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The paper describes a comparative study of multiple-objective metaheuristics on the bi-objective set covering problem. Ten representative methods based on genetic algorithms, multiple start local search, hybrid genetic algorithms and simulated annealing are evaluated in the computational experiment. Nine of the methods are well known from the literature. The paper introduces also a new hybrid genetic algorithm called Pareto memetic algorithm. The results of the experiment indicate very good performance of hybrid genetic algorithms, however, no algorithm was able to outperform all other methods on all instances. Furthermore, the results indicate that the performance of multiple-objective metaheuristics may differ radically even if the methods are based on the same single objective algorithm and use exactly the same problem-specific operators.