Waterflooding is currently the most commonly used method to improve oil recovery after primary depletion. The reservoir heterogeneity such as permeability distribution could negatively affect the performance of waterflooding. The presence of high permeability streaks could lead to an early water breakthrough at the producers and thus reduce the sweep efficiency in the field. One approach to counteract the impact of heterogeneity and to improve waterflood sweep efficiency is through optimal rate allocation to the injectors and producers. Through optimal rate control, we can manage the propagation of the flood front, delay water breakthrough at the producers and also increase the sweep and hence, the recovery efficiency. The arrival time optimization method uses a streamline-based method to calculate water arrival time sensitivities with respect to production and injection rates. It can also optimize sweep efficiency on multiple realizations to account for geological uncertainty. To extend the scope of this optimization method for more general conditions, this work utilized a finite difference simulator and streamline tracing software to conduct the optimization. Apart from sweep efficiency, another most widely used optimization method is to maximize the net present value (NPV) within a given time period. Previous efforts on optimization of waterflooding used optimal control theorem to allocate injection/production rates for fixed well configurations. The streamline-based approach gives the optimization result in a much more computationally efficient manner. In the present study, we compare the arrival time optimization and NPV optimization results to show their strengths and limitations. The NPV optimization uses a perturbation method to calculate the gradients. The comparison is conducted on a 4- spot synthetic case. Then we introduce the accelerated arrival time optimization which has an acceleration term in the objective function to speed up the oil production in the field. The proposed new approach has the advantage of considering both the sweep efficiency and net present value in the field.