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FUZZY ECONOMIC REVIEW

ISSN (print) 1136-0593 · ISSN (online) 2445-4192

FUGA, A FUZZY GREEDY ALGORITHM FOR REDISTRICTING IN MEXICO

S.G. de-los-Cobos-Silva. Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería Eléctrica. Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, México D.F., C.P. 09340, cobos@xanum.uam.mx

M. A. Gutiérrez-Andrade. Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería Eléctrica. Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, México D.F., C.P. 09340, gamma@xanum.uam.mx

E. A. Rincón-García. Universidad Autónoma Metropolitana-Azcapotzalco, Departamento de Sistemas, Av. San Pablo 180, Colonia Reynosa Tamaulipas, Del. Azcapotzalco, México D.F., C.P. 02200, rigaeral@correo.azc.uam.mx

R. A. Mora-Gutiérrez. Universidad Autónoma Metropolitana-Azcapotzalco, Departamento de Sistemas, Av. San Pablo 180, Colonia Reynosa Tamaulipas, Del. Azcapotzalco, México D.F., C.P. 02200, mgra@correo.azc.uam.mx

P. Lara-Velázquez. Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería Eléctrica. Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, México D.F., C.P. 09340, plara@xanum.uam.mx

A. Ponsich. Universidad Autónoma Metropolitana-Azcapotzalco, Departamento de Sistemas, Av. San Pablo 180, Colonia Reynosa Tamaulipas, Del. Azcapotzalco, México D.F., C.P. 02200, aspo@correo.azc.uam.mx

Abstract

Redistricting is the redrawing of the boundaries of legislative districts for electoral purposes in such a way that the generated districts fulfill federal and state requirements such as contiguity, population equality and compactness. Redistricting is a multi-objective problem which has been proved to be NP-hard. In Mexico, the redistricting process has been done using an aggregation function, considering a weighted sum of the objectives. However, if different weighting factors are used then a set of diverse, high quality solutions can be generated and a new problem arises: which solution should be implemented? In this paper we propose a novel alternative, called FuGA, to select the best solution for the redistricting problem using a fuzzyfication of the objective function. The proposed algorithm was applied in a real case, and its solutions were compared with those produced by VIKOR, a well-known algorithm for decision making. FuGA showed a better performance since it was able to avoid the selection of dominated solutions.

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