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Combining regression and mixed-integer programming to model counterinsurgency

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Abstract

Counterinsurgencies are a type of violent struggle between state and non-state actors in which one group attempts to gain or maintain influence over a certain portion of the population. When an insurgency (i.e., non-state actor) challenges a host nation (i.e., state actor), often an external counterinsurgent force intervenes. While researchers have categorized insurgencies with social science techniques and United States Army doctrine has established possible counterinsurgency strategies, little research prescribes host nation and counterinsurgent force strength. To this end, we develop a mixed-integer program to provide an estimate of the number of forces required to maximize the probability of a favorable resolution to the counterinsurgent and host nation countries, while minimizing unfavorable resolutions and the number of counterinsurgent deaths. This program integrates: (i) a multivariate piecewise-linear regression model to estimate the number of counterinsurgent deaths each year and (ii) a logistic regression model to estimate the probability of four types of conflict resolution over a 15-year time horizon. Constraints in the model characterize: (i) upper and lower limits on the number of counterinsurgent and host nation forces and their annual rates of increase and decrease, (ii) the characteristics of the type of counterinsurgency, (iii) an estimation of the number of counterinsurgent deaths, and (iv) an estimation of the probability of one of four resolutions. We use Somalia as a case study to estimate how counterinsurgent strategies affect the probability of obtaining each conflict resolution. We conclude that a strategy focusing on building and empowering a stable host nation force provides the highest probability of achieving a positive resolution to the counterinsurgency. Senior leaders can use this information to guide strategic decisions within a counterinsurgency.

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Acknowledgements

We would like to thank Dr Steven Stoddard from the Center for Army Analysis and Dr Darryl Ahner from the Air Force Institute of Technology for their support on this project.

Funding

This work was funded by the Air Force Institute of Technology’s Center for Operational Analysis (Grant No. FA8601-12-P-0288).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Colorado School of Mines, Golden, CO, 80401, USA

    Marvin L. King, David R. Galbreath & Alexandra M. Newman

  2. Department of Statistical Science, Baylor University, Waco, TX, 97140, USA

    Amanda S. Hering

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  1. Marvin L. King
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Correspondence to Alexandra M. Newman.

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Appendices

Appendix A: Developing the piecewise-linear regression model (\(\mathscr {M}\))

See Tables 4 and 5.

Table 4 Regression results for the piecewise-linear model (\(\mathscr {M}\)) (clusters #1–#4) and the Somalia-specific model (\(\mathscr {M'}\))
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Table 5 Open-source data collected for Somalia
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Appendix B: Developing the logistic regression model (\(\varvec{\mathscr {L}}\))

See Fig. 10 and Table 6.

Fig. 10
figure 10

Plots of the dependent (probability of resolution) against independent variables of the regression for each of the logistic regression models (\(\mathscr {L}\)). Each plot displays the effects of each of the independent variables, and the last plot in each row represents the logistic regression equation including all of the independent variables for the chosen model (listed in Table 6)

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Table 6 Results for the four logistic regression models (\(\mathscr {L}\))
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King, M.L., Galbreath, D.R., Newman, A.M. et al. Combining regression and mixed-integer programming to model counterinsurgency. Ann Oper Res 292, 287–320 (2020). https://doi.org/10.1007/s10479-019-03420-x

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