###### Abstract  
In a smart city environment, with increased demand for energy efficiency, information exchange and communication through wireless sensor networks (WSNs) plays an important role. In WSNs, the sensors are usually operating in clusters, and they are allowed to restructure for effective communication over a large area and for a long time. In this scenario, load-balanced clustering is the cost-effective means of improving the system performance. Although clustering is a discrete problem, the computational intelligence techniques are more suitable for load balancing and minimizing energy consumption with different operating constraints. The literature reveals that the swarm intelligence-inspired computational approaches give excellent results among population-based meta-heuristic approaches because of their more remarkable exploration ability. Conversely, in this work, load-balanced clustering for sustainable WSNs is presented using improved gray wolf optimization (IGWO). In a smart city environment, the significant parameters of energy-efficient load-balanced clustering involve the network lifetime, dead cluster heads, dead gateways, dead sensor nodes, and energy consumption while ensuring information exchange and communication among the sensors and cluster heads. Therefore, based on the above parameters, the proposed IGWO is compared with the existing GWO and several other techniques. Moreover, the convergence characteristics of the proposed algorithm are demonstrated for an extensive network in a smart city environment, which consists of 500 sensors and 50 cluster heads deployed in an area of 500 \(\times\) 500 m\({}^{2}  
objective functions mainly depends upon the constraints and the operator experience while updating every new fitness function and the problem initialization. Recently, a nature-inspired gray wolf optimization (GWO) approach was developed in [1]. The authors have explored the performance of GWO compared to the several existing computational methods, and it is found to be encouraging. The concept is derived from the fact that wolves live in a group of five to twelve members, and depending upon their skill, the role of each member is different. Therefore, the simulation performed in this optimization technique is based on the leadership hierarchy of gray wolves and their hunting behavior. In GWO, wolves are categorized into four classes, namely Alpha, Beta, Delta and Omega. In this hierarchy, Alpha is represented as the group leader, and Beta is the subordinate of the group leader. Conversely, Delta is the subordinate to both Alpha and Beta, whereas Omega are the other wolves that serve as soldiers in the group.  
The optimization function in GWO is derived from the three phases of hunting: searching the prey, encircling the prey, and attacking the prey. In the proposed work, the GWO technique is explored to obtain the load balancing of the gateways in heterogeneous WSNs, since clustering is a discrete problem and the fitness function can be improved by tweaking the existing GWO approach for different objectives with different operating constraints. In this work, an improved GWO is proposed for the sustainable WSNs in a smart city environment where the performance matrix involves the network lifetime, coverage area and energy consumption during information exchange among sensors and cluster heads for the WSN under consideration.