In this paper, optimal design of a pumping scheme for achieving the best gain and phase response in quntum--dot semiconductor optical ampliers is investigated. For the rst time, the dynamic response of the quntum-dot semiconductor optical amplier is evaluated under three dierent pumping schemes, known as optical pumping, electrical pumping, and electro-optical pumping. Simulation results show that the shortest gain recovery time in quntum-dot semiconductor optical ampliers can be achieved under the electrical pumping scheme. However, under the optical pumping and electro-optical pumping schemes, the quntum-dot semiconductor optical amplier represents a shorter phase recovery compared to the electrical pumping scheme. We found that a sub-nanosecond phase recovery in the quntum-dot semiconductor optical amplier can be achieved under the OP and electro--optical pumping schemes, which can never be achieved under the electrical pumping, because of the slow carrier dynamics of the carrier reservoir. Also, it was found that the gain recovery process in an optically pumped quntum-dot semiconductor optical amplier can be signicantly accelerated at cryogenic temperatures. This result demonstrates the superiorities of the optical pumping scheme over the electrical pumping and electro-optical pumping schemes at low temperatures, where both the gain and phase recovery times of an optically pumped quantum-dot semiconductor optical amplier are drastically decreased.