## 5 Experiment Results
### Effectiveness of the SA-Based Acceptance Criterion  
The IIG algorithm without the SA-based acceptance criterion (IIG_NS) was developed to compare with the IIG and to verify the effectiveness of the SA-based acceptance criterion. Table 5 presents the average fitness and RPI values achieved by the two compared algorithms. From Table 5 we can see that (1) the IIG achieved 41 optimal average fitness values out of 56 instances, significantly outperforming the IIG_NS. (2) In the last row, the average RPI of the IIG is 0.45, less than that achieved by the IIG_NS. These results validate the efficacy of the SA-based acceptance criterion. Figure 5 presents the ANOVA results for the two algorithms, showing that the IIG exhibits better stability compared to the IIG_NS. The \(p\)-value is 1.5457 \(\times\) 10\({}^{-4}\), which is significantly less than 0.05, indicating a significant difference between the IIG and IIG_NS algorithms.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Instances**} & \multirow{2}{*}{**Better Values**} & \multicolumn{2}{c}{**Algorithms**} & \multicolumn{2}{c}{**RPIs**} \\ \cline{3-6}  & & **IIG** & **IIG\_NS** & **IIG** & **IIG\_NS** \\ \hline rc101 & 1535.46 & 1646.27 & **1535.46** & 7.22 & **0.00** \\ rc102 & 1688.98 & 1723.15 & **1688.98** & 2.02 & **0.00** \\ rc103 & 1821.79 & 1861.14 & **1821.79** & 2.16 & **0.00** \\ rc104 & 2014.80 & **2014.80** & 2048.45 & **0.00** & 1.67 \\ rc105 & 1687.56 & 1802.07 & **1687.56** & 6.79 & **0.00** \\ rc106 & 1741.29 & **1741.29** & 1880.81 & **0.00** & 8.01 \\ rc107 & 1893.48 & **1893.48** & 1924.29 & **0.00** & 1.63 \\ rc108 & 2002.70 & 2005.98 & **2002.70** & 0.16 & **0.00** \\ rc109 & 1924.37 & **1924.37** & 1964.96 & **0.00** & 2.11 \\ rc201 & 1930.64 & 1971.68 & **1930.64** & 2.13 & **0.00** \\ rc202 & 1926.09 & **1926.09** & 1931.06 & **0.00** & 0.26 \\ rc203 & 1960.17 & 1993.15 & **1960.17** & 1.68 & **0.00** \\ rc204 & 2027.05 & 2037.70 & **2027.05** & 0.53 & **0.00** \\ rc205 & 1993.13 & 1996.43 & **1993.13** & 0.17 & **0.00** \\ rc206 & 1947.04 & **1947.04** & 1950.87 & **0.00** & 0.20 \\ rc207 & 2016.15 & **2016.15** & 2031.26 & **0.00** & 0.75 \\ rc208 & 2020.31 & 2046.07 & **2020.31** & 1.28 & **0.00** \\ rr101 & 3005.39 & 3022.86 & **3005.39** & 5.81 & **0.00** \\ rr102 & 2033.62 & **2033.62** & 2043.89 & **0.00** & 0.51 \\ rr103 & 1794.85 & **1794.85** & 1798.33 & **0.00** & 0.19 \\ rr104 & 1735.86 & **1735.86** & 1737.67 & **0.00** & 0.10 \\ rr105 & 2056.11 & 2065.52 & **2056.11** & 0.46 & **0.00** \\ rr106 & 1978.56 & 1981.65 & **1978.56** & 0.16 & **0.00** \\ rr107 & 1855.79 & **1855.79** & 1865.20 & **0.00** & 0.51 \\ rr108 & 1699.01 & **1699.01** & 1753.45 & **0.00** & 3.20 \\ rr109 & 1938.55 & 1938.55 & 1985.92 & **0.00** & 2.44 \\ rr110 & 1807.02 & **1807.02** & 1837.60 & **0.00** & 1.69 \\ rr111 & 1764.78 & **1764.78** & 1799.71 & **0.00** & 1.98 \\ rr112 & 1763.50 & **1763.50** & 1801.79 & **0.00** & 2.17 \\ rr201 & 2106.75 & **2106.75** & 2208.56 & **0.00** & 4.83 \\ rr202 & 1924.95 & **1924.95** & 2011.90 & **0.00** & 4.52 \\ rr203 & 1811.40 & **1811.40** & 1884.65 & **0.00** & 4.04 \\ rr204 & 1612.58 & **1612.58** & 1675.13 & **0.00** & 3.88 \\ rr205 & 1859.54 & **1859.54** & 1935.95 & **0.00** & 4.11 \\ rr206 & 1857.82 & **1857.82** & 1943.45 & **0.00** & 4.61 \\ rr207 & 1701.91 & **1701.91** & 1797.41 & **0.00** & 5.61 \\ rr208 & 1598.95 & **1598.95** & 1673.06 & **0.00** & 4.63 \\ rr209 & 2025.39 & 2336.35 & **2225.39** & 4.99 & **0.00** \\ rr210 & 1782.63 & **1782.63** & 1859.44 & **0.00** & 4.31 \\ rr211 & 1735.94 & **1735.94** & 1788.57 & **0.00** & 3.03 \\ rr101 & 2472.05 & **2472.05** & 2544.58 & **0.00** & 2.93 \\ rr102 & 2309.12 & **2309.12** & 2352.05 & **0.00** & 1.86 \\ rr103 & 2165.93 & **2165.93** & 2239.96 & **0.00** & 3.42 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison results of the IIG and IIG_NS.