# Dynamic Multi-Compartment Vehicle Routing Problem for Smart Waste Collection +
## 2 Literature Review
We cite [PERSON] et al. [16] studied the Vehicle Routing Problem (VRP) problem with a time window to study the static case and the dynamic case in which the appearance of new customers over time. The authors have proposed a resolution approach based on using the hybridized Ant Colony Optimization Algorithm and the Large Neighborhood Search Algorithm in the static case, and they have adopted this approach to solve the problem in a dynamic context. In 2021 [PERSON] et al. [17] proposed a model based on the neural system with modified rules and learning in combination with Firefly optimization to solve the combined version of Green VRP and Dynamic VRP with temporal windows, called DGVRPTW. In the same year, [PERSON] et al. [18] studied the dynamic green vehicle routing problem of perishable products under green traffic conditions to optimize the total cost of the active transportation network, minimize environmental influences, and increase customer satisfaction. The authors augmented an algorithm for a new augmented \(\epsilon\)-constraint heuristic approach; Moreover, robust optimization was carried out for the problem with uncertainties on request and economic parameters. In 2017 [PERSON] et al. [19] used a Modified Capacitated K-Means Algorithm and Variable Neighborhood Search to optimize dynamic routes to manage solid waste collection efficiently. We find many works in the literature based on their study of the DVRPV on the working day division into time slices. Each time slice represents a static VRP; cite [PERSON] et al. [16; 17; 18; 19; 20] (2013 and 2014) and [PERSON] et al. [21] (2018). The discretization strategy was proposed for the first time by [PERSON] et al. (1998) [22] and adopted by [PERSON] al. (2002) [23]. In the literature, there are not many works concerning the MCVRP (Multi-Compartment Vehicle Routing Problem) of separate waste collection, which consists in not mixing the different types during transport. We cite the work of [PERSON] and [PERSON] [24], who proposed a new scheme for separate waste collection. The scheme contains three levels, begin by transferring the different waste types to the separate transfer stations, where each compartment corresponds to a specific waste type and can accommodate several supplies of the same waste type, then transport these different types to the factories for treatment and finally to the landfill. In this context, they presented mathematical formulations of the waste management system using linear programs. The article adopted heuristics and metaheuristics for resolutions. [PERSON] et al. [8] (2014) studied the problem of transporting two-compartment vehicles routing problem of recycling waste collection, and to solve this problem, the authors proposed the Ant Colony System (ACS). And we cite the work of [PERSON] and [PERSON] (2010) [25], which tested on CVRP instances and MCVRP instances to assess the benefits of using multi-compartment vehicles for waste collection. [PERSON] et al. [26] (2019) presented a problem of routing vehicles with several compartments of different sizes for collecting several types of glass waste. They proposed a branch-and-cut algorithm to compare the total cost of compartment sizes. [PERSON] et al. [27] (2016) combined a close-open mixed vehicle routing problem (COMVRP) with a multi-depot vehicle routing problem (MDVRP) to formulate the multi-compartment vehicle waste collection problem. And to solve it, they used the hybrid genetic algorithm. [PERSON] et al. [28] and [PERSON] et al. [29] developed heuristics to solve the multi-compartment vehicle routing problem to collect two types of recyclable materials (paper and plastic/metal). A real case study is adopted to justify the effectiveness of the proposed approach. [PERSON] and [PERSON] (2022) [30] have proposed a mathematical model to study the problem of separate waste collection in smart cities via compartmentalized vehicles. Using electric vehicles, [PERSON], [PERSON] et al.