In today's world of large distributed systems, the need for energy efficiency of individual components is complemented by the need for energy awareness of the complete system. Hence, energy-aware scheduling of tasks on systems has become very important. Our work addresses the problem of finding an energy-aware schedule for a given system which also satisfies the precedence constraints between tasks to be performed by the system. We present a method which uses cellular automata to find a near-optimal schedule for the system. The rules for cellular automata are learned using a genetic algorithm. Though the work presented in this paper is not limited to scheduling in computing environments only, the work is validated with a sample simulation on distributed computing systems, and tested with some standard program graphs.