In this article, we consider the problem of reshaping a deformable linear object (DLO) like wires, cables, ropes, and surgical sutures. The solution to this problem would be useful for many fields, especially industrial manufacturing, where the DLO manipulation is still frequently carried out by human workers. In this work, a new model-based manipulation technique for reshaping a DLO is addressed employing a sequence of grasping and releasing primitives performed by a single-armed robot equipped with a gripper. A decision process selects the optimal grasping point exploiting an error minimization approach and chooses the related releasing point. This decision process performs a spline interpolation between the error values obtained from candidate grasping points and chooses the optimal point that owns a minimum error. The multivariate dynamic spline model of the DLO is exploited for selecting the optimal grasping point and predicting the DLO behavior during the manipulation process. Because of its advantages over other integration methods, the symplectic integrator is utilized for iteratively solving the DLO dynamic model. Simulation results of reshaping a DLO lying on a table are presented to evaluate the proposed technique. These results illustrate the intermediate deformation steps which lead the DLO from its starting state to the desired one. They demonstrate that our proposed technique can efficiently manipulate the DLO into various shapes in few steps.