Robots operating in everyday life environments are often required to switch between different tasks. While learning and evolution have been effectively applied to single task performance, multiple task performance still lacks methods that have been demonstrated to be both reliable and efficient. This paper introduces a new method for multiple task performance based on multiobjective evolutionary algorithms, where each task is considered as a separate objective function. In order to verify the effectiveness, the proposed method is applied to evolve neural controllers for the Cyber Rodent (CR) robot that has to switch properly between two distinctly different tasks: 1) protecting another moving robot by following it closely and 2) collecting objects scattered in the environment. Furthermore, the tasks and neural complexity are analyzed by including the neural structure as a separate objective function. The simulation and experimental results using the CR robot show that the multiobjective-based evolutionary method can be applied effectively for generating neural networks that enable the robot to perform multiple tasks simultaneously.