This paper proposes a new control framework for manipulating soft objects. A Deep Reinforcement Learning (DRL) approach is used to make the shape of a deformable object reach a set of desired points by controlling a robotic arm which manipulates it. Our framework is more easily generalizable than existing ones: it can work directly with different initial and desired final shapes without need for relearning. We achieve this by using learning parallelization, i.e., executing multiple agents in parallel on various environment instances. We focus our study on deformable linear objects. These objects are interesting in industrial and agricultural domains, yet their manipulation with robots, especially in 3D workspaces, remains challenging. We simulate the entire environment, i.e., the soft object and the robot, for the training and the testing using PyBullet and OpenAI Gym. We use a combination of state-of-the-art DRL techniques, the main ingredient being a training approach for the learning agent (i.e., the robot) based on Deep Deterministic Policy Gradient (DDPG). Our simulation results support the usefulness and enhanced generality of the proposed approach.