This paper studies the multi-objective hybrid flowshop scheduling problem with minimization of makespan, total tardiness and number of tardy jobs. Two meta-heuristics are analyzed: Ant Colony Optimization (ACO) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The former has been shown in the literature to be a very efficient and effective meta-heuristic to solve mono-objective HFS problem, while the latter has shown a flexible structure and a successful application to a wide range of multi-objective combinatorial optimization problems. The problem is modeled using a disjunctive graph and the basic tenets of such procedures are considered in the first instance. Experiments are carried out on standard datasets from the literature available at the ORLibrary. Prelimnary results shows the efficiency and effectiveness of both approaches, while further analysis is however required. This includes the evaluation of distance measures between two fronts, the coverage of the solutions of both meta-heuristics, the deviation with respect to a single objective, the deviation with respect to the best initial solution, and the computational time.