## 3 Manipulation of Swarms Positions and Space Solution Using Multi-Threaded Techniques
### Proposition II
In the case of proposals III, the sequential algorithm needs about 29% more iterations. Figure 1: The average error obtained for each version of the algorithm. Figure 3: Comparison of the average time needed to find the optimum for 100 individuals during 100 iterations for 100 tests for each algorithm and all tested versions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **Proposition I** & **Proposition II** & **Proposition III** \\ \hline Y & 1.11911 & 1.13374 & 1.24793 \\ \(\Phi\) & 0.18652 & 0.18896 & 0.20799 \\ \(G\) & 1.78599 & 1.79463 & 1.86089 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Obtained results from the use of parallelization for metaheuristic algorithms. Figure 2: The performance ranking of tested algorithms—the number of times the algorithm ranked first. ## 5 Conclusions

In this paper, we described six, classic meta-heuristic algorithms designed for optimization purposes and proposed three techniques for increasing not only the accuracy, but also the efficiency of the operation. Our ideas were based primarily on the action of multi-threading, which allowed placing individuals of a given population in specific places where an extreme can be located. An additional idea was to divide and manipulate the solutions space, which is interpreted as the natural environment of the individuals in given population. These types of activities have been tested and analyzed in terms of average error for selected functions and the time needed to perform the calculations to find a solution. The obtained results indicated that each proposed modification shortens the time of operation, but not all improve (significantly) the accuracy of the obtained measurements. The high scalability of the proposal indicates that the increasing number of cores speeds up the work of modifications. Moreover, each proposition showed the acceleration of the performance time as well as increasing the accuracy of the obtained solutions regardless of the chosen heuristic algorithm. While the proposed techniques of parallelization and manipulation of solution space have improved the operation of classical algorithms, they are so flexible that can be streamlined and improved by various ideas. In addition, this can allow to obtain even better results. This paper gives only an example of the parallelization approach. It seems reasonable to divide the search space in such a way that the area given to one particular core will be contained in the next and subsequent one. In addition, a model of communication between populations would be needed to exchange information about unfavorable areas. This would allow them to be removed from space and extended to another area on each core. In practice, this will eliminate unnecessary searches of uninteresting places, and at the same time increase precision (allowing individuals to move around in better places) and reduce computation time due to the reduction of the area on all cores. Authors acknowledge contribution to this project to the Diamond Grant No. 0080/DIA/2016/45 funded by the Polish Ministry of Science and Higher Education and support from Software Engineering Department at Kaunas University of Technology, Lithuania. [PERSON], [PERSON], [PERSON] and [PERSON] designed the methods, performed experiments and wrote the paper. The authors declare no conflict of interest. ## References

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