In this study, we discuss and develop a distributionally robust joint chance-constrained optimization model and apply it for the shortest path problem under resource uncertainty. In sch a case, robust chance constraints are approximated by constraints that can be reformulated using convex programming. Since the issue we are discussing here is of the multi-resource type, the resource related to cost is deterministic; however, we consider a robust set for other resources where covariance and mean are known. Thus, the chance-constrained problem can be expressed in terms of a cone constraint. In addition, since our problem is joint chance-constrained optimization, we can use Bonferroni approximation to divide the problem into L separate problems in order to build convex approximations of distributionally robust joint chance constraints. Finally, numerical results are presented to illustrate the rigidity of the bounds and the value of the distributionally robust approach.

在这项研究中，我们讨论并开发了一个分布鲁棒的联合机会受限的优化模型，并将其应用于资源不确定性下的最短路径问题。在这种情况下，鲁棒的机会约束由可以使用凸规划重新制定的约束近似。由于我们在此讨论的问题属于多资源类型，因此与成本相关的资源是确定性的；但是，对于考虑协方差和均值的其他资源，我们考虑使用一个健壮的集合。因此，机会约束问题可以用圆锥约束表示。另外，由于我们的问题是联合机会约束优化，因此我们可以使用Bonferroni逼近将问题分为L个独立问题，以建立分布鲁棒的联合机会约束的凸近似。最后，