## 3 Applications to Communication Network Design
### Overview of Selected Papers
#### 3.2.1 Models That Use Straightforwardly Algorithm(s) Dedicated to MOPPs  
Herein, we refer to representative papers on routing models that use primary resolution method algorithm(s) specifically dedicated to the calculation of solutions to MOPPs, including heuristics and metaheuristics. A summary of some essential features of these models is in Table 4.  
In the review on QoS routing models [150], lexicographic formulations of related path problems are addressed, such that there is an a priori articulation of preferences in the path selection (including as optimization objectives bandwidth, delay and number of arcs (or 'hop count')) in the context of widest-shortest (where one seeks a path of maximal bottleneck bandwidth (or width) among those of minimal length from source to destination) and shortest-widest path formulations (where the aim is to find a shortest path among those of maximal bottleneck bandwidth (or 'width')). This type of lexicographic formulation was also addressed in [149], namely concerning widest-shortest path and most-reliable shortest path problems, by proposing the use of an algebra of weights. Paper [153] addresses techniques based on the derivation of partial order rules for implementation of state-vector routing protocols aimed at seeking lexicographic optimal path solutions in IP-based networks, associated with computation procedures based on shortest path algorithms. These mathematically based procedures are shown to be very useful for efficient heuristic lexicographic routing protocol implementations--designated as 'dominant paths vectoring protocols'--namely, for widest-shortest path routing. An example of an efficient combinatorial heuristic resolution for a lexicographic path pair optimization problem with maximal disjointness objectives for application to a resilient routing model in optical GMPLS networks involving the calculation of an active and a protection path (to be used in the event of failure of the active path) can be seen in [154]; the four OFs to be minimized (in this order of priority) are the number of common nodes, the number of common arcs, the number of common failure risks and the total cost of the two paths. The two proposed heuristics are based on extensions of the 'Trap avoidance' algorithm [155] and of the 'weighted Shared Risk Link Group (SRLG) path selection' algorithm [156]. A closely related lexicographic approach for resilient routing in optical networks is in [157] that addresses a biobjective lexicographic formulation of the protection routing path pair problem which involves the calculation of an active path and a protection path seeking to minimize the number of risks (corresponding to SRLGs) common to the two paths and the two paths cost (in terms of occupied bandwidths). An exact resolution algorithm which combines a path ranking procedure (using the \(k\)-shortest path algorithm [71]) and a path labeling algorithm is proposed and compared with an ILP formulation in reference test networks. Paper [158] tackles a problem of multiobjective \(k\)-disjoint shortest (secure) paths, where the \"length\" of an edge is associated with information regarding the probability of attacks in a communication network. The multiple \"lengths\" of each edge are converted into a single \"length\" given by a weighted sum of \"lengths\", where the weight for each criterion depends on the importance assigned to that specific criterion. The weights are defined in very distinct ranges, leading to a lexicographic approach. A generalization of the Dijkstra algorithm is used to devise prioritized multicriteria \(k\)-shortest (secure) paths. For the specific value of \(k=2\), a prioritized multicriteria 2-disjoint (node/edge) shortest paths problem is proposed and solved by an approach based on the dynamic programming (DP) approach proposed in [159].