In order to operate within power supply constraints, the next generation of supercomputers must be energy efficient. Both the capacities of the target HPC system architecture and workload features impact the energy efficiency of parallel applications. These system and workload factors form a complicated optimization search space. Further, a typical workload may consist of multiple algorithmic kernels each with different power consumption patterns. Using the Parallel Research Kernels as a case study, we identify key bottlenecks that change the energy usage pattern and develop strategies that improve energy efficiency by optimizing both workload and system parameters in an automated manner. The method provides significant insights to identify repeatable, statistically significant energy saving opportunities for parallel applications at various scales.