Table 3 Hyperparameter search spaces (concise) and selected best settings by model and target.
Model | Target | Type | Settings |
|---|---|---|---|
ANN | Fragmentation | Search space | \(\eta \in \{0.001,0.01,0.1\}\); hidden \(\in \{20,32,64,100,(50,50),(65,100),(25,75)\}\); activ. \(\in \{\textrm{ReLU},\tanh ,\textrm{sigmoid}\}\); batch \(\in \{32,64\}\); opt. \(\in \{\textrm{Adam},\textrm{SGD}\}\); epochs \(\in \{100,200,300\}\). |
Best params | \(\eta =0.01\); hidden=(65, 100); activ.=ReLU; batch=32; opt.=Adam; epochs=200. | ||
ANN | PPV | Search space | (same as above). |
Best params | \(\eta =0.001\); hidden=64; activ.=ReLU; batch=32; opt.=Adam; epochs=300. | ||
RF | Fragmentation | Search space | \(n_{\text {est}}\in \{50,100,200,300\}\); depth \(\in \{10,20,30,\textrm{None}\}\); min_split \(\in \{2,5,10\}\); min_leaf \(\in \{1,2,4\}\); bootstrap \(\in \{\textrm{T},\textrm{F}\}\). |
Best params | \(n_{\text {est}}=200\); depth=30; min_split=2; min_leaf=1; bootstrap=T. | ||
RF | PPV | Search space | (same as above). |
Best params | \(n_{\text {est}}=300\); depth=None; min_split=5; min_leaf=2; bootstrap=T. | ||
ANN–RF | Fragmentation | Config | VotingRegressor (equal weights); members as above. |
ANN–RF | PPV | Config | VotingRegressor (equal weights); members as above. |
PSO–ANN | Fragmentation | Search space | PSO over ANN hyperparameters: particles encode \((\eta ,h_1,h_2)\) with \(\eta \in [10^{-3},10^{-1}]\); \(h_1,h_2\in \{32,64,100\}\); swarm size \(\in \{20,40,60\}\); \(w\in [0.4,0.9]\); \(c_1,c_2\in [1.0,2.5]\); max iter.=100. |
Best params | \(\eta =0.01\); \((h_1,h_2)=(65,100)\); swarm size=40; \(w=0.7\); \(c_1=c_2=2.0\). | ||
PSO–ANN | PPV | Search space | (same as above). |
Best params | \(\eta =0.001\); \(h_1=64,h_2=0\); swarm size=40; \(w=0.7\); \(c_1=c_2=2.0\). | ||
PSO–ELM | Fragmentation | Search space | PSO over ELM structure: hidden units \(h\in \{20,40,60,80,100\}\); activ. \(\in \{\textrm{ReLU},\tanh ,\textrm{sigmoid}\}\); ridge \(\lambda \in [10^{-5},10^{-1}]\); swarm settings as PSO–ANN. |
Best params | \(h=80\); activ.=ReLU; \(\lambda =10^{-3}\); swarm size=40; \(w=0.7\); \(c_1=c_2=2.0\). | ||
PSO–ELM | PPV | Search space | (same as above). |
Best params | \(h=60\); activ.=ReLU; \(\lambda =10^{-3}\); swarm size=40; \(w=0.7\); \(c_1=c_2=2.0\). | ||
ANN–SVR | Fragmentation | Search space | Hidden size \(h\in \{16,32,64\}\); SVR \(C\in \{10,100,1000\}\); \(\gamma \in \{10^{-3},10^{-2},10^{-1}\}\); \(\varepsilon \in \{0.001,0.01,0.1\}\); kernel=RBF. |
Best params | \(h=64\); \(C=1000\); \(\gamma =10^{-2}\); \(\varepsilon =0.01\). | ||
ANN–SVR | PPV | Search space | (same as above). |
Best params | \(h=32\); \(C=1000\); \(\gamma =10^{-2}\); \(\varepsilon =0.01\). | ||
PSO–XGBoost | Fragmentation | Search space | PSO over XGBoost: particles encode \((n_{\text {est}},\text {max\_depth},\eta , \text {subsample},\text {colsample\_bytree})\) with \(n_{\text {est}}\in [100,500]\); \(\text {max\_depth}\in \{3,4,5,6\}\); \(\eta \in [0.01,0.3]\); subsample, colsample_bytree \(\in [0.6,1.0]\). |
Best params | \(n_{\text {est}}=300\); \(\text {max\_depth}=4\); \(\eta =0.05\); \(\text {subsample}=0.8\); \(\text {colsample\_bytree}=0.8\). | ||
PSO–XGBoost | PPV | Search space | (same as above). |
Best params | \(n_{\text {est}}=350\); \(\text {max\_depth}=4\); \(\eta =0.05\); \(\text {subsample}=0.8\); \(\text {colsample\_bytree}=0.8\). | ||
GA–ANN | Fragmentation | Search space | GA over ANN architecture: chromosomes encode \((n_L,h_1,h_2,\eta )\) with \(n_L\in \{1,2\}\); \(h_1,h_2\in \{32,64,100\}\); \(\eta \in \{0.001,0.01,0.05\}\); population size=30; \(p_c=0.8\); \(p_m=0.1\); generations=50. |
Best params | \(n_L=2\); \((h_1,h_2)=(64,100)\); \(\eta =0.01\); population=30; \(p_c=0.8\); \(p_m=0.1\). | ||
GA–ANN | PPV | Search space | (same as above). |
Best params | \(n_L=1\); \(h_1=64\); \(\eta =0.001\); population=30; \(p_c=0.8\); \(p_m=0.1\). |
