###### Abstract
A universally applicable solution that covers all polygon types remains elusive [4]. The optimization of sensor placement involves several key aspects that shape the approach and solution strategies. These aspects encompass the type of coverage used, the dimensionality of the target environment, sensor detection capabilities and sensor models. The choice of coverage metric has a direct influence on the optimization process. Commonly used metrics include area coverage, point coverage and barrier coverage, each tailored to specific application requirements [11; 12]. In this work, we use area coverage, the most widely used metric, which quantifies the ratio of the area covered by the sensors to the total target area [3; 13; 14; 15; 16]. Based on the AGP mentioned above, it becomes clear that the second aspect of the problem relates to the dimension of the target environment. Environment models, such as voxel-based representations, help to capture the spatial subtleties required for accurate coverage computation. The dimensionality of the target environment model is crucial for accurate sensor placement. While two-dimensional environment models are computationally simple, they can lead to errors due to oversimplified representations. Three-dimensional environment models provide a more accurate representation, but are associated with higher computational costs [17]. In previous research, spaces are often simplified to the level of a floor plan or two-dimensional boundaries [18; 19; 20; 21; 22; 23; 24; 25; 26]. As an improvement of the two-dimensional environment models, three-dimensional models were mostly described with elevation maps [27; 28; 29]. In our previous research, we proposed three-dimensional environment models and a framework for optimizing sensor placement [15; 16]. Throughout this manuscript, both two-dimensional and three-dimensional types of environments will be examined. The detection capabilities of sensors play an important role in optimizing placement. Sensors can have binary or probabilistic sensing ability. The sensing ability of a sensor refers to whether it can perceive an object in the case of binary coverage [19; 20; 21; 22; 23; 24; 25; 26; 29; 30; 31], or how effectively it can perceive it in the case of probabilistic coverage, which provides a more refined model [15; 16; 28; 32; 33]. In addition to detection capability, the shape of the area covered by the sensor is also important. The coverage area of the sensor depends on the sensor type, mainly isotropic or directional [34]. In previous research on sensor placement optimization, various optimization algorithms have been used to improve the efficiency of sensor deployment tailored to specific needs. Early attempts that focused on the placement of binary directional [19] and isotropic sensors [21] in two-dimensional spaces employed techniques such as Integer Linear Programming, Binary Integer Programming, Greedy Search and random arrangement. Advances in optimal placement of binary sensors in two dimensions include methods based on genetic algorithms such as Individual Particle Optimization [13], Particle Swarm Optimization, Binary Genetic Algorithm, Simulated Annealing [27], Improved Cuckoo Search Algorithm and Chaotic Flower Pollination Algorithm [14]. Extending to three-dimensional spaces with height maps, studies compared deterministic methods with the Covariance Matrix Adaptation Evolution Strategy algorithm, the Limited-memory Broyden-Fletcher-Goldfarb-Shanno method and the Gradient Descent [17; 28; 32]. The Covariance Matrix Adaptation Evolution Strategy showed superior performance for smaller height maps, while Gradient Descent was effective for larger maps. Some approaches utilized exhaustive search for optimal placement of sensors to monitor deformation and detect damage in structural systems [35; 36; 37; 38]. In addition, exhaustive search has been used for the ordered placement of nodes in sensor networks.