Bi-Objective Optimization of Data-Parallel Applications on Homogeneous Multicore Clusters for Performance and Energy

Abstract

Performance and energy are now the most dominant objectives for optimization on modern parallel platforms composed of multicore CPU nodes. The existing intra-node and inter-node optimization methods employ a large set of decision variables but do not consider problem size as a decision variable and assume a linear relationship between performance and problem size and between energy consumption and problem size. We demonstrate using experiments of real-life data-parallel applications on modern multicore CPUs that these relationships have complex (non-linear and even non-convex) properties and, therefore, that the problem size has become an important decision variable that can no longer be ignored. This key finding motivates our work in this paper. In this paper, we first formulate the bi-objective optimization problem for performance and energy (BOPPE) for data-parallel applications on homogeneous clusters of modern multicore CPUs. It contains only one but heretofore unconsidered decision variable, the problem size. We then present an efficient and exact global optimization algorithm called <i>ALEPH</i> that solves the <i>BOPPE</i> . It takes as inputs, discrete functions of performance and dynamic energy consumption against problem size and outputs the globally Pareto-optimal set of solutions. The solutions are the workload distributions, which achieve inter-node optimization of data-parallel applications for performance and energy. While existing solvers for <i>BOPPE</i> give only one solution when the problem size and number of processors are fixed, our algorithm gives a diverse set of globally Pareto-optimal solutions. The algorithm has time complexity of <inline-formula><tex-math notation="LaTeX">$O(m^2 \times p^2)$</tex-math></inline-formula> where <inline-formula> <tex-math notation="LaTeX">$m$</tex-math></inline-formula> is the number of points in the discrete speed/energy function and <inline-formula> <tex-math notation="LaTeX">$p$</tex-math></inline-formula> is the number of available processors. We experimentally study the efficiency and scalability of our algorithm for two data parallel applications, matrix multiplication and fast Fourier transform, on a modern multicore CPU and homogeneous clusters of such CPUs. Based on our experiments, we show that the average and maximum sizes of the globally Pareto-optimal sets determined by our algorithm are 15 and 34 and 7 and 20 for the two applications respectively. Comparing with load-balanced workload distribution solution, the average and maximum percentage improvements in performance and energy respectively demonstrated for the first application are (13%,97%) and (18%,71%). For the second application, these improvements are (40%,95%) and (22%,127%). Assuming 5 percent performance degradation from the optimal is acceptable, the average and maximum improvements in energy consumption demonstrated for the two applications respectively are 9 and 44 and 8 and 20 percent. Using the algorithm and its building blocks, we also present a study of interplay between performance and energy. We demonstrate how <i>ALEPH</i> can be combined with <i> DVFS</i> -based Multi-Objective Optimization (MOP) methods to give a better set of (globally Pareto-optimal) solutions.