## 4 Computational Experiments
### Testing Instances and Parameters  
The 2L-VRP benchmarks generated in [4] incorporate a fleet of vehicles with a \(40\times 20\) squared units for loading and a maximum capacity of weight. According to the characteristics of the demanded items, the instances of 2L-VRP are categorized into 5 classes, as shown in Table 1. Table 2 shows the details of the number of customers (denoted by \(n\)), total number of items (denoted by \(M=\sum_{i=1}^{n}m_{i}\)), and the number of vehicles (denoted by \(|K|\)). More details can be found in Ref [3], and all 2L-VRP instances can be downloaded from [[http://www.or.deis.unibo.it/research.html](http://www.or.deis.unibo.it/research.html)]([http://www.or.deis.unibo.it/research.html](http://www.or.deis.unibo.it/research.html)), accessed on 10 May 2020. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Class**} & \multirow{2}{*}{\(|m_{i}|\)} & \multicolumn{2}{c}{**Vertical**} & \multicolumn{2}{c}{**Homogeneous**} & \multicolumn{2}{c}{**Horizontal**} \\ \cline{3-8}  & & **Length** & **Width** & **Length** & **Width** & **Length** & **Width** \\ \hline
1 & 1 & 1 & 1 & 1 & 1 & 1 \\
2 & [1,2] & [0.4 L.0.9 L] & [0.1 W,0.2 W] & [0.2 L,0.5 L] & [0.2 W,0.5 W] & [0.1 L,0.2 L] & [0.4 W,0.9 W] \\
3 & [1,3] & [0.3 L,0.8 L] & [0.1 W,0.2 W] & [0.2 L,0.4 L] & [0.2 W,0.4 W] & [0.1 L,0.2 L] & [0.3 W,0.8 W] \\
4 & [1,4] & [0.2 L,0.7 L] & [0.1 W,0.2 W] & [0.1 L,0.4 L] & [0.1 W,0.4 W] & [0.1 L,0.2 L] & [0.2 W,0.7 W] \\
5 & [1,5] & [0.1 L,0.6 L] & [0.1 W,0.2 W] & [0.1 L,0.3 L] & [0.1 W,0.3 W] & [0.1 L,0.2 L] & [0.1 W,0.6 W] \\ \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the demanded items of Classes 1–5 instances. Figure 5: Illustration of four types of wasted space (pattern areas are the wasted space). We run the proposed EATS-MOBFS method 10 times for each instance with the same parameters. Therein, the parameters of the proposed EATS-MOBFS algorithm are determined using the Irace package presented in [39]. The irace package is a general-purpose configurator and only requires the definition of a configuration scenario. Given a set of representative instances and a set of possible values for each parameter, the Irace package determines an appropriate combination of values for the parameter configuration. The Irace package iteratively applies a racing procedure in which several configurations are incrementally evaluated on bigger subsets of the training instance set. Specifically, the Irace package uses an iterative racing method or automatic configuration consisting of three steps: (i) sampling new configurations according to a particular distribution, (ii) selecting the best configurations from the newly sampled configurations by means of racing and (iii) updating the sampling distribution to drive the sampling toward the best configuration. These steps are repeated until the termination criterion is met. More details about the Irace package can be found in [39]. For the Irace scenario configuration, instances with 15, 30, 50 and 71 customers are taken as representative instances for parameter tuning. Each parameter of the EATS is provided with a set of possible values in a specified range for tuning. Namely, \(\delta_{1}\) and \(\delta_{2}\) (\(\delta_{1}>\delta_{2}\)) range from 0 to 50. Parameters \(r\) and \(\mu\) are set from 0 to 1. Parameters \(\alpha_{1}\), \(\alpha_{2}\) and \(\alpha_{3}\) range from 0 to 10. Afterward, a parameter combination is selected based on the best average result for the testing instances. Specifically, the weight adjustment algorithm is controlled by three parameters, \(\delta_{1}\), \(\delta_{2}\) and \(r\), which are set to 33, 13 and 0.25, respectively. In the diversification procedure, the removal process is controlled by three parameters: \(\alpha_{1}\), \(\alpha_{2}\) and \(\alpha_{3}\), which are 9, 2 and 5, respectively.