Display omitted •A new multi-objective firefly algorithm is used to solve big optimization problems.•The control parameters are automatically adjusted during the search process.•A crossover strategy is utilized to maintain population diversity.•The proposed approach achieves better results than NSGA-II on all test problems. 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.