## 2 Related Work  
Based on a study in [16], data communication for a sensor-node with other entities in the network consumes a large amount of energy in contrast with data processing inside the sensor-node. This axiom is the main lead to motivate for designing routing protocols in WSNs. As one of the significant works that could influence further researches in the area, in [17; 18], [PERSON] et al. proposed an approach to select some of the sensor-nodes as cluster-heads (CHs) and dismiss other non-CHs from communicating with the base-station directly that is called LEACH (Low-Energy Adaptive Clustering Hierarchy). Therefore, the sensor-nodes which are not selected as CHs should be allocated to a suitable CH. In LEACH, by defining the concept of round and implementing a probabilistic technique in each round, a set of sensor-nodes will be selected as CHs. In the next round, a new set of CHs will be selected. And after determining the set of CHs, other sensor-nodes will join to the closest CHs by considering signal strength. Despite the improvement of the approach in saving energy, the main disadvantage is its probabilistic nature without considering the location of the CHs and some other parameters such as residual energy. Therefore, it is probable that some CHs locate in the margin of the cluster and being far from the base-station. In addition, LEACH assumes that all of the sensor-nodes can contact with the base-station directly which is impractical for large-scale WSNs. To improve the accuracy of cluster-head selection by injecting some related information to the process of selection, scholars implemented different routing protocols based on probabilistic models [19; 20], swarm intelligence [21; 22; 23], and fuzzy systems [24; 25; 26]. However, in the mentioned efforts the main assumption is all of the sensor-nodes and the base-station are stationary after installation. Recently, with improvement in the new technologies, the idea of utilization a(some) mobile-sink(s) in the network is proposed in [27; 28] to harvest data from the sensor-nodes in the environment. Application of mobile-sink can improve lifetime and reliability of the network by controlling energy depletion in a uniform manner which can prevent energy holes [9; 29]. The main research question that arises is _\"the fashion of data-harvesting which the mobile-sink(s) should follow\"_. Solving this question essences to divide the question to two sub-questions. The first sub-question should determine the _\"visiting strategy\"_. And the second issue refers to the _\"movement strategy\"_. The visiting strategy can be divided to \"Direct\" and \"Indirect\". And the movement strategy can be considered as \"Constrained\" and \"Unconstrained\". In the following, we will review some of the prominent works for each division. In direct approaches, the main strategy is to visit all of the sensor-nodes one-by-one. By adopting this manner, the movement strategy for the mobile-sink in case of large-scale WSNs should be unconstrained. Since in case of constrained movement, the sensor-nodes should be installed manually in the periphery of a predefined trajectory in which the mobile-sink can reach all of the sensor-nodes one-by-one. As one of the early efforts, in [30], [PERSON] et al. defined \"data mules\" such as people, animals, or vehicles in the environment which are equipped with related devices for data-harvesting. Since the main purpose of existence of data mules in the environment is not working as mobile-sink, the random walk model is adopted to model their movement fashion. Obviously, the nature of random walk can't guarantee that all of the sensor-nodes can be visited by data mules. In [31], [PERSON] et al. proposed another solution to visit the sensor-nodes directly. Their approach also can be extended to multiple mobile-sink(s). They named the problem as the single-hop data gathering problem (SHDGP).