This study presents a novel artificial immune system for solving a multiobjective scheduling problem on parallel machines (MOSP), which has the following characteristics: (1) parallel machines are nonidentical, (2) the type of jobs processed on each machine can be restricted, and (3) the multiobjective scheduling problem includes minimizing the maximum completion time among all the machines (makespan) and minimizing the total earliness/tardiness penalty of all the jobs. In this proposed algorithm, the cells are represented by a vector group, and a local search algorithm is incorporated to facilitate the exploitation of the search space. Specially, a new diversity technique is proposed to preserve the diversity of the population and enhance the exploration of the solution space. Simulation results show the proposed algorithm outperforms the vector immune genetic algorithm (VIGA).