Abstract Performance and energy are the two most important objectives for optimization on heterogeneous high performance computing platforms. This work studies a mathematical problem motivated by the bi‐objective optimization of data‐parallel applications on such platforms for performance and energy. First, we formulate the problem and present an exact algorithm of polynomial complexity solving the problem where all the application profiles of objective type one are continuous and strictly increasing, and all the application profiles of objective type two are linear increasing. We then apply the algorithm to develop solutions for two related optimization problems of parallel applications on heterogeneous hybrid platforms, one for performance and dynamic energy and the other for performance and total energy. Our proposed solution methods are then employed to solve the two bi‐objective optimization problems for two data‐parallel applications, matrix multiplication and gene sequencing, on a hybrid platform employing five heterogeneous processors, namely, two different Intel multicore CPUs, an Nvidia K40c GPU, an Nvidia P100 PCIe GPU, and an Intel Xeon Phi.

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.

Summary Energy is one of the most important objectives for optimization on modern heterogeneous high‐performance computing (HPC) platforms. The tight integration of multicore CPUs with accelerators such as graphical processing units (GPUs) and Xeon Phi coprocessors in these platforms presents several challenges to the optimization of multithreaded data‐parallel applications for energy. In this work, the problem of optimization of data‐parallel applications on heterogeneous HPC platforms for dynamic energy through workload distribution is formulated. We propose a workload partitioning algorithm to solve this problem. It employs load‐imbalancing technique to determine the workload distribution minimizing the dynamic energy consumption of the parallel execution of an application. The inputs to the algorithm are discrete dynamic energy profiles of individual computing devices. The profiles are practically constructed using an approach that accurately models the energy consumption by execution of a hybrid scientific data‐parallel application on a heterogeneous platform containing different computing devices such as CPU, GPU, and Xeon Phi. The proposed algorithm is experimentally analyzed using two multithreaded data‐parallel applications, matrix multiplication and 2D fast Fourier transform. The load‐imbalanced solutions provided by the algorithm achieve significant dynamic energy reductions for the two applications (in average by 130% and 44%, respectively) compared with the load‐balanced solutions.

Modern HPC platforms have become highly heterogeneous owing to tight integration of multicore CPUs and accelerators (such as Graphics Processing Units, Intel Xeon Phis, or Field-Programmable Gate Arrays) empowering them to maximize the dominant objectives of performance and energy efficiency. Due to this inherent characteristic, processing elements contend for shared on-chip resources such as Last Level Cache (LLC), interconnect, etc. and shared nodal resources such as DRAM, PCI-E links, etc. This has resulted in severe resource contention and Non-Uniform Memory Access (NUMA) that have posed serious challenges to model and algorithm developers. Moreover, the accelerators feature limited main memory compared to the multicore CPU host and are connected to it via limited bandwidth PCI-E links thereby requiring support for efficient out-of-card execution. To summarize, the complexities (resource contention, NUMA, accelerator-specific limitations, etc.) have introduced new challenges to optimization of data-parallel applications on these platforms for performance. Due to these complexities, the performance profiles of data-parallel applications executing on these platforms are not smooth and deviate significantly from the shapes that allowed state-of-the-art load-balancing algorithms to find optimal solutions. In this paper, we formulate the problem of optimization of data-parallel applications on modern heterogeneous HPC platforms for performance. We then propose a new model-based data partitioning algorithm, which minimizes the execution time of computations in the parallel execution of the application. This algorithm takes as input a set ofpdiscrete speed functions corresponding top available heterogeneous processors. It does not make any assumptions about the shapes of these functions. We prove the correctness of the algorithm and its complexity ofO(m3×p3), where m is the cardinality of the input discrete speed functions. We experimentally demonstrate the optimality and efficiency of our algorithm using two data-parallel applications, matrix multiplication and fast Fourier transform, on a heterogeneous cluster of nodes where each node contains an Intel multicore Haswell CPU, an Nvidia K40c GPU, and an Intel Xeon Phi co-processor.