## 6 Numerical Experiments
### Parameter Tuning Analysis  
The developed SAEA, AEA, DPCEA, and EA algorithms have a set of parameters, and the values of these parameters must be determined to conduct the numerical experiments. The SAEA algorithm has a total of 3 parameters, including the following: (1) population size--\(\Theta\); (2) penalty terms for infeasible individuals--\(\alpha\) and \(\beta\) (see Section 4.4 of the manuscript for description of the latter parameters); and (3) maximum allowable number of generations--\(g^{lim}\). Note that in this study the penalty terms for violation of the horizontal and vertical clearance requirements were assumed to be equal (\(\alpha=\beta\)). Along with the aforementioned three parameters, the AEA and DPCEA algorithms have additional parameters to control the crossover and mutation probabilities throughout the algorithmic run. Specifically, AEA has additional three parameters: (1) crossover probability values--\(p^{cv}\); (2) mutation probability values--\(p^{mv}\); and (3) adaptive criterion--\(g^{max}\) (i.e., the maximum number of generations without changes in the objective function). The AEA will be continuously altering the crossover and mutation probabilities based on the assigned crossover and mutation probability values (in a sequential manner) using feedback from the search (i.e., if no changes in the objective function occurred after a pre-determined number of generations) [10]. Similarly, DPCEA has additional three parameters: (1) crossover probability values at the beginning and at the end of the piecewise function--\(\widetilde{p^{cv}}\); (2) mutation probability values at the beginning and at the end of the piecewise function--\(\widetilde{p^{mv}}\); and (3) number of segments in the piecewise function--\(m^{seg}\). An example of how the crossover and mutation probabilities are altered throughout the DPCEA run is presented in Figure 8. In the provided example, the \(\widetilde{p^{cv}}\) and \(\widetilde{p^{mv}}\) values are set to \(\widetilde{p^{cv}}=[0.80,\,0.40]\) and \(\widetilde{p^{mv}}=[0.04,\,0.02]\), respectively, the number of segments in the piecewise function is set to \(n^{seg}=3\), and the stopping criterion is set to \(g^{lim}=3000\) generations. Therefore, for the first 1000 generations DPCEA will set \(p^{c}=0.80\) and \(p^{m}=0.04\); then, from generation 1001 to 2000 the crossover and mutation probabilities will be adjusted to \(p^{c}=0.60\) and \(p^{m}=0.03\); and between generations 2001 and 3000 the crossover and mutation probabilities will be set to \(p^{c}=0.40\) and \(p^{m}=0.02\). As for the EA algorithm, along with the three SAEA parameters, it has additional two parameters for defining the crossover and mutation probabilities (i.e., \(p^{c}\) and \(p^{m}\)), which do not change throughout the algorithmic run. The parameter values for the SAEA, AEA, DPCEA, and EA algorithms were set based on the parameter tuning analysis. The \"full factorial design\" methodology was used to perform the parameter tuning, where each algorithmic parameter (or \"factor\"--\(f\)) had a set of candidate values (or \"levels\"--\(l\)). A total of three candidate values were tested for each parameter of the developed solution algorithms, which corresponds to \(3^{f}\) factorial design. A total of five problem instances were selected at random from the generated large size problem instances (described in Section 6.1 of the manuscript) to perform the parameter tuning. Since the developed solution algorithms are stochastic in nature, a total of ten replications were executed to estimate the average values of the objective function and computational time for each parameter combination and each algorithm. The parameter tuning analysis results are reported in Table 3, which provides the following information: (1) algorithm; (2) parameter description; (3) considered candidate values; and (4) the best value, which was identified based on a tradeoffbetween the computational time and objective function values.