## 1 Introduction  
With the rapid development of the Internet of Things (IoT) and 4G/5G networks, Wireless Sensor Networks (WSNs) are widely used in many scenarios due to their high degree of flexibility, fault tolerance, autonomy, and rapid deployment [1, 2]. However, the monitoring information of most WSNs is limited to scalar data such as temperature, pressure, vibration, humidity, etc. in the environment, which is, after all, limited and insufficient to support the application of WSNs in more complex scenarios. In contrast, Visual Sensor Networks (VSNs) have the advantages of contactless measurement, rich dimensions of sensory information, and strong anti-interference capability. The VSNs are distributed perception networks that can track targets and achieve wide-area coverage, and they are composed of multiple smart camera nodes. At the moment, VSNs are widely used in surveillance [3, 4], object detection [5], indoor patient monitoring [6], autonomous driving [7], smart city [8] and Unmanned Aerial Vehicles [9, 10]. But the emergence of VSNs also brings with it a number of difficulties. For instance, there are many nodes dispersed extensively throughout the networks, which makes node administration challenging. Additionally, the resources available to camera nodes, such as processing, storage, and network connection bandwidth, are limited, and data synchronization is subpar. Therefore, while building VSNs, variables like sensor number, location, and orientation, i.e., the sensor placement optimization problem, have a significant impact on coverage and can alter the ability of the sensor networks to identify and monitor objects. The original sensor placement research is based on the well-known Art Gallery Problem (AGP), which is concerned with determining the smallest number of guards required to cover the inside of an art gallery room [11; 12]. By adding some special constraints, AGP can be extended into a sensor placement problem. Thus, the art gallery problem is often regarded as the predecessor of the sensor placement problem [13]. Many variable parameters and constraints need to be considered, such as the location constraints of each sensor, the coverage requirements of a specific area, different types of vision sensors, and different sorts of obstacles. Therefore, this type of problem is more complicated than the traditional AGP. A number of studies on sensor coverage optimization have been conducted recently. [PERSON] et al. [14] tackle the camera placement problem based on an inverse modeling taxonomy. [PERSON] et al. [15] suggest a pilot project that uses multiresolution dynamic mode decomposition to determine where PM2.5 sensors should be placed for the best results. In order to address the optimal camera placement problem, [PERSON] [16] suggests a technique based on the Dragonfly Algorithm, which is motivated by the motion and behaviors of artificial objects in the environment. With the use of high-resolution 3D grids as a model, [PERSON] et al. [17] present a multi-resolution technique that makes it possible to apply current optimization algorithms to expansive real-world issues. [PERSON] et al. [18] propose a camera placement method to ensure extensive coverage while maintaining high-quality images and minimizing overlap between cameras. [PERSON] et al. [19] introduce a novel field-of-view model resembling the human eye. They solve the optimization problem of visual sensor placement using a nonlinear programming algorithm. There are two main types of representative discrete optimization algorithms: integer programming and heuristics algorithms. When some or all of the optimization variables are restricted to pure integers, it can be abstracted as an integer programming problem. And if part of the variables are not restricted to integers, this becomes a Mixed Integer Programming (MIP) problem [20]. The binary programming problem is a special case of the integer programming problem [21; 22], in which variables are limited to zero or one. Such a binary problem is common in sensor placement applications.