This paper presents a hybrid Particle Swarm Optimization (PSO) for solving Vehicle Routing Problem with Time Windows (VRPTW). Three versions of the algorithm were implemented. The first version is a traditional PSO. In this case, the initialization is random and the best insertion for each customer on the route is evaluated. The second version is a combination of Greedy Randomized Adaptive Search Procedure (GRASP) and Push-Forward Insertion Heuristic (PFIH) with PSO. The last version, in addition to the previous characteristics, features a mutation operator after updating speed and position of each particle. For computational experiments, the 56 Solomon's instances are used and the results obtained in each version are compared with the best known results from literature. A statistical analysis indicates that the third version has a better performance than the other versions.
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