In order to meet the needs of goods delivery and pick-up, a mixed integer programming model with simultaneous delivery and pick-up
requirement (VRPSDP) was presented for vehicle routing problem. An adaptive hybrid genetic algorithm was developed to solve VRPSDP,
a special optimal splitting procedure was used to get the fitness values and a local search was taken as the mutation operator. A novel
crossover and a population replacement scheme were designed. Measurement of population diversity and the adjustment rules of
mutation probability were also defined. Numerical computations indicated that it was an effective algorithm for solving VRPSDP and VRP.