A comparison of solution strategies for biobjective shortest path problems

We consider the biobjective shortest path (BSP) problem as the natural extension of the single objective shortest path problem. BSP problems arise in various applications where networks usually consist of large numbers of nodes and arcs. Since obtaining the set of efficient solutions to a BSP problem is more difficult (i.e. NP-hard and intractable) than solving the corresponding single objective problem there is a need for fast solution techniques. Our aim is to compare different strategies for solving the BSP problem. We consider a standard label correcting method, a purely enumerative near shortest path approach, and the two phase method, investigating different approaches to solving problems arising in phase 1 and phase 2. In particular, we propose to combine the two phase method with ranking in phase 2. In order to compare the different approaches, we investigate their performance on three different types of networks. We employ grid networks and random networks, as is generally done in the literature. Furthermore, road networks are utilized to compare performance on networks with a structure that is more likely to actually arise in applications.