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 multi-objective optimization of a dynamic multi pickup and delivery problem with time windows (Dynamic m-PDPTW). We propose a brief literature review of the PDPTW, present our approach based on Pareto dominance method and lower bounds, to give a satisfying solution to the Dynamic m-PDPTW minimizing the compromise between total travel cost and total tardiness time. Computational results indicate that the proposed algorithm gives good results with a total tardiness equal to zero with a tolerable cost.