## 1 Introduction  
Data transmission, as the core element in information and communication technology, is a crucial component of modern communication networks. Efficient methods for data acquisition and transmission paths have theoretical and practical implications in the application of WSNs that can effectively save energy, thus extending the network lifetime and improving network feasibility for real-time applications [1, 2]. Sensor nodes, which are distributed across a wide area, have the capability to acquire information at any time, in any place, and in any environment. As a result, WSNs find wide applications in industry [3], transportation [4], medical care [5], space exploration [6], and other fields that serve as the foundation for the development of the Internet of Things (IoT) [7, 8]. Nevertheless, most sensor nodes have limited energy, computing, storage, and communication capabilities because the batteries they are equipped with are almost impossible to replace or continuously charge at any time [9]. Moreover, the continuous and independent data transmission between nodes and other nodes and between nodes and the base station increases the loss of power and hastens node mortality. Therefore, scholars have focused on how to effectively and energy-efficiently utilize sensor nodes for data acquisition and transmission, as well as analysis and processing via upper-level applications and users [10]. In order to realize this goal, many strategies have been proposed, with clustering and routing protocols being identified as the most effective ways [11]. A clustering algorithm divides sensor nodes into several independent groups, referred to as clusters [12]. Each cluster consists of a cluster head (CH) node and several ordinary nodes. Intra-cluster and inter-cluster communications lower the cost of the distance between the farthest nodes and the sink, and using data aggregation to transmit information consumes significantly less energy. In general, sensor nodes are arbitrarily distributed in the network; hence, the focus of research is on allocating nodes to the nearest designated CH. Unreasonable allocation will result in an unequal number of sensor nodes, resulting in uneven residual energy. Fuzzy logic performs well in optimization decision making [13; 14; 15], which is being used to resolve uncertainties in CH selection based on predefined fuzzy rules. Unlike the conventional technique, each variable in fuzzy logic is assigned a value between 0 and 1, signifying its correctness or incorrectness [16]. Fuzzy clustering algorithms typically set fuzzy rules based on input variables such as the residual energy of nodes, the distance to nodes, or the distance to the base station (BS) as input variables. Then, candidate nodes with the highest fuzzy outputs are selected as cluster heads (CHs), resulting in the appropriate distribution of CHs in a network [17]. Fuzzy logic has almost the same structure as human logic, and it can adapt to changing environments well, according to preset rules. Most protocols modify the node energy in each round, and CHs are adjusted based on fuzzy rules that can greatly prolong the network's lifetime. However, in large networks, complex fuzzy rules demand a lot of computational resources and time. The potential parallelism and distributed characteristics of meta-heuristic algorithms can effectively solve complex nonlinear problems, and their global optimization capability is ideal for solving NP-hard problems in wireless sensor networks that can achieve outcomes with fewer parameters. A meta-heuristic algorithm converts the selection of CHs and a routing path into an optimization problem with a specific objective function. Then, it continuously iterates until the optimal solution of the function is found. For example, the cat swarm algorithm [18], fish migration optimization algorithm [19], ant colony optimization algorithm [20], and genetic algorithm [21] are used to select CHs and find routing paths in a clustering and routing protocol.