## 5 Conclusions  
In this work, a numerical method for the optimal detailed design of steel frames based on a FA has been studied and proposed. The main objective has been to make the method sufficiently efficient and robust. The algorithm has been parallelized to reduce execution times, and a migration strategy has been implemented to allow information to be transferred among subpopulations, avoiding biases. An extensive sensitivity analysis of the algorithm has allowed knowledge about its performance to be extracted. Additionally, a variant of the algorithm has been proposed that implements a parameter control strategy. This variant has been tested on the parameter that most affects performance based on the information from the previous sensitivity analysis. Finally, a study demonstrating the near  
Figure 34: _estimprop_ vs. _minpop_. Figure 33: _minpop_ vs. _nv_. dependence between one of the parameters and the number of variables considered in the examples has been carried out. Two examples of steel structures, which have been extensively studied by other authors, have served to verify the efficiency and robustness of the optimal design method proposed. The following conclusions can be drawn: * The sensitivity of the PFAM algorithm is higher for changes in parameters \(t_{c}\), \(\gamma_{0}\), and \(nt\) than for changes in parameters \(\alpha_{0}\), \(m\), and \(k_{max}\). * As expected, a close dependence between parameters \(t_{c}\), \(\alpha_{0}\), \(\gamma_{0}\), and \(m\) has been detected. Changes in the value of one produce changes in the optimal tuned values of the rest of them. * The optimal tuned values of the parameters are different when considering EEP2 semi-rigid connections (SRC) or rigid connections (RC). The optimal tuned values somewhat affected are those related to parameters \(t_{c}\) (SRC: [0.1, 0.3]; RC: [0.1, 0.5]), \(\alpha_{0}\) (SRC: [0.3, 1.0]; RC: [0.3, 0.5]), \(\gamma_{0}\) (SRC: [10, 25]); RC: [0.1, 25]), and \(m\) (SRC: [1, 2]; RC: [1, 3]). The most affected optimal tuned values are those related to parameter \(nt\) (SRC: [250, 1000]; RC: [30, 450]). * If the intersection between the above somewhat affected optimal tuned values is considered, it is concluded that the optimal tuned values are the following: \(t_{c}\subset[0.1,0.3]\); \(\alpha_{0}\subset[0.3,0.5]\); \(\gamma_{0}\subset[10,25]\); and \(m\subset[1,2]\). * The value of parameter \(k_{max}=100\) produces quite satisfactory results with a lower computational cost in all the cases considered. * The sensitivity study does not allow an interval of optimal tuned values for the parameter \(nt\) independent of the problem to be determined. * Considering different cases with constant values of some parameters, \(\beta_{0}=1\), \(k_{max}=100\), \(t_{c}=0.1\), \(\alpha_{0}=1.0\), and \(m=2\), all of them non-optimal and with a range of values for \(\gamma\) of the interval [1, 50], the PCPFAM procedure produces results as satisfactory as those obtained with the PFAM procedure and with optimal tuned values of the parameters. The fact that parameter \(\gamma\) varies in the interval [1, 50], maximizing the fitness landscape, compensates for not choosing optimal tuned values of other parameters, which makes PCPFAM more robust than PFAM. * PCPFAM can only act on parameters \(\beta_{0}\), \(\alpha\), \(\gamma\), and \(m\), which may change during the design process, but not on parameters \(t_{c}\), \(nt\), and \(k_{max}\), which remain constant. Among the latter, \(nt\) is the one that most affects the algorithm's performance. Therefore, PCPFAM cannot eliminate the uncertainty in the choice of parameter \(nt\). * The optimal tuned values of the \(nt\) parameter (_minpop_), found in the sensitivity analysis with PFAM, were very different and depended greatly on the case considered. The study was able to determine that parameter \(nt\) depends mainly on the number of variables \(nv\) considered in each case.