Energy-efficient flexible job shop scheduling problems (EFJSP) have been investigated fully; however, energy-related objectives often have lower importance than other ones in many real-life situations and this case is hardly considered in the previous works. In this study, EFJSP with sequence-dependent setup times (SDST) is considered, in which total tardiness and makespan are given higher importance than total energy consumption. A two-phase imperialist competitive algorithm (TPICA) is proposed. The importance difference among objectives is implemented by treating all objectives equally in the first phase and making energy consumption not to exceed a diminishing threshold in the second phase. A dynamical differentiating assimilation and a novel imperialist competition with the enforced search are implemented. Extensive experiments are conducted and the computational results show that TPICA is very competitive for EFJSP with SDST.
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