## 1 Introduction  
A WSN is a network made up of numerous sensor nodes dispersed within a certain region. To enable data collection, transfer, and analysis, these nodes can be wirelessly connected to one another [1, 2]. WSNs are becoming more and more appealing for a wide range of application fields, including military applications, emergency response and security, environmental monitoring, health and medical, automated industrial control, smart cities, transportation and logistics, and entertainment [3, 4, 5]. WSNs' low cost and ease of deployment have led to their widespread application in many different industries. But energy is scarce and sensor node batteries are hard to replace. Therefore, it is imperative to address the issue of the energy usage of networks and increase the network's lifespan [6, 7].  
Given that the primary cause of node energy consumption is wireless communication [8], energy-efficient communication protocols are essential for drastically reducing network energy consumption and increasing network lifetime. Of these protocols, the clustering routing protocol is a notable example of an essential subset in the field of energy-efficient WSN communication protocols. It has proven to be a very successful method for energy conservation in WSNs with limited energy supplies. Organizing sensor nodes into multiple clusters, each with a CH and additional common nodes, is the core idea behind the cluster-based routing protocol. The common nodes in each cluster gather information and send it to the CH. Following data collection, the regular nodes' data packets are received, combined, and processed by the CHs, which subsequently forward the processedand combined data to BS. The clustered routing protocol is essential for WSNs' energy conservation since it reduces energy usage and helps manage overhead traffic [9; 10; 11; 12].  
The key idea of network clustering is intimately related to how well the clustered routing protocol affects network energy consumption. As communication distance reduces, so does the amount of energy used for communication inside clusters. Given that CHs use more energy to perform functions like receiving, fusing, and transferring data than normal nodes, choosing the right CHs is essential for enhancing network load balancing. Furthermore, the utilization of a multi-hop communication technique is efficacious in mitigating communication energy consumption, particularly in light of the high energy expenditure linked to long-distance communication. This work employs the SO optimization technique to solve the NP-hard problem [13; 14; 15; 16; 17] of optimal CH selection, and the best route between CHs is determined during the data transmission phase using the GJO optimization technique. Below is a summary of this research work's main contributions:  
1. The ESO-GJO method adds a Brownian motion function to the SO algorithm's exploitation stage in order to avoid local optima.
2. The proposed approach uses SO to select the optimal CHs and considers variables such as energy and distance when building the fitness function.
3. The suggested algorithm uses GJO to determine the route from CH to BS and initializes the GJO population through backward learning.  
The structure of the rest of the article is summarized below:  
* Section 2: Summarizes previous work in related fields.
* Section 3: Introduces the energy model and network model.
* Section 4: Offers a detailed introduction to the algorithm proposed in this article.
* Section 5: Performance metrics simulation demonstration and comparison.
* Section 6: Summarizes the research work in this paper and suggests future work to be carried out.