Balanced Allocation of Multi-criteria Geographic Areas by a Genetic Algorithm

  • Shahin Sharifi NoorianEmail author
  • Christian E. Murphy
Conference paper
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


The balanced partitioning of geographic space into regions is a common problem. This Territory Design Problem (TDP) of assigning smaller areas to larger regions with equal potential is a task mainly done manually. Therefore, the result becomes subjective and provides only a roughly approximated balanced result. This work presents an automated allocation of independent areas to regions using the Genetic Algorithm (GA) , which finds an optimally balanced configuration of regions based on multiple criteria. Thereby, spatial constraints are fully respected as (1) all areas remain contiguous within a region and (2) the automated allocation facilitates a compact region shape. The developed algorithm was tested on a case study in the field of sales territory planning. The target of sales territory planning is the optimal distribution of balanced and fair sales areas based on market potentials. Results of our case study demonstrate the effectiveness of our proposed technique to find an optimal structure of sales territories in a reasonable time. The distance that salesmen need to travel is 16% lower than the existing sales territory configuration. This means that the regions are more balanced and more compact. Due to the independent nature of the GA, this method demonstrates a high flexibility to the optimization problem. It can be easily altered to any objective in territory planning as well as to familiar multi-criteria spatial allocation problems in other disciplines.


Territory design problem Combinatorial optimization Graph partitioning Genetic algorithm 



This research was supported by the WIGeoGIS GmbH. We wish to thank WIGeoGIS for kindly providing the case study data. We specially thank Michael Steigemann for insightful discussions in the conception of this work.


  1. Blais, M., Lapierre, S. D., & Laporte, G. (2003). Solving a home-care districting problem in an urban setting. The Journal of the Operational Research Society, 54, 1141–1147.CrossRefGoogle Scholar
  2. Cao, R., Li, G., & Wu, Y. (2007). A self-adaptive evolutionary algorithm for multi-objective optimization. In D.-S. Huang, L. Heutte, & M. Loog (Eds.), Advanced intelligent computing theories and applications with aspects of artificial intelligence (pp. 553–564). Berlin, Heidelberg: Springer.Google Scholar
  3. D’amico, S. J., Wang, S.–J., & Batta, R., et al. (2002). A simulated annealing approach to police district design. Computers & Operations Research, 29, 667–684.Google Scholar
  4. Drexl, A., & Haase, K. (1999). Fast approximation methods for sales force deployment. Management Science, 45, 1307–1323.CrossRefGoogle Scholar
  5. Fogel, D. B. (1995). Phenotypes, genotypes, and operators in evolutionary computation. In Proceedings of 1995 IEEE International Conference on Evolutionary Computation (Vol. 1).Google Scholar
  6. Fonseca, C. M., & Fleming, P. J. (1995). An overview of evolutionary algorithms in multiobjective optimization. Evolutionary Computation, 3, 1–16.CrossRefGoogle Scholar
  7. Gil, P. “What is ‘SaaS’ (Software as a Service)?”. Retrieved June 13, 2016 from
  8. Haase, K., & Müller, S. (2014). Upper and lower bounds for the sales force deployment problem with explicit contiguity constraints. European Journal of Operational Research, 237, 677–689.CrossRefGoogle Scholar
  9. Kalcsics, J., Nickel, S., & Schröder, M. (2005). Towards a unified territorial design approach—Applications, algorithms and GIS integration. Reports of the Fraunhofer Institute for Industrial Mathematics, 71, 1–56.Google Scholar
  10. Kazimipour, B., Li, X., & Qin, A. K. (2014). A review of population initialization techniques for evolutionary algorithms. In 2014 IEEE Congress on Evolutionary Computation (CEC) (pp. 2585–2592).Google Scholar
  11. Luque, G., & Alba, E. (2011). Parallel genetic algorithms: Theory and real world applications (Vol. 367). Springer.Google Scholar
  12. Płuciennik, T., & Płuciennik-Psota, E. (2014). Using graph database in spatial data generation. In D. A. Gruca, T. Czachórski, & S. Kozielski (Eds.), Man-machine interactions 3 (pp. 643–650). Springer International Publishing.Google Scholar
  13. Ríos-Mercado, R. Z., & Fernández, E. (2009). A reactive GRASP for a commercial territory design problem with multiple balancing requirements. Computers & Operations Research, 36, 755–776.CrossRefGoogle Scholar
  14. Schrijver, A. (2003). Combinatorial optimization: Polyhedra and efficiency. Berlin, Heidelberg: Springer.Google Scholar
  15. Sivanandam, S. N., & Deepa, S. N. (2007). Introduction to Genetic Algorithms. Berlin Heidelberg: Springer.Google Scholar
  16. Zoltners, A. A., Sinha, P., & Lorimer, S. E. (2009). Building a winning sales force: Powerful strategies for driving high performance. New York: AMACOM A division of American Management Association.Google Scholar
  17. Zoltners, A. A., & Sinha, P. (1983). Sales territory alignment: A review and model. Management Science, 29, 1237–1256.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Chair of CartographyTechnische Universität MünchenMunichGermany

Personalised recommendations