# Dynamic Multi-Compartment Vehicle Routing Problem for Smart Waste Collection +
## Experimental Study  
### Real-World Study  
The case study presented in this article is based on data from those [PERSON] et al. [10] and [PERSON] [29], with some modifications to adapt this data to our problem. These are the waste collection operations by Valorsul-Valorizacao e Tratamento de Residuos S'olidos, S.A. This company operates in the region of Lisbon, the capital of Portugal. Valorsul \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**CPLEX**} & \multicolumn{8}{c}{**HGA**} \\ \hline
**TCW1** & **TCW2** & **TVB1** & **TVB2** & **TLBO** & **TC** & **TCW1** & **TCW2** & **TVB1** & **TVB2** & **TLBO** & **TC** \\ \hline
3967 & 3405 & 34 & 32 & 0 & 7361 & 3967 & 3405 & 34 & 32 & 0 & 7361 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the results found by HGA and CPLEX. Figure 11: Example of Mutation procedure. is responsible for collecting different types of waste, including recyclable waste (glass, paper/cardboard, and plastic/metal). The collection of recyclable materials is carried out in 14 municipalities by a homogeneous fleet of vehicles based on a single depot. During compilation, the team records the fill level of the bins. It classifies them as empty (0%), less than half (25%), half (50%), more than half (75%), or full (100%). The collection system proposed by Valorsul for the collection of recyclable waste then estimates the filling level of the bins and decides whether to include these bins in the route. This estimate is calculated as follows: after having visited all the assigned collection points, the truck returns with information on the filling levels of the bins. This information and the density values provided by Valorsul from Paper and/Cardboard (PC), Plastic and/Metal (PM), and Glass (G) and the density values provided by Valorsul from PC, PM, and G (\(\rho_{\text{PC}}\) = 40 kg/m\({}^{3}\); \(\rho_{\text{PM}}\) = 20 kg/m\({}^{3}\); \(\rho_{\text{G}}\) = 300 kg/m\({}^{3}\); see densities in Table 5) were used to calculate the amount collected per bin. The formula to calculate the quantity ordered per station and per type of waste follows (1.1a), where A\({}_{\text{iw}}\) is the quantity collected at station \(i\) of type \(w\), \(\rho_{\text{w}}\) is the type density \(w\), \(\text{CP}_{\text{iw}}\) is the total capacity of all bins of waste type \(w\) in station \(i\), and \(\text{FL}_{\text{iw}}\) the average fill level of all containers of type \(w\) in station \(i\). \[\text{A}_{\text{iw}}(\text{kg})=\ \rho_{\text{w}}*\text{CP}_{\text{iw}}*\text{ FL}_{\text{iw}} \tag{1.1a}\]  
For more clarification, part of the visit sequence carried out is shown in Table 6, along with information on the filling level of each bin collected. For example, the vehicle collected 50 kg of PC in bin 2293 (marked in red in Table 6), calculated in Formula (1.1b). \[\text{A}_{\text{2293,PC}}=40*2.5*50\%=50\ \text{kg} \tag{1.1b}\]  
The estimated fill level of each bin heard by Valorsul is calculated by dividing the total fill levels recorded for each bin by the number of days in the period multiplied by the time interval between routes ([PERSON] et al. [10] and [PERSON] [29]). This estimation allows a comparison between the current situation of Valorsul and the results obtained when applying our approach. [PERSON] et al. selected three routes to collect the type (paper/cardboard) to analyze the current situation (blind collection) and the future situation (installation of sensors to obtain