This paper addresses a method for optimizing contact positioning configuration for cooperative pushing-force multi-robot system (CPF-MRS) with object manipulation and transportation tasks. It is challenging to search for optimal contact positionings of only pushing mobile robots around an any-shape object boundary for maximum wrenches when they cooperatively manipulate and transport such an object along a predefined path under frictional constraints. In this study, a Particle Swarm Optimization (PSO) framework is proposed to determine the optimal contact positioning surrounding the object boundary. Combining criteria derived from the grasp and Gram matrix analysis, a comprehensive cost function for PSO is generated to optimize cooperative pushing force-generated wrenches guiding the multi-robot system toward stable and controllable configurations. Based on optimized contact positioning configuration, a simple PID-based controller is employed to regulate desired wrenches of CPF-MRS for path tracking during the object manipulation and transportation. The simulation results demonstrate that the strategy has successfully optimized contact point configuration enabling the controlability and stability of CPF-MRS when performing object manipulation and transportation.