In this paper, a new variant of the Particle Swarm Optimization (PSO) algorithm is proposed for the solution of the Vehicle Routing Problem with Time Windows (VRPTW). Three different adaptive strategies are used in the proposed Multi-Adaptive Particle Swarm Optimization (MAPSO) algorithm. The first adaptive strategy concerns the use of a Greedy Randomized Adaptive Search Procedure (GRASP) that is applied when the initial solutions are produced and when a new solution is created during the iterations of the algorithm. The second adaptive strategy concerns the adaptiveness in the movement of the particles from one solution to another where a new adaptive strategy, the Adaptive Combinatorial Neighborhood Topology, is used. Finally, there is an adaptiveness in all parameters of the Particle Swarm Optimization algorithm. The algorithm starts with random values of the parameters and based on some conditions all parameters are adapted during the iterations. The algorithm was tested in the two classic sets of benchmark instances, the one that includes 56 instances with 100 nodes and the other that includes 300 instances with number of nodes varying between 200 and 1000. The algorithm was compared with other versions of PSO and with the best performing algorithms from the literature.