On Mathematical Optimization for the Visualization of Frequencies and Adjacencies as Rectangular Maps

Emilio Carrizosa, Vanesa Guerrero, Dolores Romero Morales

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Abstrakt

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 heart. Our experimental results demonstrate that our matheuristic provides rectangular maps with a good fit in both the frequency distribution and the adjacency relation.

OriginalsprogEngelsk
TidsskriftEuropean Journal of Operational Research
Vol/bind265
Udgave nummer1
Sider (fra-til)290-302
Antal sider13
ISSN0377-2217
DOI
StatusUdgivet - 2018

Bibliografisk note

Published online: 13. July 2017

Emneord

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

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