Multi-objective evolutionary algorithms (MOEAs) have shown good performance on many benchmark and real world multi-objective optimization problems. However, MOEAs may suffer from some difficulties when solving big data optimization problems with thousands of variables. Firefly algorithm (FA) is a new meta-heuristic, which has been proved to be a good optimization tool. In this paper, we present a hybrid multi-objective FA (HMOFA) for big data optimization. A set of big data optimization problems, including six single objective problems and six multi-objective problems, are tested in the experiments. Computational results show that HMOFA achieves promising performance on all test problems.