Robust optimization for minimizing energy consumption of multicast transmissions in coded wireless packet networks under distance uncertainty

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.