Environmental and Ecological Statistics

, Volume 22, Issue 2, pp 369–391 | Cite as

Multi-objective dynamic programming for spatial cluster detection

  • Gladston J. P. Moreira
  • Luís Paquete
  • Luiz H. Duczmal
  • David Menotti
  • Ricardo H. C. Takahashi


The detection and inference of arbitrarily shaped spatial clusters in aggregated geographical areas is described here as a multi-objective combinatorial optimization problem. A multi-objective dynamic programming algorithm, the Geo Dynamic Scan, is proposed for this formulation, finding a collection of Pareto-optimal solutions. It takes into account the geographical proximity between areas, thus allowing a disconnected subset of aggregated areas to be included in the efficient solutions set. It is shown that the collection of efficient solutions generated by this approach contains all the solutions maximizing the spatial scan statistic. The plurality of the efficient solutions set is potentially useful to analyze variations of the most likely cluster and to investigate covariates. Numerical simulations are conducted to evaluate the algorithm. A study case with Chagas’ disease clusters in Brazil is presented, with covariate analysis showing strong correlation of disease occurrence with environmental data.


Arbitrarily shaped spatial cluster Chagas’ disease Dynamic programming Multi-objective optimization Spatial scan statistic 



The authors thank the Editor and Reviewers for their thoughtful comments. This work was found by Brazilian agencies CNPq, Fapemig and CAPES, and partially supported by iCIS (CENTRO-07-ST24-FEDER-002003).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Gladston J. P. Moreira
    • 1
  • Luís Paquete
    • 2
  • Luiz H. Duczmal
    • 3
  • David Menotti
    • 1
  • Ricardo H. C. Takahashi
    • 4
  1. 1.Department of ComputingUniversidade Federal de Ouro PretoOuro PretoBrazil
  2. 2.CISUC, Department of Informatics EngineeringUniversity of CoimbraCoimbraPortugal
  3. 3.Department of StatisticsUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  4. 4.Department of MathematicsUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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