### Abstract

Language | English |
---|---|

Journal | European Journal of Operational Research |

Volume | 265 |

Issue number | 1 |

Pages | 290-302 |

Number of pages | 13 |

ISSN | 0377-2217 |

DOIs | |

State | Published - 2018 |

### Bibliographical note

Published online: 13. July 2017

### Keywords

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

### Cite this

*European Journal of Operational Research*,

*265*(1), 290-302. DOI: 10.1016/j.ejor.2017.07.023

}

*European Journal of Operational Research*, vol. 265, no. 1, pp. 290-302. DOI: 10.1016/j.ejor.2017.07.023

**On Mathematical Optimization for the Visualization of Frequencies and Adjacencies as Rectangular Maps.** / Carrizosa, Emilio; Guerrero, Vanesa; Morales, Dolores Romero.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - On Mathematical Optimization for the Visualization of Frequencies and Adjacencies as Rectangular Maps

AU - Carrizosa,Emilio

AU - Guerrero,Vanesa

AU - Morales,Dolores Romero

N1 - Published online: 13. July 2017

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Mixed integer linear programming

KW - Visualization

KW - Multidimensional scaling

KW - Rectangular maps

KW - Frequencies and adjacencies

KW - Mixed integer linear programming

KW - Visualization

KW - Multidimensional scaling

KW - Rectangular maps

KW - Frequencies and adjacencies

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U2 - 10.1016/j.ejor.2017.07.023

DO - 10.1016/j.ejor.2017.07.023

M3 - Journal article

VL - 265

SP - 290

EP - 302

JO - European Journal of Operational Research

T2 - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -