The vehicle routing problem
D-Ants: savings based ants divide and conquer the vehicle routing problem
Computers and Operations Research
A general heuristic for vehicle routing problems
Computers and Operations Research
Active-guided evolution strategies for large-scale capacitated vehicle routing problems
Computers and Operations Research
Computers and Industrial Engineering
Scatter Search and Path Relinking
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Computers and Operations Research
A hybrid genetic - Particle Swarm Optimization Algorithm for the vehicle routing problem
Expert Systems with Applications: An International Journal
A hybrid particle swarm optimization algorithm for the vehicle routing problem
Engineering Applications of Artificial Intelligence
The particle swarm - explosion, stability, and convergence in amultidimensional complex space
IEEE Transactions on Evolutionary Computation
A probability matrix based particle swarm optimization for the capacitated vehicle routing problem
Journal of Intelligent Manufacturing
A hybrid particle swarm optimization algorithm for the open vehicle routing problem
ANTS'12 Proceedings of the 8th international conference on Swarm Intelligence
Computers and Industrial Engineering
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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One of the main problems in the application of a Particle Swarm Optimization in combinatorial optimization problems, especially in routing type problems like the Traveling Salesman Problem, the Vehicle Routing Problem, etc., is the fact that the basic equation of the Particle Swarm Optimization algorithm is suitable for continuous optimization problems and the transformation of this equation in the discrete space may cause loose of information and may simultaneously need a large number of iterations and the addition of a powerful local search algorithm in order to find an optimum solution. In this paper, we propose a different way to calculate the position of each particle which will not lead to any loose of information and will speed up the whole procedure. This was achieved by replacing the equation of positions with a novel procedure that includes a Path Relinking Strategy and a different correspondence of the velocities with the path that will follow each particle. The algorithm is used for the solution of the Capacitated Vehicle Routing Problem and is tested in the two classic set of benchmark instances from the literature with very good results.