The Sectional Art Gallery and an Evolutionary Algorithm for Approaching Its Minimum Point Guard Problem

Abstract

We propose an extension of Art Galleries in Computational Geometry towards a more real world application related definition, well suited for Evolutionary Algorithms. We introduce two additional sections inside the Art Gallery. One section defines locations where guards may be placed in order to cover the Art Gallery. A second section shall be observed by these guards. We show that our definition of a Sectional Art Gallery also includes the Regular Art Gallery as a special case. Furthermore, we present an Evolutionary Algorithm which can approach Minimum Point Guard Problems in such a way, that high quality approximations can be found in Sectional Art Galleries. Our algorithm is influenced by Particle Swarm Optimizers and Particle Filters. Depending on the application, relaxations of the problem can be handled by our algorithm. This way, state of the art methods on optimally solving Minimum Point Guard Problems in Regular Art Galleries can be outperformed by multiple guards, still reaching more than 99.99% of coverage. By running our algorithm on public data sets, we show the effectiveness of our approach in both Regular and Sectional Art Galleries.