# Energy and Environment-Aware Path Planning in Wireless Sensor Networks with Mobile Sink
## 3 Problem Modeling  
This section describes the research problems and explains our primary goals. Consider that a field _F(A)_ is monitored by a set of sensor nodes for a time horizon \(T\). This monitored field is divided into equal-sized zones \(A\). A time-varying weight metric is assigned for each zone _i_\(\in\)_A_, where _t_\(\in\)_T_. This weight metric defines the importance of the observations in each zone over the horizon \(T\) (surveillance requirements). In most prior studies, sensor nodes were static and location-aware. Consequently, sink nodes, especially mobile nodes, are utilized to collect the monitored field sensor data. Because of large-scale sensor networks, sensors are organized in the form of clusters. The task of gathering data from each cluster's members who are located within one hop of it is delegated to a cluster leader. The optimization of sink node mobility comes next. An undirected weighted graph \(G\) (_V_, _E_), where \(V\) is the collection of nodes, \(E\) is the set of edges, \(V\) is the nodes set, and \(E\) is the set of edges where \(x\), _y_\(\in\)_V_. Vertices represent sensor nodes, whereas edges indicate communication connections between them. An edge only exists between nodes \(x\) and \(y\) if they can communicate. There are some assumptions made concerning the nodes' characteristics. First, it is assumed that the sensor nodes are equipped with multiple sensor modules (i.e., temperature, humidity), providing sensor nodes with the ability to perceive surrounding environmental information. Secondly, the value of the residual energy can be easily obtained by measuring the batteries' voltage level. Thirdly, sensor nodes collect the information about their neighbors through broadcasting techniques. Fourthly, it is assumed that the sensor nodes are aware of their geographic locations due to the attached GPS receivers. Finally, the MAC layer PRR [30] measures connection quality. Let us start with one of the paper's goals: designing the ideal mobile sink path to improve field coverage. High-priority observations enhance coverage. Moreover, avoiding the risk zone and choosing a safer path for the movable sink to reduce environmental impact. Data packets which did not reach the sink node must also be minimized (packetsmiss ratio). So, the mobile sink's path planning algorithm must scan received cluster head locations and choose the optimal position that meets the following restrictions:  
1. Provides minimum movement cost;
2. Is away from the danger zones to keep mobile sink path safe as much as possible;
3. Provides the maximum coverage while the observations in the highest priority zones are collected;
4. Provides the lowest end-to-end latency for real-time data transmission and eliminates sensor node buffer overflow due to limited buffer capacity. Second, this paper identifies an ideal cluster head that conserves sensor node energy to extend network lifetime. To do this, the cluster head should satisfy some constraints, including:  
1. Provides the shortest average intra-cluster distance;
2. Provides the highest possible data transfer reliability;
3. Has the maximum residual energy compared with the other candidates. Third, this article aims to shorten the routing path's communication distance to save energy and extend the network's lifetime. Moreover, energy management is considered while designing the proposed routing protocol. It also examines how to reduce environmental factors' influence on urgent data packet routing by avoiding hazardous zones and finding the safest paths to the sink. Real-time transmission of urgent data packets is discussed. Additionally, the issue of reliable routing paths is discussed. To attain this aim, the proposed route must fulfill the following criteria:  
1. Minimum communication distance;
2. Less likely to be cut off as a result of environmental reasons;
3. Maximum reliability;
4. Minimum end-to-end delay;
5.