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A vehicle must serve a collection of transportation requests by taking loads from providers to customers satisfying precedence, capacity and time constraints in the 1-PDPTW (single-vehicle pickup and delivery problem with time windows). After beginning the circuit some requests appear and need to be satisfied in the dynamic case of this problem. In this paper, a brief scientific literature review is presented on the 1-PDPTW and an evolutionary approach is proposed to solve this problem. Our evolutionary approach uses an evolutionary algorithm, with special genetic operators to minimize computing time and Pareto dominance method to provide a set of satisfying and feasible solutions to the 1-PDPTW, minimizing the compromise between total travel distance, total waiting time and total tardiness time.