The paper considers the production scheduling problem in a hybrid flow shop environment with sequence-dependent setup times and the objectives of minimizing both the makespan and the total tardiness. The multi-objective genetic algorithm is applied to solve this problem, which belongs to the non-deterministic polynomial-time (NP)-hard class. In the structure of the proposed algorithm, the initial population, neighborhood search structures and dispatching rules are studied to achieve more efficient solutions. The performance of the proposed algorithm compared to the efficient algorithm available in literature (known as NSGA-II) is expressed in terms of the data envelopment analysis method. The computational results confirm that the set of efficient solutions of the proposed algorithm is more efficient than the other algorithm.