Optimizing FSO networks resilient to adverse weather conditions by means of enhanced uncertainty sets

This work deals with dimensioning of wireless mesh networks (WMN) composed of FSO (free space optics) links. Although FSO links realize broadband transmission at low cost, their drawback is sensitivity to adverse weather conditions causing transmission degradation on multiple links. Hence, designing such FSO networks requires an optimization model to find the cheapest configuration of link capacities that will be able to carry an acceptable level of the demanded traffic in all weather states that can be foreseen in network operation. Such a model can be achieved using robust optimization techniques, and for that it is important to find a tractable way of characterizing possible link (capacity) degradation states corresponding to weather conditions not known in advance. In the paper we show how the set of link degradation states may be represented mathematically in a compact and tractable way to be exploited in optimization. To solve this task we will make use of a generalization of a combinatorial problem of finding a minimum hitting set to deduce a compact set approximating a given set of link degradation states, (called uncertainty set). Finally, we provide a mathematical model with respect to a general form of uncertainty sets and illustrate the effectiveness of our model by means of a numerical study.