In this article, a modification of multi-objective differential evolution based on simulated annealing is proposed to solve a general tri-objective non-permutation flow shop problem. The flow shop system considers the release dates, machine breakdowns, past-sequence-dependent setup times and learning effect for all the jobs. The algorithm proposed to tackle such a model combines the robustness of differential evolution with the rapid convergence and conditional diversification of simulated annealing. For small and medium low-sized problems, the solutions found by the proposed algorithm are compared with the exact solutions, achieved by augmented -constraint method. Due to the high complexity of the model, for medium high and large-sized problems, the algorithm is tested against the imperialist competitive algorithm and the multi-objective differential evolution scheduling. Comparisons of the results show a good balance between intensification and diversification in the proposed algorithm.