Abstract: Concerning at the high energy consumption of heterogeneous multi-core platforms, an algorithm for solving the optimal energy allocation scheme of periodic tasks by using optimization theory was proposed. The optimal energy consumption problem of periodic tasks was modeled and added constraints to the model. According to the optimization theory, the binary integer programming problem was relaxed to obtain the convex optimization problem. The interior point method was used to solve the optimization problem and the relaxed distribution matrix was obtained. The allocation scheme for partial tasks was obtained after the judgement processing of the decision matrix. On this basis, the iterative method was used to find the allocation scheme for the remaining tasks. Experimental results show that the energy consumption of this distribution scheme is reduced by about 1.4% compared with the similar optimization theory algorithm, and compared with the optimization theory algorithm with the similar energy consumption, the execution time of this scheme is reduced by 86%. At the same time, the energy consumption of the scheme is only 2.6% higher than the theoretically optimal energy consumption.

Key words: multiprocessor, energy saving scheduling, periodic task, utilization rate, optimization theory

摘要： 针对异构多核平台存在的高能耗问题，提出一种运用优化理论求解周期任务最优能耗分配方案的算法。该算法对周期任务的最优能耗问题进行建模，并对模型添加限制条件。根据优化理论将二进制整数规划问题松弛化后得到凸优化问题，通过内点法求解优化问题并得到松弛化的分配矩阵，对分配矩阵进行判决处理后得到部分任务的分配方案。在此基础上，通过迭代的方式求得剩余任务的分配方案。实验结果表明，该分配方案产生的能耗与同类优化理论算法相比能耗降低约1.4%，与能耗相当的优化理论算法相比执行时间减少86%，且仅比理论最优能耗值高2.6%。

关键词: 多处理器, 节能调度, 周期任务, 利用率, 优化理论