## 5 Experiment Results
### Comparisons with Several Efficient Algorithms
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instances**} & \multirow{2}{*}{**Best-Known**} & \multicolumn{6}{c}{**Algorithms**} & \multicolumn{6}{c}{**RPIs**} \\ \cline{2-11}  & & **IIG** & **IABC** & **ALNS** & **VNIG** & **SAIG** & **IIG** & **IABC** & **ALNS** & **VNIG** & **SAIG** \\ \hline rc101 & 1646.27 & **1646.27** & 1797.77 & 1725.45 & 1752.38 & 1906.85 & **0.00** & 9.20 & 4.81 & 6.45 & 15.83 \\ rc102 & 1723.15 & **1723.15** & 1774.46 & 1790.25 & 1876.03 & 1937.90 & **0.00** & 2.98 & 3.89 & 8.87 & 12.46 \\ rc103 & 1861.14 & **1861.14** & 1884.37 & 1890.11 & 1988.72 & 1965.67 & **0.00** & 1.25 & 1.56 & 6.85 & 5.62 \\ rc104 & 1917.06 & 2014.80 & 1921.70 & 1985.40 & **1917.06** & 2264.61 & 5.10 & 0.24 & 3.56 & **0.00** & 18.13 \\ rc105 & 1802.07 & **1802.07** & 1888.92 & 1908.45 & 2113.25 & 2039.27 & **0.00** & 4.82 & 5.90 & 17.27 & 13.16 \\ rc106 & 1741.29 & **1741.29** & 1796.88 & 1780.32 & 2023.76 & 1949.68 & **0.00** & 3.19 & 2.24 & 16.22 & 11.97 \\ rc107 & 1893.48 & **1893.48** & 1984.87 & 1934.17 & 2060.32 & 2298.90 & **0.00** & 4.83 & 2.15 & 8.81 & 21.41 \\ rc108 & 1932.38 & 2005.98 & 1977.62 & **1932.38** & 2052.50 & 2409.94 & 3.81 & 2.34 & **0.00** & 6.22 & 24.71 \\ rc109 & 1875.56 & 1924.37 & 1941.96 & 1878.39 & **1875.56** & 2273.27 & 2.60 & 3.54 & 0.15 & **0.00** & 21.20 \\ rc201 & 1971.68 & **1971.68** & 1990.10 & 2148.42 & 2283.46 & 2102.45 & **0.00** & 0.93 & 8.96 & 15.81 & 6.63 \\ rc202 & 1926.09 & **1926.09** & 1980.53 & 1971.66 & 1983.05 & 2112.97 & **0.00** & 2.83 & 2.37 & 2.96 & 9.70 \\ rc203 & 1893.91 & 1993.15 & **1893.91** & 1978.87 & 2117.33 & 2296.98 & 5.24 & **0.00** & 4.49 & 11.80 & 21.28 \\ rc204 & 2037.70 & **2037.70** & 2027.60 & 2060.78 & 2212.94 & 2324.72 & **0.00** & 2.94 & 1.13 & 8.60 & 14.09 \\ rc205 & 1868.28 & 1996.43 & **1868.28** & 2020.63 & 1980.78 & 2634.99 & 6.85 & **0.00** & 8.15 & 6.02 & 41.04 \\ rc206 & 1947.04 & **1947.04** & 1977.86 & 1984.33 & 2062.08 & 2649.70 & **0.00** & 1.58 & 1.92 & 5.91 & 36.09 \\ rc207 & 1938.67 & 2016.15 & **1938.67** & 2055.05 & 2059.97 & 2600.96 & 4.00 & **0.00** & 6.00 & 6.26 & 34.16 \\ rc208 & 1997.49 & 2046.07 & 2000.75 & **1997.49** & 2039.01 & 2696.20 & 2.43 & 0.16 & **0.00** & 2.08 & 34.98 \\ rr101 & 2684.64 & 3022.86 & **2684.64** & 3060.27 & 3162.39 & 3109.69 & 0.13 & **0.00** & 15.00 & 18.00 & 16.00 \\ rr102 & 2033.62 & **2033.62** & 2077.13 & 2169.49 & 2213.74 & 2167.79 & **0.00** & 2.14 & 6.68 & 8.86 & 6.60 \\ rr103 & 1794.85 & **1794.85** & 1870.71 & 1896.33 & 1972.20 & 1945.93 & **0.00** & 4.23 & 5.65 & 9.88 & 8.42 \\ rr104 & 1735.86 & **1735.86** & 1738.09 & 1903.84 & 1743.39 & 1968.11 & **0.00** & 0.13 & 9.68 & 0.43 & 13.38 \\ rr105 & 2065.52 & **2065.52** & 2127.28 & 2195.04 & 2271.79 & 2226.11 & **0.00** & 2.99 & 6.27 & 9.99 & 7.77 \\ rr106 & 1920.16 & 1981.65 & 2027.87 & 2057.64 & 2145.01 & **1920.16** & 3.20 & 5.61 & 7.16 & 11.71 & **0.00** \\ rr107 & 1792.15 & 1855.79 & **1792.15** & 1938.33 & 1836.75 & 2015.37 & 3.55 & **0.00** & 8.16 & 2.49 & 12.46 \\ rr108 & 1699.01 & **1699.01** & 1792.71 & 1925.74 & 1737.92 & 1848.04 & **0.00** & 5.51 & 13.34 & 2.29 & 8.77 \\ rr109 & 1938.55 & **1938.55** & 2019.06 & 2036.17 & 2166.92 & 2223.12 & **0.00** & 4.15 & 5.04 & 11.78 & 14.68 \\ rr110 & 1807.02 & **1807.02** & 1824.12 & 1971.65 & 1832.97 & 1906.87 & **0.00** & 0.95 & 9.11 & 1.44 & 5.53 \\ rr111 & 1764.78 & **1764.78** & 1803.27 & 1932.27 & 1918.23 & 1925.53 & **0.00** & 2.18 & 9.49 & 8.70 & 9.11 \\ rr112 & 1763.50 & **1763.50** & 1792.94 & 1937.91 & 1838.86 & 1965.29 & **0.00** & 1.67 & 9.89 & 4.27 & 11.44 \\ rr201 & 2059.73 & 2106.75 & 2072.58 & 2404.25 & **2059.73** & 2571.16 & 2.28 & 0.62 & 16.73 & **0.00** & 24.83 \\ rr202 & 1924.95 & **1924.95** & 1971.59 & 2130.51 & 2002.56 & 2256.09 & **0.00** & 2.42 & 10.68 & 4.03 & 17.20 \\ rr203 & 1811.40 & 18114.00 & 1860.81 & 2040.99 & 2064.73 & 2104.38 & **0.00** & 2.73 & 12.67 & 1 To provide a clear and intuitive representation of the evolution process for all compared algorithms, Figure 8 presents the convergence curves for four selected instances, i.e., rc105, rr103, rrc107, and rrc208.