## 5 Numerical Experiments and Analysis
### Computational Results and Analysis
#### 5.2.2 Comparison Between NHALNS and Other Heuristics  
Considering that GUROBI can obtain the optimal solutions only for small-scale instances, we next examine the performance of NHALNS for large-scale instances by comparing it with other heuristic methods. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**GUROBI**} & \multicolumn{4}{c}{**NHALNS**} \\ \cline{2-7}
**Inst** & \multicolumn{2}{c}{**TC**} & \multicolumn{2}{c}{**Time (s)**} & \multicolumn{2}{c}{**TC**} & \multicolumn{2}{c}{**Time (s)**} \\ \cline{3-7}  & **TC** & **Time (s)** & **Best** & **Avg** & **SD** & \\ \hline c101C5 & **2596.75** & 0.89 & **2596.75** & 2596.75 & 0.00 & 0.69 \\ r105C5 & **2524.56** & 0.91 & **2524.56** & 2524.56 & 0.00 & 0.74 \\ r202C5 & **1303.87** & 1.01 & **1303.87** & 1303.87 & 0.00 & 0.88 \\ r203C5 & **1346.73** & 1.02 & **1346.73** & 1346.73 & 0.00 & 0.85 \\ rc105C5 & **2592.38** & 0.91 & **2592.38** & 2592.38 & 0.00 & 0.72 \\ rc108C5 & **2601.87** & 0.81 & **2601.87** & 2601.87 & 0.00 & 0.77 \\ rc204C5 & **1342.26** & 0.91 & **1342.26** & 1342.26 & 0.00 & 0.86 \\ rc208C5 & **1335.09** & 0.99 & **1335.09** & 1335.09 & 0.00 & 0.96 \\ c104C10 & 2615.17 & 1000 & 2615.17 & 2615.17 & 0.00 & 5.08 \\ r103C10 & 2560.39 & 1000 & 2560.39 & 2560.39 & 0.00 & 3.44 \\ r201C10 & 2575.35 & 1000 & 1407.68 & 1407.68 & 0.00 & 5.24 \\ r203C10 & 1377.33 & 1000 & 1377.33 & 1377.33 & 0.00 & 6.64 \\ rc102C10 & **5143.96** & 114.66 & **5143.96** & 5143.96 & 0.00 & 3.25 \\ rc108C10 & 3883.00 & 1000 & 3883.00 & 3883.00 & 0.00 & 3.98 \\ rc201C10 & 2653.15 & 1000 & 2653.15 & 2653.15 & 0.00 & 3.65 \\ rc205C10 & 2681.07 & 1000 & 2681.07 & 2681.07 & 0.00 & 3.88 \\ r102C15 & 6136.48 & 1000 & 6136.48 & 6136.48 & 0.00 & 10.12 \\ r202C15 & 2715.92 & 1000 & 2702.32 & 2702.32 & 0.00 & 13.43 \\ r209C15 & 2667.93 & 1000 & 2649.51 & 2649.51 & 0.00 & 11.41 \\ rc103C15 & 6338.14 & 1000 & 6334.56 & 6334.56 & 0.00 & 12.92 \\ \hline \hline \end{tabular} Note: The optimal values are marked in bold.  
\end{table} 
Table 4: Comparison between NHALNS and GUROBI on the robust instances. First, we compare our algorithm with the two-phase heuristic method, which is proposed by [PERSON] et al. [9]. In their algorithm, the LNS framework is combined with a conventional local search to construct a pool of robust routes in the first phase, then the set partitioning (SP) procedure is used in the second phase to generate a complete robust solution. We denote their algorithm as LNS + SP. Because LNS + SP is used to solve EVRP under energy consumption uncertainty without consideration about time windows, we make some adaptation to LNS + SP by adding the relative operators used in this paper, such as RCwPS, RCwSS, WURR, TBI, GIE, and GIEC, to LNS + SP in order to justify the comparison. The number of iterations for each algorithm is set to 300. The results are shown in Table 5.  
It is easy to find that NHALNS can not only achieve a better solution for more than half of the instances but also consume much less computation time than LNS + SP. Even for the instances in which NHALNS does not behave as well as LNS + SP in objective values, the difference is not significant. The typical convergence patterns of the two algorithms are illustrated in Figure 2, with instances c104_21 and c105_21 as examples. Apparently, NHALNS exhibits a satisfactory convergence speed, reaching a satisfactory solution faster than LNS + SP. Based on the above evidence, we can confirm the efficacy of our modification on general NHALNS. Improvements may come from three aspects. First, the proposed repair operators in NHALNS can achieve the near-optimal solution more quickly than the normal repair operators used in LNS + SP. Secondly, neighborhoods adopted in the LS phase of the NHALNS are more effective than that of the normal LS neighborhoods in the LNS + SP algorithm. Thirdly, operator selection by roulette wheel is more efficient than a random choice. \begin{table}