## 1 Introduction  
Wireless sensor networks (WSNs), which contain with operation-driven sensors in wireless networks, reveal a major system of wireless environments for many application systems in the modern world, such as solar systems [1], mobile systems [2], railway systems [3], agricultural systems [4], 3-D camera systems [5], traffic systems [6], Internet of Things (IoT) [7], smart cities [8], and body sensing systems [9]. Because of their greater flexibility and efficiency over wired networks [10, 11, 12, 13, 14], sensors are deployed, operated, and embedded widely in devices, buildings, vehicles, and other items to model, gather, sense, investigate, and exchange data; to interconnect objects; and to improve production efficiency and offer more efficient resource consumption [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14]. The sensing coverage problem is one of the fundamental issues in wireless sensor networks, which is a kind of tool used to measure the quality of service (QoS). Coverage in wireless sensor networks refers to the extent of the area to which the wireless signals are transmitted. Thus, the sensing coverage problem has attracted much research investment in recent years. For example, [PERSON] and [PERSON] optimized the sensing coverage by the deployment of sensing nodes using the machine learning method in radio networks in 2019 [15], [PERSON] and [PERSON] enhanced the sensing coverage by finding the sensing coverage holes using the chord-based hole covering approach in 2020 [16]. [PERSON] et al. addressed sensing coverage by the detection of sensing coverage using the reactive real-time control method for unmanned aerial vehicles in 2020 [17]. [PERSON] et al. optimized the sensing coverage using a reciprocal decision approach for unmanned aerial vehicles in 2018 [18]. [PERSON] et al. maximized the sensing coverage and minimized the distance of objective nodes and the sensor nodes by the deployment of nodes using a non-dominated method in 2021 [19], and [PERSON] et al. targeted coverage by a routing design with minimized costs in WSN [20]. The increase in the sensing coverage rate requires considerable investment. However, most sensing coverage studies have seldom discussed the cost limitation. Therefore, how to maximize the sensing coverage rate within the budget limitation is an important research topic, which is the subject of this work. Research on coverage enhancing, either comprehensive coverage-enhancing studies or the k-coverage over the years, shows that sensor deployment is a very effective method. Therefore, numerous studies have used the sensor deployment strategy to optimize the coverage in WSNs [21; 22; 23; 24; 25; 26]. For example, [PERSON] and [PERSON] aimed to optimize sensor coverage by planning the sensor deployment in mobile WSNs [21]. [PERSON] and [PERSON] investigated sensor deployment via planning of the optimal locations to place sensors to maximize the sensor coverage with consideration of cost by a harmony search approach in WSNs [22]. [PERSON] deployed the minimum number of sensors to achieve optimal sensor coverage under cost limitation in a transport WSN [23]. [PERSON] and [PERSON] maximized the sensor coverage by planning an optimal strategy of sensor deployment in a WSN [24]. [PERSON] et al. focused on optimizing a decided area of sensor coverage, i.e., k-coverage, by sensor deployment planning under limited energy in a WSN [25]. [PERSON] et al. guaranteed a predefined range of coverage, such as Q-coverage, by the sensor deployment strategy with an energy constraint using the greedy heuristic method in a WSN [26]. To achieve enhanced coverage by the sensor deployment approach, perfect sensor planning is necessary. However, one of the challenges is planning sensor deployment to maximize coverage if the required number of sensors is known and fixed. For some unstructured WSN types, such as battleground monitoring and plantation administering, it is impossible to plan the sensor deployment.