Bicriterion shortest hyperpaths in random time‐dependent networks

In relevant application areas, such as transportation and telecommunications, there has recently been a growing focus on dynamic networks, where arc lengths are represented by time-dependent discrete random variables. In such networks, an optimal routing policy does not necessarily correspond to a path, but rather to an adaptive strategy. Finding an optimal strategy reduces to a shortest hyperpath problem that can be solved quite efficiently. Bicriterion shortest path problems have been extensively studied for many years. Recently, extensions to dynamic networks have been investigated. However, no attempt has been made to study bicriterion strategies. This is the aim of this paper. Here we model bicriterion strategy problems in terms of bicriterion shortest hyperpaths. For several problems arising in this context, optimal solutions can be found quite efficiently. Moreover, the general problem of listing efficient strategies can be successfully dealt with by means of heuristic methods. A computational experience is reported, where we consider several variants of the above problems. Finally, the relevant features of the bicriterion hyperpath model are discussed and compared to the classical bicriterion path approach.