This paper investigates the multi-objective optimization design of planar cable-driven parallel robots by using the evolutionary optimization algorithm. Since in cable-driven parallel robots, the cables should remain in tension in all configurations, the extent of the controllable workspace is considered as one of the design indices. This objective function is of utmost importance to the design of cable-driven parallel robots, since it considers the unidirectional properties of the cables in the analysis. In addition, in order for the robot to have suitable dexterity and accuracy and to be able to manipulate any arbitrary task in all the required directions, various kinematic indices such as global condition number, translational and rotational kinematic sensitivity indices are used. Through analysis of the conflict of these objectives within the workspace of the robot, it is shown that use of multi-objective optimization is an effective method to reach to a suitable trade-off. Furthermore, by applying multi-objective optimization methods such as the non-sorting genetic algorithm and the adaptive weighted particle swarm optimization algorithm, the optimal pareto front for the design parameters for the cable robot is obtained such that to draw a compromise between the robot designs.