Exploring the Optimal Camera Placement Problem and Its Relationship with the Set Covering Problem

Optimal Camera Placement (OCP) is the process of finding a subset of cameras that either maximises the coverage, such that the cost of cameras is reduced, or minimises the total cost of cameras, such that coverage constraints are satisfied. By adopting the latter formulation, the OCP problem can be formulated as a Set Covering Problem (SCP), as the concepts of the two problems are inherently similar. Until recently, the literature has not explicitly discussed this similarity. Hence, this paper examines the OCP problem by leveraging the formulation established in prior research. Our focus lies in the practical application, as we implement the model on all instances to derive meaningful insights. Furthermore, we explore techniques from the SCP literature that can be applied to address the OCP problem in future studies. In this study, we address 69 problem instances, utilising a benchmark set generated by other researchers. These instances were employed as part of the GECCO 2021 competition on the optimal camera placement problem and the unicost set covering problem. We provide detailed results, and we conclude with recommendations for future research.