## 1 Introduction
The basic idea behind SDN is the separation between the network control logic and the underlying devices that implement the forwarding of traffic flows, this being achieved by the direct control of specific types of hardware devices by using common management interfaces. This is an important development in a wider trend directed to the'softwarization' of key network functionalities, based on the concept of separation of the functions of the control plane (where the 'intelligence' of the routing mechanism is located) from the data/message transport plane. Another area where extremely rapid progresses occurred is mobile networks, driven by the exponential increase in the demand for mobile data and video services, including fast Internet access, associated with the spread of fifth-generation (5G) networks, providing important quantitative and qualitative advancements in terms of bandwidth access (enabling new and better QoS data streaming services) and transmission latency (with more stringent requirements for real-time services). Also, the development of specialized IP-based local wireless networks, namely Wireless Sensor Networks (WSNs) and ad hoc wireless networks (ad hoc WNs), pose specific requirements and limitations to the routing models, resulting from the fully distributed nature of the routing control and the limited capacities of the routers in terms of available network information. In Section 3 of this paper, we outline background concepts related to telecom network routing models and present an overview of selected papers considered as representative of different types of applications of multiobjective path problem (MOPP) formulations and algorithms. A broad characterization of major types of path problems relevant to telecom routing models, namely single path, path pair and multipath problems (and their main variants) will be mentioned, in the context of the overview of contributions concerning different technological and architectural network environments. Representative examples of routing models for application in various network environments that involve the formulation of MOPPs will be addressed, focusing on the essential features of the routing model and of the associated MOPP and the resolution approaches that are either exact or approximate. Concerning the types of approaches used for tackling MOPPs in the context of this overview of routing models, we distinguish those that use a primary resolution procedure algorithm(s) specifically dedicated to the calculation of solutions to MOPPs, including heuristics and metaheuristics, from those which use instrumentally, as auxiliary resolution procedures, MOPP-dedicated algorithm(s), including shortest path and \(k\)-shortest path algorithms. A further distinction will be made by considering a third type of model that involved explicitly, as an objective of the mathematical formulation, the calculation of paths that are solutions to MOPPs by recurring to OR approaches which are not specifically dedicated to path problems, such as network flow, integer linear programming (ILP), mixed integer linear programming (MILP), non-linear programming (NLP) and other more general types of network optimization approaches. The models of the two latter types appear frequently in routing methods where the route/path calculation and selection cannot be mathematically separated from the assignment of node-to-node traffic flows to the selected paths, which happens in all models for which the routing method embodies a teletraffic engineering mechanism. Typical examples are models with traffic splitting, where each node-to-node offered bandwidth can be divided by several paths, models in circuit-switched networks with alternative routing (where a primary route/path and an alternative route are calculated such that the alternative route is used whenever the primary route is blocked) and routing models for GMPLS-based networks using the Resource Reservation Protocol--Traffic Engineering (RSVP-TE) routing protocol.