## 3 Applications to Communication Network Design
### Overview of Selected Papers
#### 3.2.1 Models That Use Straightforwardly Algorithm(s) Dedicated to MOPPs
A reference point approach to the important problem of selecting a Pareto optimal solution in the context of a multiobjective shortest path model for a network routing model, considering that the final routing solution has to be defined in an automated manner was presented in [41]. That proposal, in [41], uses an algorithm for minimizing a weighted Chebyshev distance to reference points specified in each priority region; this method is applied to a biobjective video traffic routing problem formulated as a BOPP with various QoS constraints. A multiobjective routing model for the Internet using a multiobjective path formulation is presented in [164]; the model uses as path metrics number of arcs, total mean delay and residual bandwidth, and it is solved by an exact algorithm that obtains the set of efficient solutions for connections from one node to all the other nodes and a method for selecting a solution that uses a weighted Chebyshev distance to the ideal point. In [125], a multiobjective shortest path problem is also formulated, for application to a QoS routing model, that considers the metrics optimized maximal bandwidth and minimal delay. The MOPP is solved by a genetic algorithm. The authors in [165] address a new multiciteria approach for routing in IP-based networks using the principle of \"routing-as-a-service\" such that users/companies may choose from a set of 'path services' offered by various network providers competing in an \"open marketplace\". This leads to a routing model where paths are calculated and chosen dynamically from a biobjective time-constrained path problem seeking to optimize cost and expected delay under QoS and time-constrained requirements. The resolution method is a dynamic programming procedure that uses [PERSON]'s \(k\)-shortest path algorithm [73], enabling us to obtain efficient solutions for a given time interval partition, one to be chosen by the customer. A key path problem in WDM optical network routing is the Route and Wavelength Assignment (RWA) problem which involves, in general, the calculation of lightpaths (topological paths in the optical transport networks) and the assignment of wavelengths to each arc (optical link) along a lightpath (a classic overview in this area is [166]). The work in [167] addresses a formulation of this problem as a multiobjective shortest path problem where the OFs are the number of arcs (optical links), the number of free wavelengths and the path blocking probability. Solutions are obtained with a shortest path algorithm applied to the weighted sum of the objective functions. In [168], there is the development of a biobjective path problem formulation for a RWA problem designated as dynamic lightpath establishment problem with incremental traffic with regards to the topological lightpath calculation subproblem. The first objective function is additive and expressed in the bandwidth usage of the path arcs, and the second is the number of arcs (or 'hops'), both to be minimized. The exact resolution approach of this key subproblem uses a \(k\)-shortest path algorithm and preference thresholds for defining preference regions in the OFs space. The used topological lightpath is selected automatically by using a reference point procedure as in [41]. The choice of wavelengths along the lightpath is performed by a heuristic based on path wavelength bottleneck bandwidth. The OFs considered in the first level are path costs and the number of arcs of the path, and the second level OFs are bottleneck bandwidth and the expected packet delay on the path. The model is solved exactly by calculating the Pareto optimal solutions of the first-level functions with an exact biobjective shortest path algorithm, which are \"filtered\" by using bounds defined through the second-level OFs. Next, we will refer to applications of MOPP algorithms to _multipath routing models_.