Abstract
This work presents a hybrid approach called GA-NN for solving the Capacitated Vehicle Routing Problem (CVRP) using Genetic Algorithms (GA) and Nearest Neighbor heuristic (NN). The first technique was applied to determine the groups of customers to be served by the vehicles while the second is responsible to build the route of each vehicle. In addition, the heuristics of Gillett & Miller (GM) and Downhill (DH) were used, respectively, to generate the initial population of GA and to refine the solutions provided by GA. In the results section, we firstly present experiments demonstrating the performance of the NN heuristic for solving the Shortest Path and Traveling Salesman problems. The results obtained in such experiments constitute the main motivation for proposing the GA-NN. The second experimental study shows that the proposed hybrid approach achieved good solutions for instances of CVRP widely known in the literature, with low computational cost. It also allowed us to evidence that the use of GM and DH helped the hybrid GA-NN to converge on promising points in the search space, with a small number of generations.
Highlights
The Vehicle Routing Problem (VRP) consists in defining the routes that a set of vehicles must follow to supply the demand of certain customers, respecting the operational restrictions imposed by the context in which the problem is inserted (Laporte, Gendreaub, Potvinb, & Semetc, 2000).In recent years, the VRP has attracted an increasing attention from researchers due to the great difficulty of its solution and its presence in various practical situations (Cordeau, Laporte, Potvin, & Savelsbergh, 2007)
This information was essential because we could make sure that the use of Nearest Neighbor heuristic (NN) coupled to Genetic Algorithms (GA) is a good alternative for solving Capacitated Vehicle Routing Problem (CVRP), since the all graphs from Christofides and TSPLIB instances have average clustering coefficients equal to 1
The first contribution of this study consists of the experiments with NN for solving Shortest Path Problem (SPP) and Traveling Salesman Problem (TSP), which demonstrates that NN heuristic can produce great solutions for CVRP in networks presenting high clustering coefficients
Summary
The Vehicle Routing Problem (VRP) consists in defining the routes that a set of vehicles must follow to supply the demand of certain customers, respecting the operational restrictions imposed by the context in which the problem is inserted (Laporte, Gendreaub, Potvinb, & Semetc, 2000).In recent years, the VRP has attracted an increasing attention from researchers due to the great difficulty of its solution and its presence in various practical situations (Cordeau, Laporte, Potvin, & Savelsbergh, 2007). The Vehicle Routing Problem (VRP) consists in defining the routes that a set of vehicles must follow to supply the demand of certain customers, respecting the operational restrictions imposed by the context in which the problem is inserted (Laporte, Gendreaub, Potvinb, & Semetc, 2000). The VRP has several variants, which take into account the capacity (each vehicle has a specific capacity), time windows (customers are taken care of in time), vehicle fleet heterogeneous (distinct vehicles), and multiple depots The Capacitated Vehicle Routing Problem (CVRP) is a variant of the VRP, and it consists, basically, in determining the routes to be followed by a fleet of homogeneous vehicles (in terms of capacity), to serve a given number of customers, without violating the capacities of the vehicles (Lee & Nazif, 2011)
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