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In this paper, we propose a novel research scheme to solve the single vehicle pickup and delivery problem (PDPTW) with time window constraints. The family competition genetic algorithm (FCGA) is a modern approach that has been successfully applied to solve the traveling salesman problem. We illustrate the FCGA and give the experimental results that show the FCGA is an effective algorithm for solving the single vehicle PDPTW. Genetic algorithms (GA) have been successful applied to solve the combinatorial computation problems. The family competition will improve the achievements for obtaining optimal solutions and the probability to hit the feasible solutions. By comparing FCGA with traditional GA, this excellent approach does not need enormous resources. Applying FCGA to single vehicle PDPTW, it succeeded in finding feasible solutions for all problems and obtained efficient results in our experimentation.