A Practicable Robust Counterpart Formulation for Decomposable Functions: A Network Congestion Case Study
提出一种新的鲁棒优化公式，解决成本函数非线性且可分解为单决策变量之和时的计算难题，并在电信网络分组路由拥塞问题中验证其优于确定性方法。
Robust optimization is a powerful means to handle optimization problems where there is a set of parameters that are uncertain. The effectiveness of the method is especially noticeable when these parameters are only known to lie inside some uncertainty region. Unfortunately, there are important computational considerations that have prevented the methodology from being fully adopted in fields of practice where the cost function that needs to be robustified is nonlinear with respect to such parameters. In this paper, we propose a new robust optimization formulation that circumvent the computational burden in problems where the cost decomposes as the sum of costs that each involve a single decision variable. This is done by exploiting the fact that in this formulation the worst-case cost function can be expressed as a convex combination between a nominal and an upper-bounding cost function. One can still control the conservatism of the robust solution by adjusting how many terms of this total cost can simultaneously reach their respective most pessimistic value. To demonstrate the potential of this “practicable robust counterpart” formulation, we present how it can be employed for the robust optimization of packet routing on a telecommunication network with congestion. In such problems, an important source of uncertainty stems from the queueing delay, which is usually approximated by a nonlinear convex function using the theory of M/M/1 queues. Computational results on a large number of problem instances of realistic size confirm that it is possible to identify robust solutions that significantly outperform a deterministic approach in terms of both the amount of congestion and the risks of excessive congestion. Moreover, our proposed method also improves significantly the quality of solutions that are obtained using two other natural approximation schemes.