Multicast transmissions in coded wireless packet networks can be affected by uncertain factors such as the distance between nodes. We develop a robust optimization method to minimize the energy consumption of such multicasts. We therefore consider the distances to belong to closed convex uncertainty sets. As solution, we select the optimum in the worst case over these uncertainty sets. We prove that the complexity of obtaining this robust solution is similar to that of determining a solution of the problem without uncertainty. Numerical results show that the proposed solution significantly reduces the energy consumption of a multicast connection and that it can be obtained quickly enough for practical applications. Compared with the optimal solution of the deterministic problem, the robust results only exhibit a small performance loss, even if the size of the uncertainty set is notably large.

编码无线分组网络中的组播传输可能会受到诸如节点之间的距离等不确定因素的影响。我们开发了一种强大的优化方法来最大限度地减少此类多播的能耗。因此，我们认为距离属于闭凸不确定性集。作为解决方案，我们在这些不确定性集上选择最坏情况下的最优方案。我们证明，获得这种鲁棒解决方案的复杂性与确定问题的无不确定性的解决方案的复杂性相似。数值结果表明，所提出的解决方案显着降低了多播连接的能耗，并且可以足够快地获得实际应用。与确定性问题的最优解相比，鲁棒结果仅表现出很小的性能损失，