A Tabu Search Algorithm for a Routing and Container Loading Problem
Transportation Science
A Tabu search heuristic for the vehicle routing problem with two-dimensional loading constraints
Networks - Special Issue In Memory of Stefano Pallottino
A dichromatic framework for balanced trees
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Ant colony optimization for the two-dimensional loading vehicle routing problem
Computers and Operations Research
An Exact Approach for the Vehicle Routing Problem with Two-Dimensional Loading Constraints
Transportation Science
Two memetic algorithms for heterogeneous fleet vehicle routing problems
Engineering Applications of Artificial Intelligence
A particular approach for the Three-dimensional Packing Problem with additional constraints
Computers and Operations Research
Computers and Operations Research
Computers and Operations Research
Computers and Operations Research
Engineering Applications of Artificial Intelligence
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This paper addresses an extension of the capacitated vehicle routing problem where the client demand consists of three-dimensional weighted items (3L-CVRP). The objective is to design a set of trips for a homogeneous fleet of vehicles based at a depot node which minimizes the total transportation cost. Items in each vehicle trip must satisfy the three-dimensional orthogonal packing constraints. This problem is strongly connected to real-life transportation systems where the packing of items to be delivered by each vehicle can have a significant impact on the routes. We propose a new way to solve the packing sub-problem. It consists of a two-step procedure in which the z-constraints are first relaxed to get a (x,y) positioning of the items. Then, a compatible z-coordinate is computed to get a packing solution. Items can be rotated but additional constraints such as item fragility, support and LIFO are not considered. This method is included in a GRASPxELS hybrid algorithm dedicated to the computation of VRP routes. The route optimization alternates between two search spaces: the space of VRP routes and the space of giant trips. The projection from one to the other is done by dedicated procedures (namely the Split and the concatenation algorithms). Moreover, a Local Search is defined on each search space. Furthermore, hash tables are used to store the result of the packing checks and thus save a substantial amount of CPU time. The effectiveness of our approach is illustrated by computational experiments on 3L-CVRP instances from the literature. A new set of realistic instances based on the 96 French districts are also proposed. They range from 19 nodes for the small instances to 255 nodes for the large instances and they can be stated as realistic since they are based on true travel distances in kilometers between French cities. The impact of the hash tables is illustrated as well.