# Data Reduction of Digital Twin Simulation Experiments Using Different Optimisation Methods
## 5 Simulation Optimiser
### The Speed in Finding a Solution Candidate

The speed of the optimisation method in finding a solution candidate is the number of performed simulation experiments until the optimum/best solution candidate (sub-optimum) was found in each series. If the optimisation method is effective, the volume of generated data (solution candidates) is quite small. The local search seems similar to the fastest optimisation method, but this method does not find the global optimum of the AGV's simulation model--see Figure 14. Other methods such as differential evolution, downhill simplex, and simulated annealing are also fast. Some methods (especially evolu

Figure 13: Simulation optimiser GUI—optimisation experiment with AGVs DT. tionary computation methods) need to perform a large number of simulation experiments (representing individuals in the population) ensuring the escape from the local extremes of the objective function. This feature is particularly suitable for the multimodal objective function, but it generates a large volume of data. The dimension of the search space is 15. The problem is how to display the objective function landscape containing millions of solution candidates. We calculated the relative frequencies of the mapped objective function values of the solution candidates considering the smaller intervals of the objective function values--see Figure 15. The objective function of the AGV model is maximised, and the higher values of relative frequencies with higher values of the objective function predominate in the chart. The probability of finding an acceptable solution is good. The relative frequencies of the objective function values (how often the objective function values occur within different ranges of objective function values) can also be used when we do not map all the solution candidates and their objective function values in the whole search space. The series also contains the solution candidates whose objective function values are not the same as the objective function of the global optimum (we accepted the solution candidates as the global optimum if their objective function value is within the defined tolerated deviation \(\varepsilon=0.001\)). The next box plot chart shows the number of simulation experiments until the suboptimum was found-see Figure 16. The box plot chart shows big differences in the efficiency of searching for the optimum. differential evolution, downhill simplex, and simulated annealing are the winners in the AGV model. Figure 14: Box plot of the speed in finding a global optimum of the objective function. Figure 15: The percentage of relative frequency of the objective function values. We proposed other criteria, i.e., quality of solution candidates using the distances of quartiles between optimum and suboptimum or the quartiles of the objective function values of the solution candidates. The other criterion is the convergence of the objective function values of the generated solution candidates in the series. We calculated the weighted sum of the proposed evaluation criteria using the specified weights for each criterion. The next box plot chart shows the weighted sum of the proposed evaluation criteria calculated for each series--see Figure 17. Differential evolution, downhill simple, and self-organizing migrating algorithm (SOMA) are effective methods for finding the global optimum in the search space of the AGV model. ### Settings of the Optimisation Methods

Many of the optimisation methods are very sensitive to the settings of their parameters. The application we developed for evaluating the series also allows the user to filter 25% of the best series (the settings of the optimisation method parameters) using the calculated weighted sum for each series. The next box plot chart shows the calculated characteristics of the number of simulation experiments until the suboptimum was found--see Figure 18. If we compare this box plot chart with the chart in Figure 16, some methods are sensitive to bad settings of their parameters.