# Optimization of Submodularity and BBO-Based Routing Protocol for Wireless Sensor Deployment
## 1 Introduction  
Wireless sensors are widely deployed on a large scale in commercial fields [1; 2], but are limited by node costs, communication efficiency between nodes, and energy consumption [3; 4; 5], e.g., in forest and grassland fire risk monitoring and early warning. The problem of wireless sensor deployment is considered as deploying a certain number of nodes to meet monitoring needs, that is, finding the number and location of deployed nodes. The goal of solving this problem is to find as few sensors as possible to meet the monitoring requirements and reduce the communication cost. It is transformed into an optimal sensor node solution set, which is an NP-hard problem. The sensor deployment problem has diminishing returns, e.g., submodularity [6; 7; 8]. Initially, when a small number of sensors are deployed, each new sensor will significantly improve its deployment utility. As more sensors are placed, the improvement in utility from adding new sensors diminishes. [PERSON] [9] showed that for problems with submodularity, at least the \((1-1/e)\) approximation of the optimal solution can be obtained using the greedy algorithm. Many methods have been proposed for sensor deployment. In [10], [PERSON] et al. assumed that the node's perception ability is a circular area. That is, targets within the circular area are fully perceived,and targets outside the circular area will not be perceived. In [11], [PERSON] et al. proposed the use of mutual information-based optimization criteria so that the set of deployed nodes contains information about unselected points, and the monitoring is quite accurate. In [12], [PERSON] et al. proposed a Markov random field model to describe the data correlation between sensor nodes. In [9], [PERSON] deployed sensors with a greedy algorithm to maximize the amount of information, but neglecting the influence of the communication distance between nodes. In [13], [PERSON] et al. improved the greedy algorithm and proposed the Padded Sensor Placements at Informative and cost-Effective Locations (pSPIEL) algorithm to solve the problem of sensor deployment optimization under the constraint of communication distance; however, a large number of sensors needed to be deployed. In [14], [PERSON] et al. established a Gaussian model, improved the greedy algorithm under the constraint of fixed costs, and proposed the SUPSUB method to minimize the submodular set function, while neglecting the influence of the communication distance between nodes on the deployment. The sensor placement problem considering communication distance is a constrained optimization problem. The bi-projection neural network proposed by [PERSON] et al. [15] can effectively solve large-scale constrained optimization problems, and has good stability and faster convergence [16]. [PERSON] et al. [17] proposed a ML-OAXSMT-PSO construction algorithm, which can significantly reduce the total cost. During communication transmission, wireless sensors have limited energy, but effective clustering nodes can better save energy and extend the life cycle of the entire network. There are various energy-saving methods. [PERSON] et al. [18] proposed the FTAOA algorithm to minimize task completion time to save node energy. [PERSON] et al. [12] proposed the NSA algorithm to reasonably deploy nodes and significantly improve network lifetime. [PERSON] et al. [19] proposed the KPNS algorithm to appropriately select more active nodes for monitoring, so that the energy is fully utilized. Effective node clustering can greatly save energy and extend the life cycle of the entire network. The LEACH protocol balances the energy of each sensor in the entire network by randomly selecting cluster heads [20]. However, it has the problem of uneven number and distribution of cluster heads [21], for not having considered the transmission distance. This causes either the nodes far away from the base station to be selected as the cluster head or the nodes far away from the cluster head to die prematurely [22].