A group of small sensors can participate in the wireless network infrastructure and make appropriate transmission and communication sensor networks. There are numerous uses for drones, including military, medical, agricultural, and atmospheric monitoring. The power sources available to nodes in WSNs are restricted. Furthermore, because of this, a diverse method of energy availability is required, primarily for communication over a vast distance, for which Multi-Hop (MH) systems are used. Obtaining the optimum routing path between nodes is still a significant problem, even when multi-hop systems reduce the cost of energy needed by every node along the way. As a result, the number of transmissions must be kept to a minimum to provide effective routing and extend the system's lifetime. To solve the energy problem in WSN, Taylor based Gravitational Search Algorithm (TBGSA) is proposed, which combines the Taylor series with a Gravitational search algorithm to discover the best hops for multi-hop routing. Initially, the sensor nodes are categorised as groups or clusters and the maximum capable node can access the cluster head the next action is switching between multiple nodes via a multi-hop manner. Initially, the best (CH) Cluster Head is chosen using the Artificial Bee Colony (ABC) algorithm, and then the data is transmitted utilizing multi-hop routing. The comparison result shows out the extension of networks longevity of the proposed method with the existing EBMRS, MOGA, and DMEERP methods. The network lifetime of the proposed method increased by 13.2%, 21.9% and 29.2% better than DMEERP, MOGA, and EBMRS respectively.