## 2 Related Works  
Many scholars have conducted detailed research on the DV-Hop algorithm [16]. Different improvement schemes have been proposed for the original algorithm, and good progress has been made. The DV-Hop algorithm had three phases. Phase 1: The minimum number of hops between the unknown node and the anchor node was calculated [17]. Phase 2: The estimated distance was calculated by multiplying the minimum number of hops and the average distance per hop [18]. Phase 3: The specific coordinate of the unknown node was calculated based on the trilateration localization mechanism or the excellent likelihood appraisal method [9; 19].  
Considering the localization error, many researchers have optimized phases 1 and 2 of DV-Hop. For example, [PERSON] et al. [20] optimized the minimum number of hops by increasing the communication radius (R) and setting two communication radii. A medium access control (MAC) method based on the Chinese remainder theorem (CRT) protocol sequence has been proposed for DV-Hop localization [21]. To overcome the low accuracy and high energy consumption, the enhanced weighted centroid DV-Hop (EWCL) algorithm was proposed by [PERSON] et al. [22]. The weighting factor in the EWCL algorithm was a function of hop count, average hop distance, and transmission radius.  
Other scholars have also optimized phase 3 of DV-Hop. Recently, with intelligent computing showing excellent performance in various complex optimization problems, various nature-inspired schemes have been presented [13; 23]. For instance, a DV-Hop improvement algorithm based on bacterial foraging optimization was raised in the literature by [PERSON] et al. [24], and the algorithm was a nature-inspired intelligent parallel search algorithm. The application of the DV-Hop algorithm based on the gray-wolf optimization technique in 2D and 3D WSNs has been noticed [25]. A hybrid chaotic strategy firefly swarm optimization algorithm was proposed based on chaotic variation and chaotic inertia weight update [26]. In the literature [27], the proposed algorithm eliminates communication from one of the steps by calculating hop size at unknown nodes. The hybrid DV-Hop algorithm combined with cuckoo search [28], also known as CS-DV-Hop, showed better localization performance than DV-Hop [29]. In the literature [30], the DV-Hop algorithm based on the bacterial foraging algorithm (BFA) and glow-worm swarm optimization (GSO) (BFO-GSO) was described in detail. The BFO algorithm was a new evolutionary algorithm inspired by the foraging behavior of Escherichia coli. A coupled scheme in the light of the bacterial foraging algorithm and the glow-worm swarm optimization algorithm was chosen for this improved algorithm. This scheme had tremendous convergence speed and BFO local search capability; however, due to the use of BFO-GSO, computation time was increased slightly.  
It is well known that localization algorithms for WSNs need to consider practical application scenarios. New characteristic factors need to be considered for specific complex deployment environments (such as indoor environments, coal mine tunnels, canyon terrain, and lake terrains [31; 32; 33]) and their corresponding node topologies. The non-dominant sorting genetic algorithm (NSGA-II) has advantages [34]. Consequently, a multi-objective DV-Hop based on NSGA-II, also known as NSGA-II-DV-Hop, has been proposed in the literature [35]. Furthermore, detailed simulations and evaluations were performed in four application contexts, and the experimental results show that NSGA-II-DV-Hop significantly outperformed the original DV-Hop.