# Adaptive Gene Level Mutation
## 5 Results
### Exploiting the Tuning of the Power Parameter  
The importance of each loss (partial fitness) can be changed by using a power function which can raise the partial fitness vector to a power (_Pow_). Using a power function with _Pow_ = 0, you get the uniform mutation back making our approach an extension of the original method. For further illustration, we will go back to the previous example as in Figure 1. Partial fitness, which is the main bulk calculating the mutation rate of each gene, \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Instance** & **VNS Loc** & **VNS Base** & **SA Loc** & **SA Base** & **GA Loc** & **GA Base** & **Optimal** \\ \hline att48 & **38,074.95** & 38,349.60 & **66,162.13** & 78,766.73 & **125,478.95** & 127,962.10 & **10,628** \\ \hline berlin52 & **8633.02** & 8718.89 & **15,005.75** & 16,852.92 & **24,670.25** & 25,154.85 & **7542** \\ \hline burma14 & **24.99** & 25.56 & 27.11 & **26.83** & **40.70** & 44.78 & 30.89 \\ \hline eil51 & **477.05** & 487.21 & **827.75** & 951.21 & **1375.58** & 1410.37 & **426** \\ \hline eil76 & **605.78** & 626.56 & **1387.55** & 1570.88 & **2167.07** & 2209.15 & **538** \\ \hline kroA100 & **25,923.15** & 26,478.45 & **90,299.24** & 103,019.28 & **148,699.96** & 150,347.27 & **21,282** \\ \hline kroB100 & **25,248.30** & 25,437.91 & **88,441.77** & 102,262.19 & **145,522.35** & 148,050.07 & **22,141** \\ \hline kroC100 & **24,983.77** & 25,042.63 & **88,651.16** & 102,050.32 & **146,813.87** & 147,521.41 & **20,749** \\ \hline kroD100 & **26,225.47** & 26,276.29 & **87,275.06** & 100,001.28 & **142,412.64** & 142,597.61 & **21,294** \\ \hline kroE100 & **24,608.56** & 24,779.56 & **90,021.99** & 104,828.39 & **148,325.58** & 150,791.90 & **22,068** \\ \hline pr76 & **129,505.66** & 132,538.60 & **315,049.50** & 354,149.35 & **491,017.72** & 500,005.56 & **108,159** \\ \hline rat99 & **1386.94** & 1388.55 & **4412.32** & 5126.53 & **7280.52** & 7344.15 & **1211** \\ \hline rd100 & **9580.81** & 9697.09 & **30,877.39** & 34,885.76 & **49,093.79** & 49,482.80 & **7910** \\ \hline st70 & **750.11** & 769.31 & **1902.85** & 2161.98 & **3091.04** & 3149.35 & **675** \\ \hline ulysses16 & **52.01** & 55.33 & **59.52** & 61.09 & **100.05** & 101.36 & 73.98 \\ \hline ulysses22 & **55.18** & 55.66 & **73.00** & 75.17 & **129.77** & 133.62 & 75.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison between baseline (Base) and locus (Loc) mutation for three different algorithm,genetic algorithm (GA), simulated annealing (SA) and Variable neighborhood search (VNS). We applied these algorithms on 16 different instances from TSPLIB dataset. In most cases, locus mutation is enhancing the performance of the algorithms. equals [1 2 2 1 0 0 1 1]. Using the _Pow_ parameter, we would have the following updated partial fitness values:  
\[ \begin{array}{l}[1\,2\,2\,1\,0\,0\,1\,1]^{0}=\\ [1\,1\,1\,1\,1\,1\,1\,1]\,\approx\\ \\ [1\,2\,2\,1\,0\,0\,1\,1]^{1}=\\ [1\,2\,2\,1\,0\,0\,1\,1]\,\approx\\ \\ [1\,2\,2\,1\,0\,0\,1\,1]\,\approx\\ \\ [1\,2\,2\,1\,0\,0\,1\,1]^{2}=\\ [1\,4\,4\,1\,0\,0\,1\,1]\,\approx\\ \\ [1\,2\,2\,1\,0\,0\,1\,1]^{3}=\\ [1\,8\,8\,1\,0\,0\,1\,1]\,\approx\\ \\ [1\,2\,2\,1\,0\,0\,1\,1]^{\infty}=\\ \\ [0\,1\,1\,0\,0\,0\,0\,]\,\approx\\ \\ \end{array} \]  
\[ \begin{array}{l}[1\,2\,2\,1\,0\,0\,1\,1]^{0}=\\ [1\,1\,1\,1\,1\,1\,1\,1]\,\approx\\ \\ [0.12\,0.12\,0.12\,0.12\,0.12\,0.12\,0.12\,0.12\,0.12\,0.12\,0.12\,0.12]\\ \\ [1\,2\,2\,1\,0\,0\,1\,1]^{1}=\\ [0.12\,0.25\,0.25\,0.12\,0.00\,0.00\,0.12\,0.12]\\ \\ [1\,4\,4\,1\,0\,0\,1\,1]\,\approx\\ \\ [1\,2\,2\,1\,0\,0\,1\,1]^{3}=\\ [1\,8\,8\,1\,0\,0\,1\,1]\,\approx\\ \\ [1\,2\,2\,1\,0\,0\,1\,1]^{\infty}=\\ [0\,1\,1\,0\,0\,0\,0\,0]\,\approx\\ \\ [0.00\,0.50\,0.50\,0.00\,0.00\,0.00\,0.00\,0.00]\\ \\ \end{array} \]  
We can notice that when \(Pow=0\) we will get back to the uniform distribution where all genes have the same probability for a mutation. When \(Pow=1\), queens 2 and 3 have a bigger chance for a mutation.