Recent trends in Wireless Sensor Network (WSN) have been adopted as an emerging networking paradigm called Software-Defined Wireless Sensor Network (SD-WSN) to dynamically and efficiently managing the network functionality. Generally, smart sensor devices suffer from low battery and could not be replaced after a deployment. Therefore, This work is focusing on the energy-efficient clustering routing problem in SD-WSN. In SD-WSN, Control Server (CS) assigns the tasks to selected Control Nodes (CNs) dynamically. Thus, CNs selection is formulated as an optimization problem in SD-WSNs. To solve this, a nature-inspired approach i.e. Gray-Wolf Optimization (GWO) is applied to balance the normal nodes' energy. Thus, proposed approach is referred to as the Energy-balanced Grey-wolf optimizer (EBGWO). Further, a fitness function is designed that considers several parameters e.g., CS to CNs distance, intracluster distance, node residual energy, and cluster size. Thus, the EBGWO perform balanced, energy-efficient clustering and prolong the network lifespan. The comparative simulation results show that the EBGWO approach outperforms the NWPSO concerning network lifespan, residual energy, network throughput, and convergence rate.