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A combination of genetic algorithm and particle swarm optimization (PSO) for vehicle routing problems with time windows (VRPTW) is proposed in this paper. The improvements of the proposed algorithm include: using the particle real number encoding method to decode the route to alleviate the computation burden, applying a linear decreasing function based on the number of the iterations to provide balance between global and local exploration abilities, and integrating with the crossover operator of genetic algorithm to avoid the premature convergence and the local minimum. The experimental results show that the proposed algorithm is not only more efficient and competitive with other published results but can also obtain more optimal solutions for solving the VRPTW issue. One new well-known solution for this benchmark problem is also outlined in the following.

A Combination of Genetic Algorithm and Particle Swarm Optimization for Vehicle Routing Problem with Time Windows