## 3 Applications to Communication Network Design
### Overview of Selected Papers
#### 3.2.3 Models That Include the Resolution of MOPPs by Non-Dedicated Path Approaches
A very particular constrained multipath lexicographic path problem is addressed in [190], aiming at minimizing the number of active paths with the maximal number of arcs in a resilient routing model where active and backup paths (to be used in the event of failure of service path(s)) have to be calculated simultaneously, all with a bounded number of arcs; ILP formulations are used for obtaining exact solutions. In [191], a specific biobjective path-related problem in packet-switched Software Defined Networks is formulated. The first objective is the minimization of the consumption of the sum of the energy of the switches, the active controllers and the active links. The second objective is the minimization of the sum of all the delays between the active switches and the respective domain controller. An ILP is formulated aiming at the calculation of (i) whether a switch, a controller or a link should be on or off; (ii) whether a path is active; and (iii) which controller should a switch be linked to. A weighted sum method is used for solving the problem and compared with two heuristic procedures. A 'critical disruption path problem' involves the identification of the loopless paths for a source-destination pair, such that their removal will maximize the disruption of the network, in terms of operability. A multiobjective formulation of this problem is proposed in [126]. Considering an induced subgraph obtained when a path is deleted, the tackled problem aims at the minimization of the size of the largest connected component, the maximization of the number of connected components and the minimization of the cost of the disruption path. A MILP formulation is presented, and an evolutionary metaheuristic resolution approach consisting of a hybrid algorithm including modified-NSGA-II and Variable Neighborhood Search (VNS) is used to find an approximation to the Pareto front. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Reference** & **\# Objectives** & **Type of Model** & **Resolution Approach** \\ \hline ([PERSON] and [PERSON] 2001) [178] & 4 & Multiobjective disjoint path pair routing & MILP solved with iterative heuristic \\ ([PERSON] and [PERSON] 2003) [134] & 2 & Biobjective constrained routing & Integer multicommodity flow solved with heuristic (GRASP) \\ ([PERSON] et al., 2013) [124] & 3 & Multiobjective constrained routing & Metaheuristic: genetic algorithm VN-MGA (based on NSGA-II) \\ ([PERSON] 2003) [179] & 3 & Multiobjective routing with traffic splitting & Metaheuristic: evolutionary algorithm \\  & & Hierarchical stochastic & Metaheuristics: simulated annealing; tabu-search \\ ([PERSON] et al., 2009) [120] & 2 & biobjective constrained routing & MILP solved by exact approach based on a modified constraint method \\  & & & MILP solved by exact approach based on a modified constraint method \\  & & & MILP solved by exact approach based on a modified constraint method and a \(k\)-shortest path algorithm \\ ([PERSON] and [PERSON] 2006) [183] & 3 & Multiobjective routing & Heuristic using a specific utility function \\ ([PERSON] et al., 2009) [184] & 2 & Biobjective constrained dynamic distributed routing & ILP solved by a heuristic \\ ([PERSON] et al., 2014; [PERSON] et al., 2015; [PERSON] et al., 2015; [PERSON] et al., 2017) [185; 186; 187; 188] & 3 & Multiobjective constrained dynamic distributed routing & Heuristics using a multiattribute utility function \\ ([PERSON] et al., 2016) [190] & \(k\) & Lexicographic multipath routing with path protection & ILP solved by exact lexicographic approach \\ ([PERSON] et al., 2021) [191] & 2 & Specific biobjective path related model & ILP solved by a weighted sum method or by heuristics \\ ([PERSON] and [PERSON] 2023) [126] & 3 & Multiobjective critical disruption path model & MILP solved by evolutionary metaheuristic \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of some essential features of models that include the resolution of MOPPs by non-dedicated path approaches.