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The PDPTW is an optimization vehicles routing problem which must meet requests for transport between suppliers and customers satisfying precedence, capacity and time constraints. We present, in this paper, a genetic algorithm for optimization of a multi pickup and delivery problem with time windows (m-PDPTW). We purposes a brief literature review of the PDPTW, present an approach based on genetic algorithms to give a satisfying solution to the m-PDPTW minimizing the total travel cost.