# A Microbial Screening in Silico Method for the Fitness Step Evaluation in Evolutionary Algorithms
## 4 Discussion  
In general, the results obtained allow us to conclude that the main goal of the work has been successfully achieved. The possibility of simulating the microbial screening procedures used in the \begin{table}
\begin{tabular}{c c c} \hline
**Gro Version** & **2-SAT** & **3-SAT** \\ \hline
[14] & 4 min & 8 min \\ \hline
[16] & 3 min & 6 min \\ \hline \end{tabular}
\end{table} 
Table 4: Run times as a function of complexity and Gro version. Figure 13: Spectra of solutions for the 2-SAT problem solved with the SGA, evaluating fitness with screening tools based on (**A**) the chemotaxis screening procedure, (**B**) the Lac operon screening procedure and (**C**) the antibiotic screening procedure. laboratory of microbiology, biotechnology or synthetic biology to obtain a fitness evaluation function, opens up interesting possibilities in evolutionary computing. The simulation of a colony of synthetic bacteria, in which we applied a method of screening in silico, also allows us to explore and generate a representative evolutionary surface for the problem addressed. Consequently, the present approach could be useful both in evolutionary computation and in synthetic biology experiments. It is interesting to note that in SGA and SMGA, there are no differences in their evolutionary convergence to an average maximum fitness. However, we can observe that when recombination is simulated with the Harvey algorithm [19], then the average fitness of the population is slightly higher than the average fitness achieved by classical one-point recombination. Likewise, it is worth noting that of the three procedures studied, the best screening procedure is the one that simulates the presence of antibiotics, a method that constitutes one of the standard protocols in microbiology and synthetic biology laboratories. Nevertheless, even when the proposed method to obtain the fitness function performs satisfactorily, the fact that it is based on the exponential growth of a bacterial colony could represent a high computational cost. Since the Gro simulator assumes that a synthetic bacterium is a single computational unit, then the screening routines are executed in parallel, one per bacterium. Therefore, the run-time complexity is of the order of O(\(N^{2}\)), with \(N\) being the number of synthetic bacteria. As the simulated colony grows exponentially, simulations could become computationally demanding. In order to prevent such a scenario, in each of the screening in silico experiments, the simulation time, \(t_{s}\), was limited to 150 simulated minutes (in real time it is equivalent to seconds). This approach avoids the excessive consumption of computer resources, obtaining the fitness output expected to be included in a genetic algorithm. However, many questions remain open for further study. For example, the effectiveness of screening procedures depends on the nature of the optimization problem to be solved. In the case of the 2-SAT problem, the fitness values vary gradually when the selection and evaluation of the fitness is conducted with the Lac operon, whereas in the case of screening based on antibiotic resistance, the fitness varies in a stepwise fashion (Figure 13B,C). Furthermore, the fitness values obtained by the antibiotic screening method are more homogeneous in terms of score. However, the Lac operon method yields score values that differ significantly between sequences with a different number of clauses. Therefore, in a 2-SAT problem, the antibiotic-based screening technique is the most suitable tool to differentiate between optimal and remaining solutions. However, if we want to identify the number of clauses fulfilling a given sequence, screening with the Lac Operon is more efficient. Therefore, we can conclude that the results obtained with the microbial screening procedures suggest that the selection by antibiotic better solves the problems of discontinuous type, while the selection with the Lac operon provides a better performance for the problems of continuous nature.