## 2 Literature Review  
This section aims to provide a description of the two-echelon capacitated vehicle routing problem (2E-CVRP) and highlight the primary resolution strategies designed for effective convergence to a solution while maintaining favorable values relative to the optimum. The mathematical model defining the problem consists of a directed graph, denoted as \(G=(V,A)\), with vertices encompassing the central depot, customers, and satellites. The arcs connect the depot to satellites and satellites to customers, as outlined in the formal description provided in Figure 1[11]. In this formal representation, products initially located at the central depot are transported by a fleet of homogeneous freight vehicles to the satellites. The satellites, in turn, execute the final delivery of the products to customers with heterogeneous demand, utilizing a fleet of smaller homogeneous vehicles. The vehicles in the first echelon (FE) and second echelon (SE) possess transport capacities denoted as \(Q^{1}\) and \(Q^{2}\), with a specific number of trips, represented as \(m_{s}\), that the set of vehicles at each satellite can undertake. Additionally, within the problem, customers exhibit heterogeneity, each having their individual demand, denoted as \(d_{i}\), which must be entirely serviced by the same vehicle. Other categories of strategies, discussed below, include local search heuristics, constructive heuristics, and genetic algorithms. However, similarly to exact algorithms, it is noted that many of them tend to take a long time to reach their final results, sometimes extending to hours, making them unfeasible for use in interactive DSS. For the 2E-CVRP and its variants, the predominantly employed solution strategies revolve around exact branch-and-cut algorithms [12; 13] and decomposition methods [14]. These approaches successfully tackle problems involving up to 5 satellites and 50 customers for the first group, and 15 satellites with 300 customers for the second group, with an average computational time of one hour. The use of Genetic Algorithms (GAs) in the context of 2E-CVRP involves research that models the chromosome in various ways. The main approach is to use chromosomes that represent a complete solution to the problem [15], with each gene representing a route from the first (FE) or second (SE) echelon. Another approach considers a complete solution as an individual composed of several chromosomes [16], where each chromosome symbolizes a route, and its genes correspond to the nodes of the problem. An extra chromosome is introduced to establish connections between the chromosomes of the FE and SE. In addition, various constructive heuristics are used to build the initial population of a GA [17; 18], and the process of selecting individuals for reproduction includes techniques such as Random Selection, Tournaments, Roulette, and Best Fitness. After selection, the process of exchanging chromosome code is done based on the following operators: the order-based operator [19; 20], the route copy operator [15; 18], the cycle crossover operator also [19], the Partially Mapped Crossover (PMX) operator [21], and an operator specific to the 2E-CVRP problem developed by [PERSON] et al. [16]. The authors use a criterion for stopping based on a limit of iterations without improvements. Many of the heuristics for the 2E-CVRP commonly share the strategy of generating an initial solution with constructive heuristics by dividing the problem into two separate subproblems, one for the SE and one for the FE, and first solving the VRP related to the SE. Furthermore, constructive heuristics are exclusively employed in generating the initial solution, followed by a second improvement phase due to their rapid computational time. Two approaches to the routing problem of the SE are described by [PERSON] [4]. In the first, customers are assigned to the nearest satellites, solving independent CVRP problems. In the second, a multi-depot CVRP is solved.