposed an integer linear programming formulation of the problem and developed a two‐level solution method in which VNS was embedded with the sequential VND and a multilayer local search approach.…”