In this paper we address the problem of visualizing a frequency distribution and an adjacency relation attached to a set of individuals. We represent this information using a rectangular map, i.e., a subdivision of a rectangle into rectangular portions so that each portion is associated with one individual, their areas reflect the frequencies, and the adjacencies between portions represent the adjacencies between the individuals. Due to the impossibility of satisfying both area and adjacency requirements, our aim is to fit as well as possible the areas, while representing as many adjacent individuals as adjacent rectangular portions as possible and adding as few false adjacencies, i.e., adjacencies between rectangular portions corresponding to non-adjacent individuals, as possible. We formulate this visualization problem as a Mixed Integer Linear Programming (MILP) model. We propose a matheuristic that has this MILP model at its core. Our experimental results demonstrate that our matheuristic provides rectangular maps with a good fit in both the frequency distribution and the adjacency relation.

Publication information

Original languageEnglish
JournalEuropean Journal of Operational Research
Number of pages26
StatePublished - 13 Jul 2017

Bibliographical note

Epub ahead of print. Published online: 13. July 2017


  • Mixed integer linear programming, Visualization, Multidimensional scaling, Rectangular maps, Frequencies and adjacencies

ID: 46834574