## 3 Applications to Communication Network Design
### Overview of Selected Papers
#### 3.2.1 Models That Use Straightforwardly Algorithm(s) Dedicated to MOPPs
Paper [169] proposes a multiobjective resilient multipath routing model for transport telecom networks, the aim of which is the simultaneous calculation of an active efficient shortest path seeking to minimize 'load cost' (an additive bandwidth related metric) and hop count and a maximally disjoint protection path; an exact resolution method is described which is based on a \(k\)-shortest path algorithm, applied to the convex combination of the two OFs, enabling all supported and unsupported efficient solutions to be obtained. The work [170] presents a biobjective resilient routing model with path protection leading to the formulation of a biobjective maximally SRLG-disjoint/minimal cost path pair problem the aim of which is to minimize the number of risks, corresponding to SRLGs common to both the active and the protection path, and the path pair cost. An exact resolution method enabling the whole set of Pareto optimal solutions to be calculated, based on the algorithm which combines a path ranking method and path labeling in [111], is described and the performance analyzed in reference test networks. In paper [171], the problem of finding the set of efficient solutions of a MOPP seeking the calculation of paths from one source node to different destination nodes is tackled, for application to cloud computing. The resolution process is based on the extension of a Pareto BFS method proposed in [172], with which it is possible to enumerate all paths from one source node to a destination node and uses a pruning strategy to readily identify the paths which are not efficient. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **\# Objectives** & **Type of Path Problem** & **Resolution Approach** \\ \hline ([PERSON] 2002) [149] & 2 & Multipath; widest–shortest path; most-reliable–shortest path & Lexicographic (a variant of Dijkstra algorithm) \\ ([PERSON] and [PERSON] 2020) [153] & 2 & Shortest–widest path; widest–shortest path & Heuristics based on algebraic framework (a lexicographic approach) \\ ([PERSON] et al., 2016) [154] & 4 & Lexicographic maximally risk–disjoint path pair & Heuristic (based on trap avoidance and weighted sum model) \\  & & Lexicographic maximally risk–disjoint /minimal cost & Exact a priori lexicographic (path ranking and path pair \\  & & path pair & path labeling) \\ ([PERSON] et al., 2021) [158] & \(\geq 2\) & \(k\)-disjoint shortest (most secure) paths & Lexicographic (based on a weighted sum method) \\ ([PERSON] et al., 1999) [162] & 2 & Biobjective shortest paths & Exact a priori (based on a weighted sum method) \\ ([PERSON] et al., 2003) [18] & 2 & QoS constrained biobjective shortest paths & Exact a priori (based on a weighted sum method) \\ ([PERSON] et al., 2006) [41] & 2 & Biobjective path (video traffic) & Exact a priori (based on weighted Chebyshev distance to reference points) \\  & & & Exact (based on a reference point approach using a weighted Chebyshev distance) \\ ([PERSON] and [PERSON] 2006) [164] & 3 & Multiobjective path & Point approach using a weighted Chebyshev distance \\  & & & Metaheuristic (Genetic algorithm) \\ ([PERSON] et al., 2022) [125] & 2 & Biobjective path & Exact a posteriori (uses a dynamic programming procedure) \\  & & & \\  & & & \\ ([PERSON] and [PERSON] 2016) [165] & 2 & \(k\)-time constrained path problem & Exact a priori (uses a weighted sum method) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of some essential features of models that use straightforwardly algorithms dedicated to MOPPs.