Robots generally have a structure that combines rotational joints and links in a serial fashion. On the other hand, various joint mechanisms are being utilized in practice, such as prismatic joints, closed links, and wire-driven systems. Previous research have focused on individual mechanisms, proposing methods to design robots capable of achieving given tasks by optimizing the length of links and the arrangement of the joints. In this study, we propose a method for the design optimization of robots that combine different types of joints, specifically rotational and prismatic joints. The objective is to automatically generate a robot that minimizes the number of joints and link lengths while accomplishing a desired task, by utilizing a black-box multi-objective optimization approach. This enables the simultaneous observation of a diverse range of body designs through the obtained Pareto solutions. Our findings confirm the emergence of practical and known combinations of rotational and prismatic joints, as well as the discovery of novel joint combinations.