## 5 Experimental Results
### Stability and Convergence of the GA Method  
The following subsection introduces and discusses the experienced behavior of the optimization method as well as studies its dependence on the particular parameters. All of the collected results represent the average figures obtained by running 50 simulations with random initial parameters of traffic signals.  
The first discussed topic is the dependence of the population size (the number of genomes) within each generation. Let us denote the population size parameter as \(ps\). This being said, Figure 8 illustrates the development of the appropriate objective function for each generation in the optimization of both scenarios, respectively. One can conclude that an overly small population may result in unstable or even divergent optimization process. The minimal population size needed for the asymptotically convergent solution clearly grows with the complexity of the problem at hand. This property has a potential to be crucial for the increase in the time consumption. However, it does not disqualify the use of the proposed model considering the time requirements of each simulation.  
We also analyze the behavior pertaining to the tournament selection ratio. Let us denote the tournament selection ratio as \(ts\). The value of \(ts\) may be adjusted within the range from zero to one. The \(ts\) parameter determines the proportion of population to be removed by the tournament selection at the end of each generation simulation. As shown in Figure 9a, it can be generally argued that the higher the \(ts\) value is, the faster the convergence becomes, since more of the weak genomes are removed and replaced by mutations and offspring of stronger survivors. However, if the \(ts\) value is close or equal to one, then the solution may become unstable or even divergent. This is because a very low number of strong genomes survive and may eventually lose the tournament selection to other genomes.  
To remedy this effect, we may borrow a solution from the simulated annealing [84] or greedy algorithm [88] approaches. However, the ability to achieve the global minimum may still be impaired. We discussed that an impactful parameter is the ratio between the mutation and the interbreeding of genomes while restoring the population back to its maximum size after each tournament selection procedure. Let us denote the ratio in question as \(mr\). Then, as said, the value of this parameter may vary within the range between zero (all new genomes are created as offspring of couples of random surviving genomes) and one (all new genomes are created as mutated clones of a random surviving genome).  
Figure 8: Optimization results with respect to the population size. (**a**) Classical T-shaped junction scenario; (**b**) Real-life scenario.  
To this end, Figure 9b highlights the actual influence of the \(mr\) ratio on the convergence of the optimization process. We conclude that the preferred behavior of our solution in the real-life scenario is observed with the \(mr\) value set to somewhere between 0.1 and 0.5. This finding corresponds to the processes in nature all around us--a generally more successful approach leads to interbreeding in the population, but a small chance exists that an exceptionally strong genome would be impaired by interbreeding with others.