A Novel Algorithm for Bi-objective Performance-Energy Optimization of Applications with Continuous Performance and Linear Energy Profiles on Heterogeneous HPC Platforms

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

“…In Reference 13, we studied a more general continuous bi‐objective optimization problem for a generic case of $$$ k $$$ heterogeneous processors. The problem is motivated by the bi‐objective optimization for the performance and dynamic energy of data‐parallel applications on heterogeneous HPC platforms.…”

“…In this work, we applied the problem and the algorithm proposed in Reference 13 to solve 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. First, we formulated and solved the bi‐objective optimization problem for performance and dynamic energy.…”

“…In Reference 13, we solve the continuous optimization problem for such shapes of performance and dynamic energy functions. We first formulate the mathematical problem, which for a given positive real number $$$ n $$$ aims to find a vector $$$ X=\left\{{x}_0,\cdots \kern0.3em ,{x}_{k-1}\right\}\in {\mathbb{R}}_{\ge 0}^k $$$ such that $$$ {\sum}_{i=0}^{k-1}{x}_i=n $$$, minimizing the max of $$$ k $$$‐dimensional vector of functions of objective type one and the sum of $$$ k $$$‐dimensional vector of functions of objective type two.…”

“…We first formulate and solve a bi‐objective optimization problem of parallel applications on heterogeneous hybrid platforms for performance and dynamic energy. The solution to the problem is a straightforward application of our algorithm proposed in Reference 13.…”

“…The proposed algorithms (in Reference 13 and this work) are then employed to solve the two bi‐objective optimization problems for two data‐parallel applications, matrix multiplication and gene sequencing, employing five heterogeneous processors, two Intel multicore CPUs, an Nvidia K40c GPU, an Nvidia P100 PCIe GPU, and an Intel Xeon Phi (Figure 1). For the workloads and the platform employed in our experiments, the algorithms provide continuous piecewise linear Pareto fronts for performance and dynamic energy and performance and total energy where the performance‐optimal point is the load balanced configuration of the application.…”