## 2 Literature Review  
The camera placement problem is closely related to the art gallery problem (AGP), which is the problem of determining the minimum number of guards required to cover the interior of an art gallery [5]. The AGP assumes that all guards have similar capabilities and unlimited visibility, which implies an infinite visual distance. However, realistically, the visibility of a camera is limited by its visual distance and visual angle, and a camera placement problem with identical cameras rarely exists. Furthermore, various constraints, including various types of cameras having different specifications and occlusions, further complicate the camera placement problem, where even a three-dimensional AGP is NP-hard [6]. Table 1 summarizes the existing literature on this problem, which it categorizes by space, objective function, and the approach of the solution. In terms of objective functions, the maximization of coverage has been widely studied and many solution approaches have been suggested [2; 3; 4; 7; 8; 9; 11; 12; 13; 14; 15; 16]. Furthermore, multi-objective problems, including maximizing coverage and visibility while minimizing the total cost, have been studied [10; 11]. However, the camera placement problems with an objective of maximizing coverage under a cost constraint or minimizing cost under a coverage constraint in multi-camera systems are usually far less studied [18]. With respect to solution approaches to the camera placement problem, mathematical approaches have achieved better performances than other heuristic methods. [PERSON] and [PERSON] [8] formulated a problem for effective camera locations in 2D space. They proposed binary integer programming (BIP) to minimize the cost of sensors to completely cover the sensor field. However, even though optimization software capable of solving BIP problems exists, the extremely long calculation time needed for larger problems makes it impractical to obtain an exact solution for any reasonable-sized camera placement problem. For this reason, heuristic or meta-heuristic algorithms have been applied to obtain good solutions within a reasonable amount of time. [PERSON] and [PERSON] [2] proposed a greedy algorithm and dual sampling algorithm to maximize the coverage provided by a given number of cameras and minimize the total price of the sensor array. [PERSON] et al. [10] developed a greedy algorithm based on an image-based model for the automatic camera placement problem in 3D space. To maximize the weighted coverage, [PERSON] et al. [15] proposed a collaboration-based local search algorithm (COLSA) for the camera placement problem in 3D space. In particular, evolutionary algorithms, including particle swarm optimization (PSO), simulated annealing (SA), and the genetic algorithm (GA), have been widely used to solve the camera placement problems. To maximize weighted coverage for different sub-regions, [PERSON] et al. proposed a novel coverage-enhancement algorithm that included an occlusion-free surveillance model based on GA [9]. [PERSON] et al. [17] proposed a binary particle swarm optimization (BPSO) algorithm to solve the camera network placement problem based on simulation results for 2D and 3D scenarios. [PERSON] et al. also proposed a 3D directional-sensor coverage-control model with tunable orientations, and they developed an SA-based algorithm to enhance area coverage. [PERSON] et al. [10] compared the use of the non-dominated sorting genetic algorithm (NSGA-II) and the covariance matrix adaptation-evolution strategy (CMA-ES) to address the multi-objective sensor placement problem. In addition to solution approaches, various constraints have been studied, including PTZ cameras and occlusions. [PERSON] et al. [19] addressed the camera placement problem by using various cameras