Designed to provide pervasive access to distributed resources in parallel ways, heterogeneous scheduling is extensively applied in large-scale computing system for its high performance. Conventional real-time scheduling algorithms, however, often overlook energy-efficiency while focusing on stringent timing constraints. To engage in green heterogeneous computing, a reusable energy-aware cloud model is first presented via mathematical formulation and quantization of the system parameters such as dynamic voltage and frequency scaling (DVFS), and dynamic power management (DPM). In addition, multidisciplinary context for multi-objective global optimization meta-heuristic is proposed and accomplished based on the supercomputer hybrid architecture. Furthermore, some technological breakthroughs are achieved with respect to boundary conditions for different heterogeneous computing and cloud scheduling, and descriptions of real-time variation of scheduling indexes (stringent timing constraints and energy-efficiency). Extensive simulation experiments highlight higher efficacy and better scalability for the proposed approaches compared with the other three meta-heuristics; the overall improvements achieve 8%, 12% and 14% for high-dimension instances.