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On Mathematical Optimization for the visualization of frequencies and adjacencies as rectangular maps

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  • Carrizosa, Emilio
  • Guerrero, Vanesa
  • Romero Morales, Dolores

Abstract

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.

Suggested Citation

  • Carrizosa, Emilio & Guerrero, Vanesa & Romero Morales, Dolores, 2018. "On Mathematical Optimization for the visualization of frequencies and adjacencies as rectangular maps," European Journal of Operational Research, Elsevier, vol. 265(1), pages 290-302.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:1:p:290-302
    DOI: 10.1016/j.ejor.2017.07.023
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    1. Carrizosa, Emilio & Guerrero, Vanesa & Romero Morales, Dolores, 2019. "Visualization of complex dynamic datasets by means of mathematical optimization," Omega, Elsevier, vol. 86(C), pages 125-136.

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