The Capacitated Vehicle Routing Problem (CVRP) is a NP – Complete problem and according to this definition there is no exact solution for it. So researchers try to achieve a near optimum solution for it, by using meta – heuristic algorithms. The aim of CVRP is to find optimum route for every vehicle as a sequence of customers, that vehicle served. We employ Particle Swarm Optimization to solve ...

In this paper, we develop an extended guided tabu search (EGTS) and a new heuristic packing algorithm for the two-dimensional loading vehicle routing problem (2L-CVRP). The 2L-CVRP is a combination of two well-known NP-hard problems, the capacitated vehicle routing problem, and the two-dimensional bin packing problem. It is very difficult to get a good performance solution in practice for these...

The Vehicle Routing Problem (VRP) is a hard combinatorial problem with numerous industrial applications. Among the large number of extensions to the canonical VRP, we study the Capacitated VRP (CVRP), which is mainly characterized by using vehicles of the same capacity. A cellular Genetic Algorithm (cGA)—a kind of decentralized population based heuristic—is used for solving CVRP, improving seve...

This paper provides a review of the recent developments that had a major impact on the current state-ofthe-art exact algorithms for the vehicle routing problem (VRP). The paper reviews mathematical formulations, relaxations and recent exact methods for two of the most important variants of the VRP: the capacitated VRP (CVRP) and the VRP with time windows (VRPTW). The paper also reports a compar...

In the paper we examine a modification of the classical Vehicle Routing Problem (VRP) in which three-dimensional shapes of transported cargo are accounted for. This approach, in contrast to the standard capacitated VRP (CVRP) formulation, is appropriate when transported commodities are not perfectly divisible, but have fixed and heterogeneous dimensions. However, nesting a version of a threedim...

This paper presents a discussion arisen after reading ”A hybrid genetic algorithm that optimizes capacitated vehicle routing problem”, by Chung-Ho Wang and Jiu-Zhang Lu, (2009). Expert System with Applications (35)(pp. 2921-2936). The discussed paper presents a hybrid genetic algorithm applied to the Capacitated Vehicle Routing Problem (CVRP). When the authors present the results obtained by th...

Capacitated Vehicle Routing Problem (CVRP) is a type of NP-Hard combinatorial problem that requires high computational process. In the case CVRP, there an additional constraint in form capacity limit owned by vehicle, so complexity from CVRP to find optimum route pattern for minimizing travel costs which are also adjusted customer demand and vehicle distribution. One method solving can be done ...

This work presents a multistart algorithm for solving the capacitated vehicle routing problem with 2D loading constraints (2L-CVRP) allowing rotation of goods. Research dedicated to graph theory and symmetry considered as classical application. has complex aspects that stimulate use advanced algorithms in graphs. The modeling 2L-CVRP by undirected allowed high performance algorithm. developed i...

The purpose of this work is to present a developed three-axes rotation algorithm improve the solving methodology for relaxed 3L-CVRP (Three-Dimensional Capacitated Vehicle Routing Problem). Although there are reported works on approaches that consider product optimize load capacity, three axes has not been thoroughly studied. In aspect, explicitly explores and its impact capacity optimization. ...

Multi-echelon distribution systems are quite common in supply-chain and logistic management. They are used by public administrations in their transportation and traffic planning strategies as well as by companies to model their distribution systems. In the literature, most studies address issues related to the movement of flows throughout the system from the origins to their final destinations....