In wireless sensor networks (WSNs), energy efficiency is a significant design challenge that can be resolved by clustering and routing approaches. They are considered as Non-deterministic Polynomial (NP)-hard optimization problems, and the optimal or near-optimal solutions can be determined by using Swarm-Intelligence (SI) based algorithms. With this inspiration, this study focuses on two approaches, viz. the Hybrid Butterfly and Ant Colony optimization algorithm along with Static sink node (HBACS) and HBAC along with Mobile sink node (HBACM), which is a hybridization of Butterfly Optimization (BOA) and Ant Colony Optimization (ACO) algorithm. BOA determines the optimal cluster head, and ACO performs energy-efficient routing, thereby minimizing the energy consumption and maximizing the network’s lifetime. Furthermore, in this study, mobility of the sink node is used to eliminate the multi-hop communication between cluster heads and sink nodes, hence addressing the hot-spot issue and further extending the network lifetime. The proposed HBACS and HBACM approaches are implemented in the NS2 simulator. The simulation findings reveal that the HBACS shows percentage improvement regarding residual energy by 24.23%, 41.98%, and 66.67%; an improved number of alive nodes by 28.19%, 37.81%, and 53.12%; and improved throughput by 8.11%, 14.29%, and 17.65% over CRWO, ERP, and IHSBEER algorithms respectively. Moreover, the HBACM approach performs better in LDN by 18.76%, 63.66%, and 66.28%; HDN by 8.35%, 56.26%, and 58.15%, and FDN by 7.77%, 52.76%, and 74.29% over HGWSFO, SFO, and GWO based approaches, respectively.