## 5 Results
### Comparing Computation Effort  
In order to evaluate whether the simulation effort and thus the computational effort can be reduced with the presented 2-phase algorithm, a comparison of the simulation effort between the strategy for generating the initial population and the randomized generation of the initial population is necessary. The strategy for optimization of the initial population is called copied in the following, the strategy for the random generation of the initial population is called random. The simulation effort \(SA_{ICR}\) to generate the initial population with an initial copy rate of \(ICR>0.0\) is higher in contrast to the simulation effort of the randomized population \(SA_{rand}\) with an initial copy rate of \(ICR=0.0\). In order to equate the simulation effort \(SA_{ICR}=SA_{rand}\), the following assumptions for calculation of the simulation effort are made and demonstrated using a calculation example: The deterministic simulation effort \(SA_{det}\) for the first phase of the 2-phase algorithm with \(pop=100\), generation amount \(GA_{det}=100\), and \(|W|=10\) repetitions is \(SA_{det}=100\),000 \((GA_{det}\cdot pop\cdot|W|)\). Selection of the 100 best solutions with respect to the objective value out of 10 repetitions \(|W|\) with subsequent stochastic simulation with \(|N|=100\) scenarios to generate the stochastic initial population leads to a further simulation effort of \(SA_{init}=100\),\(000(pop\cdot|N|\cdot|W|)\) simulations, so that the total simulation effort is \(SA_{ICR}=200\),\(000(SA_{det}+SA_{init})\). To compare the simulation effort, for example, more randomized solutions can be generated \(SA_{init}=SA_{rand}=200 pop\cdot 100|N|\cdot 10|W|=200\),000. Another possibility is to leave the population size \(pop\) unchanged at \(pop=100\)\(SA_{init}=100 pop\cdot 100|N|\cdot 10|W|=100\),000 and additionally to perform a generation step \(GA_{stoch}=1\) within the framework of stochastic optimization at \(SA_{stoch}=1 GA_{stoch}\cdot 100 pop\cdot 100|N|\cdot 10|W|=100\),000, so that the simulation effort with the randomized initial population also corresponds to \(SA_{rand}=200\),\(000(SA_{init}+SA_{stoch})\). The latter option was chosen for comparison purposes, since it also uses the mode of action of the genetic algorithm, which requires a certain calculation time and thus makes the results more comparable. Figure 6 illustrates the performance of the different strategies for generating the initial population (randomized \(ICR=0.0\) and copied \(ICR=0.2\)-1.0). Figure 5: Boxplot correlation between the deterministic \((DET)\) and stochastic \((STD,M)\) solutions. One possibility to evaluate the effectiveness of a copied initial population \(ICR=0.2\)-1.0 is to compare the objective fulfillment of the best solution \(Best\) per experiment (Figure 7). A condensed evaluation is the relative frequency with which an \(ICR\) achieves the best value for the objective value \(Best\) per individual experiment. Of the 96 possible individual experiments (\(2 VarK_{lognorm}\cdot 8M\cdot 6f\)), a copied initial population (\(ICR=0.2\)-1.0) achieves the best objective value \(Best\) in 79.17% of the individual experiments. In 20.83% of the experiments, a randomized initial population achieves the best objective value (\(ICR=0.0\)). The initial copy rate of \(ICR=0.4\) and \(ICR=0.6\) is more often used to achieve the best objective value \(Best\) (22.5%) than the initial copy rates \(ICR=0.2,0.8\), and \(1.0\)(12%). The following conclusions can be drawn from the distribution of the frequency:  
* An optimization of the initial population does not necessarily lead to the best result with respect to the objective value \(Best\). * A low and a too high initial copy rate lead less frequently to the best objective value \(Best\).