## 2 Literature Review
In [28], [PERSON] and [PERSON] proposed a cluster-based HRP of two stages. In the first stage, the election of CHs is performed based on nodes' residual energy and their relative position to the base satiation. In the second stage, the CHs forward the collected data to the BS indirectly via multi-hop forwarding, which prolongs network lifetime and saves energy, as proven by their simulation results. [PERSON] et al. proposed a centralized WSN clustering approach based on Discrete Particle Swarm Optimization (DPSO) used in the context of the traveling sales-man problem [29]. In their approach, the BS collects status information about sensor nodes, then runs their own modified version of the DPSO algorithm to find the optimal topology for the WSN. This approach achieved 15% enhancement over LEACH in terms of WSN lifetime and showed higher ability to balance energy consumption among WSN nodes. In [30], the authors proposed a clustering technique for WSN based on applying a non-deterministic approach and adopting intra-phase and inter-phase clustering. In each phase of the non-deterministic approach, the optimal participation of clusters' members in the process of selecting the corresponding CHs is enforced. This technique achieved enhancement of 42% over the standard LEACH in terms of WSN lifetime. In [31], a comparison study of genetic algorithm, differential evolution, and particle swarm optimization for efficient and fast WSN clustering was presented. In addition, the authors compared these techniques in terms of achieved fitness value. Based on their results, these techniques had significant improvements over LEACH in terms of network life-cycle and energy saving. A centralized clustering approach for HRP in WSN based on residual energy for sensor nodes, remaining energy variance, and coverage density was proposed in [32]. The proposed approach outperformed the existing protocols in terms of network lifetime. [PERSON] et al. [33] applied a prediction-based data reduction scheme for energy-efficient routing protocol design, where WSN is divided initially into grids, then CH election takes place. The authors in [10; 11; 15; 16; 34], Refs. [35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47] proposed fuzzy logic approaches for CH election in cluster-based HRPs. Each of these fuzzy logic-based approaches uses the partial combination of the parameters, residual energy, BS proximity, local distance, concentration, centrality, etc., to select CHs, but none of them uses an effective combination. Fuzzy logic-based clustering approaches proposed in the literature vary among centralized, distributed, and hybrid. However, most of them are centralized because fuzzy logic-based CH election requires high CPU cycles and high memory capacities. Furthermore, fuzzy logic-based clustering algorithms require global knowledge about sensors' attributes, which would be costly in terms of energy and bandwidth if exchanged via the sensors themselves. Therefore, for fuzzy logic-based clustering in WSN, the centralized approaches are preferred [10; 11]. Another way to design routing protocols for ad hoc networks and/or WSN is the cross-layer approach. Some examples of cross-layer protocols appeared in [48; 49; 50]. It has been observed that many of the cross-layer approaches rely on fuzzy logic. The authors in [51] proposed a fuzzy logic-based cross-layer routing algorithm for mobile ad hoc networks, while the research in [49] proposed a fuzzy logic-based cross-layer routing algorithm for WSNs. The different classes of WSN routing protocols for single-layer and cross-layer are summarized in Table 1.