# Data Reduction of Digital Twin Simulation Experiments Using Different Optimisation Methods
## 4 Methodology
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Optimisation Method** & **Optimisation Method Parameter** & **Step** & **Lower Boundary** & **Upper Boundary** \\ \hline Random search & Option to generate same solution candidates (Boolean) & 1 & 0 & 1 \\ \hline \multirow{3}{*}{Downhill simplex (Nealder-Mead method)} & Expansion coefficient & 0.2 & 0 & 1.6 \\ \cline{2-5}  & Reflection coefficient & 0.2 & 0 & 1.6 \\ \cline{2-5}  & Contraction coefficient & 0.2 & 0 & 0.8 \\ \cline{2-5}  & Reduction coefficient & 0.2 & 0 & 0.8 \\ \hline Local search & Number of steps & 2 & 1 & 29 \\ \hline \multirow{3}{*}{Hill climbing} & Population size & \(n\) & \(n\) & \(6*n\) \\ \cline{2-5}  & Number of steps & 2 & 1 & 29 \\ \hline \multirow{3}{*}{Tabu search} & Population Size & \(n\) & \(n\) & \(6*n\) \\ \cline{2-5}  & Number of steps & 2 & 1 & 29 \\ \cline{2-5}  & Tabu length & \(4*n\) & \(4*n\) & \(20*n\) \\ \hline \multirow{3}{*}{Simulated annealing} & Mutate randomly selected gene (Boolean) & 0 & 0 & 1 \\ \cline{2-5}  & Non-negative parameter of temperature reducing & 0.1 & 0.1 & 0.4 \\ \cline{2-5}  & Minimum temperature & 0.005 & 0.005 & 0.01 \\ \cline{2-5}  & Use step (Boolean) & 1 & 0 & 1 \\ \cline{2-5}  & Number of steps & 2 & 1 & 29 \\ \cline{2-5}  & Reduce temperature by acceptance worse & \multirow{2}{*}{1} & \multirow{2}{*}{0} & \multirow{2}{*}{1} \\  & solution candidate (Boolean) & & & 1 \\ \cline{2-5}  & Return to the found best solution candidate of all & \multirow{2}{*}{1} & \multirow{2}{*}{0} & \multirow{2}{*}{1} \\  & Iterations (Boolean) & & & 1 \\ \cline{2-5}  & Number of previous iterations to remember the & \multirow{2}{*}{5} & \multirow{2}{*}{5} & \multirow{2}{*}{10} \\  & found best solution candidate & & & \(6*n\) \\ \hline \multirow{3}{*}{Differential evolution} & Population size & \(n\) & \(n\) & \(6*n\) \\ \cline{2-5}  & Parameter of the Adaptive Rule—Differential Evolution & \multirow{2}{*}{0.2} & \multirow{2}{*}{0.2} & \multirow{2}{*}{0.8} \\ \cline{2-5}  & Probability of a Crossover—Differential Evolution & \multirow{2}{*}{0.2} & \multirow{2}{*}{0.2} & \multirow{2}{*}{0.8} \\ \hline \multirow{3}{*}{Evolution strategy} & Population size & \(n\) & \(n\) & \(6*n\) \\ \cline{2-5}  & Number of offspring & \(n\) & \(n\) & \(6*n\) \\ \cline{2-5}  & Number of success (the offspring is better than & \multirow{2}{*}{\(n\)} & \multirow{2}{*}{\(n\)} & \multirow{2}{*}{\(6*n\)} \\  & the parent) to be monitored & & & \(6*n\) \\ \cline{2-5}  & Number of other contestants per tournament & \(n\) & \(n\) & \(6*n\) \\ \cline{2-5}  & Probability of individual selection & 0.1 & 0.1 & 0.6 \\ \cline{2-5}  & Cut-off value & \(n\) & \(n\) & \(6*n\) \\ \hline \multirow{3}{*}{Self-organising migrating algorithm (SOMA)} & Mass (stopping distance from the leader) & 0.5 & 1.1 & 2.6 \\ \cline{2-5}  & Step (distance of the currently selected individual and the leader) & \multirow{2}{*}{0.4} & \multirow{2}{*}{0.11} & \multirow{2}{*}{1.31} \\ \cline{2-5}  & Perturbation (probability of movement to leader) & 0.1 & 0.1 & 0.6 \\ \cline{2-5}  & Population size & \(n\) & \(n\) & \(6*n\) \\ \cline{2-5}  & Number of migration loops & 10 & 10 & 10 \\ \cline{2-5}  & Type of strategy of individuals movement & 1 & 0 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specification of optimisation methods parameters. * Step 13--The behaviour of the tested optimisation methods is random. We had to repeat many optimisation experiments to identify the pure nature of the optimisation methods (reduce the randomness of the method behaviour) to compare the efficiency of the tested optimisation methods. * Step 14--The next flowchart shows the basic phases of simulation optimisation running on the simulation optimiser--see Figure 9 in Section 5 Simulation optimiser. * Step 15--The simulation optimiser performs an evaluation of the series after the completion of each series.