Constrained shortest path problems: state-of-the-art and recent advances

Constrained shortest path problems are special shortest path problems with additional constraints imposed on a path to be considered feasible. There are many possible variants of additional constraints that can be imposed. For example, the solution path can be constrained to cross or to avoid a given subset of nodes and/or to cross a given number of nodes and/or to involve nodes within a given covering distance of every node in the network, and so on. Useless to say that constrained shortest path problems arise in many real-life applications, ranging from railroad management, military aircraft management systems, and routing in road networks to scheduling problems. This paper presents a brief introduction to some constrained shortest path problems with special attention to the resource constrained version, the most studied variant. The problem is mathematically formulated and its properties analyzed. The most popular solution techniques are surveyed.