## 1 Introduction  
A very important area of the application of shortest path problems in general and multiobjective path problem formulations in particular is telecommunication network design, namely in the context of the development and implementation of advanced routing methods. Routing is a most important network functionality and a key part of network operational design and has strong impacts on network performance both in technical and economic aspects, including the quality of experience of the customers for a given service. Routing methods are essentially focused on the calculation and selection of a loopless path (corresponding to a sequence of network resources or 'route') or a set of loopless paths from an originating node to one or multiple terminating node(s)--assuming that the representation of the communication network is a connected network normally composed of arcs of limited transmission capacity--seeking to optimize one or more objective(s) while satisfying certain constraint(s) of a technical/economic nature. Although routing models and methods deal with a number of issues other than path calculation, we can say that at the heart of any routing method, in any communication network application environment, there is the need to calculate one or more paths seeking to satisfy some optimizing criterion/criteria and relevant technical-economic constraints. Telecommunication networkshave experienced extremely rapid progress in terms of technologies, architectures and provided services, driven by two major forces: technical innovations and accelerated traffic growth, associated with the demand for more advanced services, such as audio, video services, video conferencing and cloud computing. These trends and the need for explicit consideration of different Quality of Service (QoS) metrics (usually of heterogeneous nature) in the routing methods make it necessary or advantageous for the development of routing models where various technic-economic aspects, often conflicting, should be tackled. This has fostered, in recent decades, an increasing interest in the development of multiobjective routing models so that QoS constraints and trade-offs between different objectives could be treated in a consistent manner in mathematical terms. It could be noted that, in many situations, taking into account essential characteristics of the network environment, routing models become more effective if different metrics are explicitly applied by considering an adequate set of optimization objectives rather than just aggregating some of them a priori in a single objective function (OF) and transforming the other OFs into constraints as has often been carried out in Operations Research (OR) application models in this area. There are many applications where there is the need for an a priori aggregation of criteria, namely for on-line routing or for off-line automatized dynamic routing with very short route updating times, but even in these cases, there is a potential advantage in addressing explicitly multicriteria modelling since it enables a deeper insight concerning the persecution of several issues regarding the interplay and possible trade-off between some of the criteria. Thence, it is clear both from an Operations Research and from a network design perspective that it is important to address multiobjective shortest path problems and develop resolution approaches adequate for the envisaged applications in a telecom network routing design which constitutes the major motivation for this work. A state-of-the-art survey on applications of multicriteria decision analysis to telecommunication network design with a section on multicriteria routing methods is in [1], and an overview also with references in this area is included in [2]. A conceptual framework for explicitly multicriteria modelling in QoS-based routing is proposed in [3].