# Parallelized Swarm Intelligence Approach for Solving TSP and JSSP Problems
## 4 Discussion  
The proposed mushroom-picking algorithm was validated using benchmark datasets from the TSP and JSSP publicly available repositories. The first of the reported experiments aimed at identifying the best combination of the available agents. For the TSP, the best combination denoted **BR** consists of the **bestMove** and **randomReverse** agents plus the **crossover. ** The **BR,** with mean error averaged over all considered dataset at the level of 0.28% was significantly better than RR, BB, RB with the respective mean errors of 0.36%, 0.41% and 0.45%. The above finding was confirmed by the Friedman ANOVA by ranks test at the significance level of 0.05. In the case of the TSP also differences between mean computation times have proven to be statistically significant. The **BR** not only provides the smallest mean error, but also assures the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & \multirow{2}{*}{**MPA**} & \multicolumn{2}{c}{**DWPA**} & \multicolumn{2}{c}{**Naga**} \\  & & & [33] & & [32] \\  & **Err** & **Time (s)** & **Err** & **Time (s)** & **Err** \\ \hline la01 & 0.00\% & 0.5 & 0.0  
shortest mean computation time, which was again established by the Friedman ANOVA by ranks test at the significance level of 0.05. For the JSSP, the best combination denoted **RR** consists of the **randomMove** and **randomReverse** agents plus the **crossover. ** The **RR,** with the mean computation error averaged over all considered dataset at the level of 3.75% was significantly better than **BR** with the respective mean error of 11.53%. The above finding was confirmed by the Wilcoxon Signed Rank Test at the significance level of 0.05. However, comparison of the mean computation times by the same method have confirmed that there are no significant differences between mean computation times of **RR** and **BB**. Another feature of the MPA is its stability. In the case of the TSP, the mean value of the standard deviation of the computation error, averaged over all considered datasets, is 0.18% with maximum deviation at 0.95% and minimum at 0.0%. In the case of the JSSP the respective values are 0.92% with maximum at 3.43% and minimum at 0.0%. Convergence analysis in the case of both TSP and JSSP shows that increasing the number of threads rapidly decreases computation errors. The rule is valid up to certain number of threads. Further increasing of this number decreases computation errors in a much lower pace until a zero or stable error level was reached. Computation time analysis shows that up to a point where the stable computation error was reached, increasing the number of threads increases the computation time at a slow rate. The above dependency is clearly visible in the case of the JSSP as opposed to the case of the TSP where the growth of the computation time with the increase of the number of threads is nearly linear. The performance of the MPA was compared with performances of the recently published algorithms for solving the TSP and JSSP. Data from Table 6 show that for the TSP, MPA outperforms other competing approaches including DSOS, NDDE and CII. Unfortunately, due to the high number of missing values for the DSOS and NDDE performance, we were not able to carry out a full statistical analysis of the compared results. The mean computation error in the case of the TSP, calculated over all sample datasets for the MPA is 0.25% while the same value for the CII algorithm is 3.5%. In return, the CII algorithm is much quicker with the mean computation time of 17.05 ms versus 22.17 s in the case of the MPA (both values calculated without pcb442 and pr1002 datasets). Data from Table 8 show that for JSSP our approach outperforms DWPA and NAGA. Unfortunately, due to the high number of missing values in the case of the NAGA we were not able to carry out the Friedman ANOVA by ranks test. The mean computation error in the case of the JSSP, calculated over all sample datasets for the MPA is 1.44% and 3.53% for the DWPA.