# Parallelized Swarm Intelligence Approach for Solving TSP and JSSP Problems
## 3 Results
### MPA Performance Analysis  
Performance analysis of the proposed mushroom-picking algorithm applied to solving the TSP problem, was based on 23 benchmark instances. For each dataset experiments of four different kinds were run with different sets of agents involved in the process of improving solutions. In each case the **crossover** was used as two-argument agent and one-argument agents were chosen as follows:  
* **RR--randomMove** and **randomReverse**;
* **BR--bestMove** and **randomReverse**;
* **BB--bestMove** and **bestReverse**;
* **RB--randomMove** and **bestReverse**. In the experiment 50 threads were used, _searchTime_ (time period used in _applyOptimizations_) was set to 1 second, stopping criterion was defined as no improvement in the best fitness for 2 rounds. Mean errors and the respective mean computation times obtained in the experiment are shown in Table 1. In most cases results produced using pair **BR** are better than other results. Table 2 presents standard deviations of errors and times obtained in the same experiment. To determine whether there are any significant differences among mean errors produced by different combinations of agents we used the Friedman ANOVA by ranks test. The null hypothesis states that there are no such differences. With [PERSON] statistics equal to 21.85 and \(p\)-value = 0.00007 the null hypothesis should be rejected at the significance level of 0.05. In terms of the computation error **BR** outperforms the remaining sets of agents. For a similar analysis involving computation times under the null hypothesis that there are no significant differences among mean computation times the Friedman statistics is equal to 46.49 and \(p\)-value \(<\) 0.00000. Hence, also in the case of mean computation times the null hypothesis should be rejected. In terms of the computation time needed the **RR** is a looser. However, there are no statistically significant differences between computation times required by the remaining sets of agents. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{4}{c}{**Error (\%)**} & \multicolumn{4}{c}{**Time (s)**} \\  & **RR** & **BR** & **BB** & **RB** & **RR** & **BR** & **BB** & **RB** \\ \hline bier127 & 0.31\% & **0.23\%** & 0.53\% & 0.42\% & 17.5 & 8.1 & 8.1 & 7.4 \\ ch130 & 0.27\% & **0.24\%** & 0.47\% & 0.60\% & 14.6 & 6.2 & 6.9 & 7.0 \\ ch150 & 0.48\% & **0.33\%** & 0.53\% & 0.62\% & 13.8 & 7.1 & 7.3 & 7.3 \\ d198 & 0.79\% & **0.32\%** & 0.69\% & 0.85\% & 48.6 & 29.7 & 14.3 & 15.7 \\ eil101 & **0.06\%** & 0.11\% & 0.32\% & 0.37\% & 6.5 & 5.2 & 5.8 & 6.4 \\ eil51 & 0.05\% & **0.02\%** & 0.05\% & 0.12\% & 3.2 & 3.2 & 3.3 & 3.4 \\ eil76 & **0.04\%** & 0.07\% & 0.23\% & 0.19\% & 4.7 & 3.6 & 3.9 & 3.9 \\ kroA100 & 0.00\% & 0.00\% & 0.02\% & 0.00\% & 8.0 & 3.4 & 4.2 & 4.3 \\ kroA150 & **0.20\%** & 0.21\% & 0.79\% & 0.75\% & 17.8 & 9.1 & 9.5 & 10.0 \\ kroB100 & 0.44\% & 0.45\% & 0.41\% & **0.40\%** & 9.5 & 4.4 & 4.5 & 5.3 \\ kroC100 & 0.00\% & 0.00\% & 0.00\% & 0.01\% & 7.5 & 3.9 & 4.7 & 5.2 \\ kroD100 & 0.01\% & 0.01\% & 0.06\% & 0.06\% & 7.6 & 4.4 & 5.2 & 5.9 \\ kroE100 & 0.11\% & 0.09\% & 0.09\% & 0.11\% & 8.9 & 4.6 & 5.3 & 5.3 \\ lin105 & 0.18\% & 0.17\% & 0.17\% & 0.17\% & 7.9 & 3.7 & 3.9 & 4.1 \\ pr107 & 0.02\% & 0.01\% & 0.01\% & 0.01\% & 11.8 & 4.9 & 5.3 & 5.4 \\ pr124 & 0.13\% & **0.04\%** & 0.06\% & 0.06\% & 22.9 & 10.5 & 5.8 & 5.9 \\ pr144 & 0.22\% & 0.02\% & 0.02\% & 0.03\% & 16.6 & 8.1 & 6.4 & 6.8 \\ rat99 & 0.01\% & 0.01\% & 0.07\% & 0.06\% & 6.0 & 4.2 & 4.9 & 5.8 \\ rd100 & 0.00\% & 0.00\% & 0.00\% & 0.02\% & 7.7 & 3.9 & 4.6 & 5.5 \\ st70 & **2.74\%** & 2.76\% & 2.76\% & 2.82\% & 4.6 & 4.0 & 3.8 & 3.6 \\ Tnm100 & 0.00\% & 0.00\% & 0.00\% & 0.02\% & 6.7 & 3.9 & 5.0 & 5.2 \\ tsp225 & 2.05\% & **1.35\%** & 2.01\% & 2.28\% & 24.0 & 16.6 & 18.7 & 21.8 \\ uTo identify significant differences among standard deviations produced by different combinations of agents we again used the Friedman ANOVA by ranks test. The null hypothesis state that there are no such differences.