Energy predictive modeling is the leading method for determining the energy consumption of an application. Performance monitoring counters (PMCs) and resource utilizations have been the principal source of model variables primarily due to their high positive correlation with energy consumption. Performance events, however, have come to dominate the landscape due to their better prediction accuracy compared to utilization variables. Recently, the theory of energy of computing has been proposed whose practical implications for constructing accurate and reliable linear energy predictive models are unified in a consistency test that includes a selection criterion of additivity for model variables. In this work, we analyze the prediction accuracy of models employing utilization variables only, PMCs only, and combination of both utilization variables and PMCs, through the lens of this theory for modern multicore CPU platforms. We discover that employing utilization variables only in linear energy predictive models does not capture all the energy-consuming activities during an application execution. However, combination of utilization variables with PMCs that are highly additive and highly correlated with energy consumption, gives the most accurate linear energy predictive model. Our experimental results show that application-specific and platform-level models using both utilization variables and PMCs exhibit up to 3.6× and 2.6× better average prediction accuracy respectively when compared with models employing utilization variables only and highly additive PMCs only.

Performance and energy are the two most important objectives for optimization on modern parallel platforms. In this article, we show that moving from single-objective optimization for performance or energy to their bi-objective optimization on heterogeneous processors results in a tremendous increase in the number of optimal solutions (workload distributions) even for the simple case of linear performance and energy profiles. We then study full performance and energy profiles of two real-life data-parallel applications and find that they exhibit shapes that are non-linear and complex enough to prevent good approximation of them as analytical functions for input to exact algorithms or optimization software for determining the Pareto front. We, therefore, propose a solution method solving the bi-objective optimization problem on heterogeneous processors. The method's novel component is an efficient and exact global optimization algorithm that takes as an input performance and energy profiles as arbitrary discrete functions of workload size, which accurately and realistically take into account resource contention and NUMA inherent in modern parallel platforms, and returns the Pareto-optimal solutions (generally speaking, load imbalanced). To construct the input discrete energy functions, the method employs a methodology that accurately models the energy consumption by a hybrid data-parallel application executing on a heterogeneous HPC platform containing different computing devices using system-level power measurements provided by power meters. We experimentally analyse the proposed solution method using three data-parallel applications, matrix multiplication, 2D fast Fourier transform (2D-FFT), and gene sequencing, on two connected heterogeneous servers consisting of multicore CPUs, GPUs, and Intel Xeon Phi. We show that it determines a superior Pareto front containing the best load balanced solutions and all the load imbalanced solutions that are ignored by load balancing methods.