Neural network methods in combinatorial optimization
Computers and Operations Research - Special issue on neural networks and operations research
An additive bounding procedure for the asymmetric travelling salesman problem
Mathematical Programming: Series A and B
New insertion and postoptimization procedures for the traveling salesman problem
Operations Research
The traveling salesman problem with backhauls
Computers and Operations Research
Heuristic approaches to vehicle routing with backhauls and time windows
Computers and Operations Research
Self-organizing maps
Computers and Operations Research
A heuristic for the pickup and delivery traveling salesman problem
Computers and Operations Research
A neural network algorithm for the traveling salesman problem with backhauls
Computers and Industrial Engineering - Special issue: Focussed issue on applied meta-heuristics
Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research
INFORMS Journal on Computing
Performance of Various Computers Using Standard Linear Equations Software
Performance of Various Computers Using Standard Linear Equations Software
A novel two-phase heuristic method for vehicle routing problem with backhauls
Computers & Mathematics with Applications
Recognition of Western style musical genres using machine learning techniques
Expert Systems with Applications: An International Journal
Expert Systems with Applications: An International Journal
Clustering the ecological footprint of nations using Kohonen's self-organizing maps
Expert Systems with Applications: An International Journal
A psycho-cognitive segmentation of organ donors in Egypt using Kohonen's self-organizing maps
Expert Systems with Applications: An International Journal
A neuro-computational intelligence analysis of the global consumer software piracy rates
Expert Systems with Applications: An International Journal
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In the Vehicle Routing Problem with Backhauls (VRPB), a central depot, a fleet of homogeneous vehicles, and a set of customers are given. The set of customers is divided into two subsets. The first (second) set of linehauls (backhauls) consists of customers with known quantity of goods to be delivered from (collected to) the depot. The VRPB objective is to design a set of minimum cost routes; originating and terminating at the central depot to service the set of customers. In this paper, we develop a self-organizing feature maps algorithm, which uses unsupervised competitive neural network concepts. The definition of the architecture of the neural network and its learning rule are the main contribution. The architecture consists of two types of chains: linehaul and backhaul chains. Linehaul chains interact exclusively with linehaul customers. Similarly, backhaul chains interact exclusively with backhaul customers. Additonal types of interactions are introduced in order to form feasible VRPB solution when the algorithm converges. The generated routes are then improved using the well-known 2-opt procedure. The implemented algorithm is compared with other approaches in the literature. The computational results are reported for standard benchmark test problems. They show that the proposed approach is competitive with the most efficient metaheuristics.