## 2 Related Work
[48] describe three main alternative route computing strategies:  
* Edge-penalty, where link weights are incremented iteratively for each shortest path found until k paths are found [43; 49; 50; 51]. * Using link plateaus formed by the intersections of the k-shortest paths obtained from direct and reverse routing from source to destination. Alternative paths are obtained routing from the source and destination to the plateaus [52; 53]. * Path disjoint level (dissimilarity), where semi-disjoint k-shortest paths (Dj-kSP) are obtained iteratively removing edges from the calculation graph [16; 17; 54; 55; 56]. The disjoint paths problem is a foundational challenge within algorithmic graph theory and combinatorial optimization. Given a graph G and a collection of k pairs of terminals in G, the problem centers on determining whether k vertex-disjoint paths can be found to link each terminal pair. [PERSON] and [PERSON] [57] demonstrated the existence of an \(n^{3}\) algorithm for any fixed k. A variant of this problem focuses on obtaining the shortest paths. It was introduced by [PERSON] [14] and dubbed the disjoint shortest paths problem. She established a polynomial time solution for the case when k = 2. This problem has recently garnered increased attention, particularly following [PERSON] and [PERSON]'s proposed a polynomial time algorithm in the directed scenario for k = 2 [58]. [PERSON] [59] demonstrated that irrespective of the specific value of k, a polynomial time algorithm can be devised for the disjoint shortest paths problem. Path disjoint level refers to a ratio between one path and a set of previously selected paths, that typically include the shortest path [13; 60]. Disjoint-level metrics usually refer to the number of edges in common but other criteria may be also considered: the number of nodes in common, the total cost of the route, the total length of the route, or even the number of traversed links. A certain path overlapping is commonly accepted using a minimum disjoint level ratio [16; 54] to obtain feasible Dj-kSP routing solutions for the so-called k-Shortest Paths with Limited Overlap Problem (kSPwLO). Polynomial time algorithms for _kSPwLO_ solving are proposed and compared in [16]. Specifically, the ESX-C algorithm provides a good balance between the quality of routes and computing effort. It iterates over the previously calculated shortest paths removing selected edges applying removal criteria, and recalculating the new shortest paths. Edge removal criteria may refer to their weights or their relative contribution to the shortest paths or the number of shortest paths that traverse it. Optimal route assignment is part of the TAP problem, and evolutionary algorithms (GA) have been used to find non-analytical solutions for it [24; 61]. In one paper [24], [PERSON] uses a GA to find the optimal distribution of the free-flow K-Shortest Paths to the vehicles. KSPs are calculated for each origin/destination (O/D) flow under free-flow and all-or-nothing routing methods, assuming that they will be the preferred routes for each flow during the assignment process using iterative methods. This method is applied to the synthetic network proposed by [5]. Optimization objectives are network total travel time and individual's mean travel time. The advantage of these methods is that computation times are low, as there is no need to compute KSP iteratively. However, the complexity of the proposed GA depends on the number of vehicles (demand) and assumes that vehicles will always follow the KSP delivered by the algorithm. In addition, there should be a balance between network complexity and the number of considered KSP, as many of the KSP only have subtle variations, not disjoint paths as described in [62]. This previous model has been generalized to cope with multi-objective GA analysis as described in [61].