We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex conic programs, and its important special case of distributionally-robust two-stage stochastic mixed-integer second order conic programs. This generalizes the algorithm proposed by Sen and Sherali [Mathematical Programming 106(2): 203–223, 2006]. We show that the proposed algorithm is finitely convergent if the second-stage problems are solved to optimality at incumbent first stage solutions, and solution to an optimization problem to identify worst-case probability distribution is available. The second stage problems can be solved using a branch and cut algorithm, or a parametric cuts based algorithm presented in this paper. The decomposition algorithm is illustrated with an example. Computational results on a stochastic programming generalization of a facility location problem show significant solution time improvements from the proposed approach. Solutions for many models that are intractable for an extensive form formulation become possible. Computational results also show that for the same amount of computational effort the optimality gaps for distributionally robust instances and their stochastic programming counterpart are similar.

我们为分布鲁棒的两阶段随机混合整数凸圆锥程序开发了一种分解算法，以及分布鲁棒的两阶段随机混合整数二阶圆锥程序的重要特例。这概括了 Sen 和 Sherali [Mathematical Programming 106(2): 203–223, 2006] 提出的算法。我们表明，如果在现有的第一阶段解决方案中将第二阶段问题求解为最优，则所提出的算法是有限收敛的，并且可以使用优化问题的解决方案来识别最坏情况的概率分布。第二阶段的问题可以使用分支和切割算法或本文提出的基于参数切割的算法来解决。分解算法举例说明。设施位置问题的随机规划泛化的计算结果表明，所提出的方法显着改善了求解时间。许多模型难以处理广泛的形式公式的解决方案成为可能。计算结果还表明，对于相同数量的计算工作，分布鲁棒的实例和它们的随机编程对应物的最优性差距是相似的。