This paper presents an adaptive genetic algorithm (GA) to solve the Vehicle Routing Problem with Time Windows (VRPTW) to near optimal solutions. The algorithm employs a unique decoding scheme with the integer strings. It also automatically adapts the crossover probability and the mutation rate to the changing population dynamics. The adaptive control maintains population diversity at user-defined levels, and therefore prevents premature convergence in search. Comparison between this algorithm and a normal fixed parameter GA clearly demonstrates the advantage of population diversity control. Our experiments with the 56 Solomon benchmark problems indicate that this algorithm is competitive and it paves way for future research on population-based adaptive genetic algorithm.