A Multiobjective Algorithm for Redistricting

 

E. A. Rincón-García*¹, M. A. Gutiérrez-Andrade,² S. G. de-los-Cobos-Silva,² P. Lara-Velázquez,¹ A. S. Ponsich,¹ R. A. Mora-Gutiérrez³

 

¹ Universidad Autónoma Metropolitana-Azcapotzalco Departamento de Sistemas México, D. F., México. *rigaeral@correo.azc.uam.mx.

² Universidad Autónoma Metropolitana-Iztapalapa Departamento de Ingeniería Eléctrica México, D. F., México.

³ Universidad Nacional Autónoma de México Facultad de ingeniería México, D. F., México.

 

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. In this paper we solve the problem by means of a single objective and a multiobjective simulated annealing algorithm. These algorithms were applied in two real examples in Mexico. The results show that the performance of the multiobjective approach is better, leading to higher quality zones.

Keywords: redistricting, simulated annealing, mutiobjective.

 

RESUMEN

La distritación consiste en modificar los límites de zonas electorales de tal forma que se cumplan los requerimientos federales y estatales tales como conexidad, compacidad y equilibrio poblacional. En este trabajo se utiliza un algoritmo basado en recocido simulado y un algoritmo multiobjetivo basado en recocido simulado para diseñar zonas con dichas características. Ambos algoritmos fueron aplicados a dos estados de México. Los resultados muestran que la técnica multiobjetivo es superior, obteniéndose soluciones de mayor calidad.

 

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References

[1] R.G. González-Ramírez et al., "A Hybrid Metaheuristic Approach to Optimize the Districting Design of a Parcel Company", Journal of Applied Research and Technology, vol. 9, no. 1, pp. 19-35, 2011.         [ Links ]

[2] M. Altman, "Is Automation the Answer: The Computational Complexity of Automated Redistricting", Rutgers Computer and Law Technology Journal, vol. 23, pp. 81-141, 1997.         [ Links ]

[3] K. C. Gilbert et al., "A Multiobjective Discrete Optimization Model for Land Allocation", Management Science, vol. 31, pp. 1509-1522, 1985.         [ Links ]

[4] M. A. Gutiérrez-Andrade and E. A. Rincón-García, "Redistriccting by square cells", LNAI 5845, vol. 5845, pp. 669-679, 2009.         [ Links ]

[5] C. Chou and S. P. Li, "Spin systems and political districting problem", Journal of Magnetism and Magnetic Materials, vol. 310, pp. 2889-2891, 2007.         [ Links ]

[6] H. P. Young, "Measuring the Compactness Of Legislative Districts", Legislative Studies Quarterly, vol. 13, pp. 105-115, 1988.         [ Links ]

[7] R. G. Niemi et al., "Measuring Compactness and the Role of a Compactness Standard in a Test for Partisian and Racial Gerrymandering", Journal of Politics, vol. 52, pp. 1155-1181, 1990.         [ Links ]

[8] S. Kirkpatrick et al., "Optimization by simulated annealing", Science, vol. 220, pp. 671-680, 1983.         [ Links ]

[9] A. Suppapitnarm et al., "Simulated annealing: An alternative approach to true multiobjective optimization", Engineering Optimization, vol. 33, pp.59, 2000.         [ Links ]

[10] L. E. Ulungu et al., "MOSAMethod: A Tool for Solving Multiobjective Combinatorial Optimization Problems", Journal of Multicriteria Decision Analysis, vol. 8, pp. 221-236, 1999.         [ Links ]

[11] S. Balram, "Study of simulated annealing based algorithms for multiobjective optimization of a constrained problem", Computers and Chemical Engineering, vol. 28, pp. 1849-1871, 2004.         [ Links ]