Future paths for integer programming and links to artificial intelligence
Computers and Operations Research - Special issue: Applications of integer programming
Future Generation Computer Systems
Classical heuristics for the capacitated VRP
The vehicle routing problem
Metaheuristics for the capacitated VRP
The vehicle routing problem
An Exact Method for the Vehicle Routing Problem with Backhauls
Transportation Science
Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research
INFORMS Journal on Computing
A Lower Bound for the Split Delivery Vehicle Routing Problem
Operations Research
Advances in evolutionary computing
Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem
Mathematical Programming: Series A and B
A general heuristic for vehicle routing problems
Computers and Operations Research
An efficient variable neighborhood search heuristic for very large scale vehicle routing problems
Computers and Operations Research
An Exact Algorithm for the Multiple Vehicle Pickup and Delivery Problem
Transportation Science
A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows
Transportation Science
A variable neighborhood search for the multi-depot vehicle routing problem with loading cost
Expert Systems with Applications: An International Journal
Combining metaheuristic algorithms to solve a scheduling problem
HAIS'12 Proceedings of the 7th international conference on Hybrid Artificial Intelligent Systems - Volume Part II
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The vehicle routing problem (VRP) is an important scientific problem addressed in distribution management. In classical VRP and its variants, the vehicle load is often regarded as a constant during transportation; therefore the loading cost associated with the amount of the load on the vehicle, are neglected in the objective function when optimizing a vehicle routine. However, in real-world, the vehicle load varies from one customer to another in a vehicle route. Thus, the vehicle route without considering the effect of loading cost may lead to sub-optimal routes. In this paper, we investigate VRP with loading cost (VRPLC), which considers the costs associated with the amount of the load on the vehicle when determining the vehicle routes. Considering the features of the VRPLC, a scatter search (SS) is proposed. By introducing customer-oriented three-dimensional encoding method, sweep algorithm and optimal splitting procedure are combined to obtain better trial solutions. The arc combination and improved nearest neighbor heuristic are adopted as a solution combination method and an improvement method to generate and improve new solutions, respectively. Computational experiments were carried out on benchmark problems of capacitated VRP with seven categories of distribution scenarios. The computational results show that the SS is competitive and superior to other algorithms on most instances, and that the VRPLC can more reasonably and exactly formulate the vehicle routing problem with more cost savings than general VRP models.