The flowshop sequence-dependent group scheduling problem (FSDGSP) with the production efficiency measures has been extensively studied due to its wide industrial applications. However, energy efficiency indicators are often ignored in the literature. This paper considers the FSDGSP to minimize makespan, total flow time and total energy consumption, simultaneously. After the problem-specific knowledge is extracted, a mixed-integer linear programming model and a critical path-based accelerated evaluation method are proposed. Since the FSDGSP includes multiple coupled sub-problems, a greedy cooperative co-evolutionary algorithm (GCCEA) is designed to explore the solution space in depth. Meanwhile, a random mutation operator and a greedy energy-saving strategy are employed to adjust the processing speeds of machines to obtain a potential non-dominated solution. A large number of experimental results show that the proposed algorithm significantly outperforms the existing classic multi-objective optimization algorithms, which is due to the usage of problem-related knowledge.