Inverse optimization is the study of imputing unknown model parameters of an optimization problem using past observed solutions to that problem. In inverse linear programming, recent work uses multiple observations as input, while inverse integer programming has, to date, mostly focused on the case of a single observed data point or the case where a given cost vector needs to be minimally perturbed in order to make observations optimal. In this paper, we propose models to impute objective function coefficients of linear integer optimization problems from multiple integer observations without any prior knowledge of the cost vector. An exact method using an extension of a cutting-plane algorithm from the literature is proposed and compared with an LP-relaxation heuristic method

逆向优化是使用过去观察到的对该问题进行求解的方法，对优化问题的未知模型参数进行估算的研究。在逆线性规划中，最近的工作使用多个观测值作为输入，而迄今为止，逆整数规划主要集中在单个观测数据点的情况下，或者需要最小程度地扰动给定成本向量以使得最佳观察。在本文中，我们提出了从多个整数观测值中推算线性整数优化问题的目标函数系数的模型，而无需对成本向量有任何先验知识。提出了使用文献中的切割平面算法扩展的精确方法，并将其与LP松弛启发式方法进行了比较