# Data Reduction of Digital Twin Simulation Experiments Using Different Optimisation Methods
## 5 Simulation Optimiser  
The principle of performing the optimisation experiment on the remote simulation optimiser is described in the flowchart--see Figure 9.  
Figure 9: Flowchart of the optimisation experiment on the parallel simulation optimiser. Step 1 and 2--The simulation optimiser selects the optimisation method and sets the range of the optimisation method parameters for the series. This method is set according to the setting sent from the client. If a suitable optimisation method is used, the volume of generated data stored in the memory is significantly reduced. * Step 3 and 4--The simulation optimiser also sets the termination criteria and the range of decision variables (lower and upper bound of the simulation model input parameters) according to the sent settings. The same termination criteria must be satisfied for each optimisation method in the series. We specified the first termination criterion--value to reach--because we mapped all the solution candidates in the search space, and we know the best solution for the modelled problem. This best solution candidate represents the global optimum of the objective function. If the optimisation method finds a solution candidate whose objective function value is within the defined tolerated deviation (\(\epsilon=0.001\) in our case) from the objective function value of the global optimum, the optimisation experiment is stopped. The second termination criterion is the maximum number of simulation runs that the simulation optimiser can perform in the optimisation experiment for each model. We performed many optimisation experiments in the initial stage of testing, and we confirmed that the settings of the optimisation method could significantly affect the performance of the optimisation method. Hence, we tested many different settings of the optimisation methods to reduce the number of bad settings of the optimisation methods parameters and reduce the random nature of the selected optimisation methods (each of the selected methods uses random distribution). We calculated this maximum number using information entropy known as the Shannon entropy. The number of all possible solutions in the search space is reduced using information entropy [6]. The reduction coefficient is as follows:  
\[\delta=\max\Bigl{\{}0,1-\beta\cdot log\widetilde{X}\Bigr{\}},\ \delta\in[0,1] \tag{10}\]  
where  
* \(\widetilde{X}\) denotes the size of the search space--the number of all possible solutions in the search space;
* \(\beta\) denotes the coefficient of search space reduction. The maximum number of simulation runs that it is possible to perform in each optimisation experiment, which is the second termination criterion, is expressed as follows:  
\[\widetilde{X}_{H}=\left\lfloor 2^{\beta\cdot log_{2}\widetilde{X}}\right\rfloor \tag{11}\]  
We tested this termination criterion using the entropy function on different discrete event simulation models to specify the \(\beta\) coefficient. The curve in the chart shows the dependence of the second termination criterion on the number of possible solutions in the search space of the discrete-event simulation model--see Figure 10. The second termination criterion is not much reduced if the number of possible solutions in the search space is small. We set the coefficient \(\beta=0.05\) according to our optimisation experiments. To verify this approach, we tested the same settings of the optimisation method on the same models with two specified types of the second termination criterion--the information entropy.