Abstract. In this paper, we study the problem of energy and deadline constrained static resource allocation where a collection of independent tasks ("bag-of-tasks") is assigned to a heterogeneous computing system. Computing systems often operate in environments where task execution times vary (e.g., due to data dependent execution times), therefore we model the execution time of tasks stochastically. This research focuses on the design of energy-constrained resource allocation heuristics that maximize robustness against the uncertainties in task execution times. We design and evaluate a new resource allocation heuristic based on Tabu Search that employs dynamic voltage and frequency scaling (DVFS) and exploits heterogeneity by incorporating novel local search techniques.