A new metaheuristic approach for the art gallery problem

Abstract: In the problem "Localization and trilateration with the minimum number of landmarks", we faced the 3-Guard and classic Art Gallery Problems. The goal of the art gallery problem is to find the minimum number of guards within a simple polygon to observe and protect its entirety. It has many applications in robotics, telecommunications, etc. There are some approaches to handle the art gallery problem that is theoretically NP-hard. This paper offers an efficient method based on the Particle Filter algorithm which solves the most fundamental state of the problem in a nearly optimal manner. The experimental results on the random polygons generated by Bottino et al. \cite{bottino2011nearly} show that the new method is more accurate with fewer or equal guards. Furthermore, we discuss resampling and particle numbers to minimize the run time.