In this paper, we propose an algorithm to solve multiobjective optimization problems (either constrained or unconstrained) using the clonal selection principle. Our approach is compared with respect to another algorithm that is representative of the state-of-the-art in evolutionary multiobjective optimization. For our comparative study, two metrics are adopted and graphical comparisons with respect to the true Pareto front of each problem are also included. Results indicate that the proposed approach is very promising.