In cellular communication systems with frequency reuse factor of one, user terminals (UT) at the cell-edge are prone to intercell interference. Joint processing is one of the coordinated multipoint transmission techniques proposed to mitigate this interference. In the case of centralized joint processing, the channel state information fed back by the users need to be available at the central coordination node for precoding. The precoding weights (with the user data) need to be available at the corresponding base stations to serve the UTs. These increase the backhaul traffic. In this article, partial joint processing (PJP) is considered as a general framework that allows reducing the amount of required feedback. However, it is difficult to achieve a corresponding reduction on the backhaul related to the precoding weights, when a linear zero forcing beamforming technique is used. In this work, particle swarm optimization is proposed as a tool to design the precoding weights under feedback and backhaul constraints related to PJP. The precoder obtained with the objective of weighted interference minimization allows some multiuser interference in the system, and it is shown to improve the sum rate by 66% compared to a conventional zero forcing approach, for those users experiencing low signal to interference plus noise ratio.