TY - JOUR

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

AU - Carrizosa, Emilio

AU - Guerrero, Vanesa

AU - Romero Morales, Dolores

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 heart. 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 heart. 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

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

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -