Applications of Wireless Sensor Networks (WSNs) are endless in the life, including monitoring of environment and animal, safety, and healthcare. However, energy constraints are one of the central concerns in WSN. Among the various methods aimed at overcoming this issue, sleep-awake scheduling via selection of disjoint groups of nodes called dominating set has been the most common applied approach. Each group carries out tasks on behalf of nearby nodes. This approach helps extend the network’s lifetime by distributing data-gathering responsibilities across different groups. One group handles the tasks for a specific period, after which it is replaced by another group. The aim of the paper is determination of the energy-aware disjoint dominating sets, which support the extension of the total network lifetime in a given network containing nodes with heterogeneous energy. To achieve this target, we present two methods known as Cautious algorithm and Bees algorithm-based method. The efficiency of the proposed algorithms is demonstrated through simulations.