The repeated p-dispersion problem

Abstract

The grey pattern problem is to select a pattern of p points in a square that is replicated in adjacent squares so that they are spread out as uniformly as possible. The goal is to cover a large area with many squares of the same pattern of p points. In the original formulation a special objective function is designed. In this paper we suggest the criterion of maximizing the minimum distance between points in the same square and in the eight adjacent squares, four with a common side and four with a common vertex. We prove properties of the proposed objective, and propose alternate formulations of the model. Extensive computational experiments are reported on instances using Euclidean distances and Manhattan distances with good results.