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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结合回归和混合整数规划来模拟反叛乱

反叛乱是国家和非国家行为者之间的一种暴力斗争，其中一个团体试图获得或维持对特定人口的影响。当叛乱（即非国家行为者）挑战东道国（即国家行为者）时，通常会有外部反叛乱力量进行干预。虽然研究人员用社会科学技术对叛乱进行了分类，并且美国陆军条令已经建立了可能的反叛乱战略，但很少有研究规定东道国和反叛乱的力量。为此，我们制定了一个混合整数计划，以提供对最大限度地提高对反叛乱国家和东道国有利解决方案的可能性所需的部队数量的估计，同时尽量减少不利的决议和反叛乱的死亡人数。该程序集成了：(i) 多元分段线性回归模型，用于估计每年的反叛乱死亡人数；(ii) 逻辑回归模型，用于估计 15 年时间范围内四种类型的冲突解决的概率。模型中的约束表征：(i) 反叛乱和东道国部队数量的上限和下限及其年增减率，(ii) 反叛乱类型的特征，(iii) 数量估计反叛乱死亡人数，以及 (iv) 对四种决议之一的可能性的估计。我们使用索马里作为案例研究来估计反叛乱策略如何影响获得每个冲突解决方案的可能性。我们得出的结论是，专注于建立和增强稳定的东道国军队的战略最有可能实现积极解决反叛乱的问题。高级领导人可以使用这些信息来指导反叛乱中的战略决策。