Efficient exact algorithms for continuous bi‐objective performance‐energy optimization of applications with linear energy and monotonically increasing performance profiles on heterogeneous high performance computing platforms

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.

OpenH: A Novel Programming Model and API for Developing Portable Parallel Programs on Heterogeneous Hybrid Servers

“…The decomposition of the matrix A is computed using a model-based workload partitioning algorithm [26], [27] Therefore, the output by the algorithm is an array d of three elements, where d[0], d [1], and d [2], respectively, contain the number of rows of A and C assigned to {S CPU , S GPU 1 , S GPU 2 }.…”

“…The OpenH matrix multiplication application performs the best since it employs the performance-optimal workload distribution and mapping of the software components to the CPU cores of the hybrid server. Furthermore, the performanceoptimal workload distribution is the load-balanced distribution between the three software components ( [28], [27]) since their execution times are linear functions of workload size.…”

“…For the OpenH matrix multiplication application, we employ the workload partitioning algorithms proposed in [28], [29], [27] to determine the partitioning of the matrices between A and C that minimizes the total dynamic energy consumption of the application. Specifically, the matrices A and C are partitioned horizontally among the three software components to minimize the application's total dynamic energy consumption.…”

“…Therefore, the profiles are linear functions of the workload size since the workload size 2 × M × N 2 of each data point is proportional to M (N is a constant). The authors [27], [30] show that for the case of linear dynamic energy profiles that the workload distribution optimizing the application for dynamic energy has the total workload assigned to the most energy-efficient processor, the processor with linear energy function with the lowest slope (multicore CPU in this case). Figure 13 compares the dynamic energy consumptions of the three matrix multiplication applications.…”