Flexible job shop scheduling has been widely researched due to its application in many types of fields. However, constraints including setup time and transportation time should be considered simultaneously among the realistic requirements. Moreover, the energy consumptions during the machine processing and staying at the idle time should also be taken into account for green production. To address this issue, first, we modeled the problem by utilizing an integer programming method, wherein the energy consumption and makespan objectives are optimized simultaneously. Afterward, an improved Jaya (IJaya) algorithm was proposed to solve the problem. In the proposed algorithm, each solution is represented by a two-dimensional vector. Consequently, several problem-specific local search operators are developed to perform exploitation tasks. To enhance the exploration ability, a SA-based heuristic is embedded in the algorithm. Meanwhile, to verify the performance of the proposed IJaya algorithm, 30 instances with different scales were generated and used for simulation tests. Six efficient algorithms were selected for detailed comparisons. The simulation results confirmed that the proposed algorithm can solve the considered problem with high efficiency. •The FJSPs with transportation and setup time are considered.•Two objectives are optimized simultaneously.•Seven different types of local search approaches are proposed.•SA-based acceptation criterion is embedded.