Heterogeneous cluster architectures with different types of compute devices are wide-spread in the field of high performance computing introducing new kind of challenges. Time-efficient distribution of work onto heterogeneous devices is much more intricate than in the homogeneous case. Moreover, the use of heterogeneous devices makes it necessary to address energy efficiency as well. This results in bi-criteria optimization problems whereby often time efficiency and energy efficiency are conflicting objectives pushing in different directions. In this paper we define four optimization problems which are of particular interest for developers, give a formal description of these problems, and try to find optimal solutions for them efficiently with minimal effort. Essential is the fact that a user may specify time or energy constraints for which optimal work distributions onto the devices are determined. In addition, we raise the question how to recommend reasonable solutions, if no constraints have been specified. An experimental section examines the solutions obtained from our algorithms.

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