ML-based slope stability prediction has progressed from early artificial neural network (ANN) applications in geotechnical engineering [18] and slope stability [19], including site-specific studies [20], to ensemble and metaheuristic-hybrid approaches [21]. Published performance figures are not directly comparable because datasets, outputs (FOS or stable/unstable class) and validation protocols differ, and many studies report a single random split. A remaining gap is the systematic reporting of group-aware validation, uncertainty and decision-threshold errors for FOS surrogate models.

XGBoost [11] implements gradient boosting with L1/L2 regularisation [22], tree pruning and column/row subsampling. LightGBM [12] introduces gradient-based one-side sampling (GOSS) and exclusive feature bundling (EFB) with leaf-wise tree growth. CatBoost [13] employs ordered boosting and symmetric trees to reduce gradient estimation bias, with l2_leaf_reg providing regularisation. These algorithms have not, to our knowledge, been compared under identical regularisation and group-aware validation for slope FOS surrogate modelling.

ICA [14], inspired by socio-political imperialism, operates through assimilation (colonies moving toward imperialists), revolution (random perturbation), empire competition and collapse. ICA has been applied to engineering optimisation problems [23] and to geotechnical prediction tasks including tunnel boring machine (TBM) penetration rate [15], tunnel squeezing [16] and soil strength prediction [17]. The present study uses ICA with a penalised objective for gradient boosting hyperparameter search and tests whether the penalty adds value over unpenalised search.

The Tarkwa mining district hosts multiple large gold operations within the Birimian-Tarkwaian sequence. [4] reported cohesion of 5 - 35 kPa and friction angles of 15˚ - 32˚ for lateritic soils in the Tarkwa area. Pore water pressure is commonly an important time-variable control on slope stability in tropical open-pit mines, and is represented here by the pore pressure ratio. To our knowledge, no ML-based slope stability study specific to this geological context has been published.

The dataset comprises 281 slope case records compiled from Iduapriem Mine investigations, published geotechnical literature and numerical simulations. Seven input parameters (RMR, unit weight, cohesion, friction angle, slope angle, slope height and pore water pressure ratio) and one output (FOS, computed by Bishop’s Simplified Method [6]) are recorded per record. RMR is used as supplied in the compiled dataset (values 0.69 - 0.98, i.e. a normalised rating rather than the conventional 0 - 100 scale [24]). The unit of analysis is a unique slope-parameter record (a unique combination of the seven inputs). The compiled file does not carry a per-record source identifier; the numbers of records originating from Iduapriem investigations, published cases and numerical simulations are therefore not reported, and source-level validation was not possible (Section 4.8). Duplicate and related records were identified as follows (Table 1): records with identical values for all seven inputs and FOS were treated as exact duplicates and removed (178 of 281 records); the three input vectors that appeared with different FOS values (for example identical inputs with FOS = 0.80 and 1.86) were merged by averaging FOS; and the remaining 100 unique input vectors were grouped into 62 slope families, defined as records sharing identical unit weight, cohesion, friction angle and slope height (differing only in slope angle, pore pressure ratio and/or RMR). Families were never split between partitions, which also acts as a conservative proxy for records from the same source or simulation series. Identical inputs yielding different FOS values indicate that some inputs governing the LEM calculation (for example detailed geometry or slip-surface settings) are not captured by the seven recorded predictors.

FOS generation. FOS was computed for every record with Bishop’s Simplified Method [6], a limit-equilibrium method for circular slip surfaces. The compiled dataset stores the resulting FOS and the seven inputs, but not the analysis settings (software, slip-surface search, number of slices, slope geometry beyond slope angle and height, or groundwater model beyond the pore pressure ratio ru, which is the only groundwater descriptor available). These settings could therefore not be reported or varied. Because FOS is a deterministic function of the same inputs used as model predictors, the machine-learning models are LEM surrogates, and no independent comparison with observed slope performance was made. Descriptive statistics of the 100 unique input vectors are summarised in Table 2.

Table 1.Source-by-source account and duplicate handling for the 281 compiled records.

Table 2.Descriptive statistics of the analysis dataset (100 unique input vectors).

SD = standard deviation.

In the analysis dataset, 19 records (19%) have FOS < 1.0 (unstable), 56 (56%) have 1.0 ≤ FOS < 1.5 (marginal) and 25 (25%) have FOS ≥ 1.5 (stable). Figure 1 presents the Pearson correlation heatmap.

All three base learners were configured with explicit regularisation (Table 3). The configurations adopted are as follows.

XGBoost: n_estimators = 300, learning_rate = 0.05, max_depth = 4, subsample = colsample_bytree = 0.80, reg_alpha = 0.50, reg_lambda = 2.00, min_child_weight = 5, gamma = 1.0.

LightGBM: n_estimators = 300, learning_rate = 0.05, max_depth = 5, num_leaves = 20, subsample = colsample_bytree = 0.80, reg_alpha = 0.50, reg_lambda = 2.00, min_child_samples = 15.

CatBoost: iterations = 300, learning_rate = 0.03, depth = 5, l2_leaf_reg = 8.0, rsm = 0.80, Bernoulli bootstrap with subsample = 0.80 (no early stopping). Random seed = 0 for all models (xgboost 3.4.1, lightgbm 4.7.0, catboost 1.2.10, scikit-learn 1.8.0).

Figure 1.Pearson correlation heatmap of the analysis dataset. Friction angle (r = 0.26 with FOS), unit weight (r = 0.21), slope angle (r = −0.20) and slope height (r = −0.19) are the strongest linear correlates; no predictor correlates strongly with FOS.

3.3.1. Anti-Overfitting Objective Function

The ICA objective augments cross-validated RMSE with an overfitting penalty, as given in Equation (1):

where RMSE_CV is the 3-fold group-aware cross-validated RMSE on the training portion (families kept intact), RMSE_train is the RMSE of the model refitted on that whole training portion, and λ = 0.3. The penalty is positive when generalisation error exceeds training error. A penalty of the form max (0, RMSE_train − RMSE_CV) would be identically zero in practice, because training error is almost always below cross-validated error. The coefficient λ = 0.3 was fixed a priori and was not tuned; its effect is examined by comparing with λ = 0 (Section 4.1).

3.3.2. ICA Algorithm and Configuration

ICA was configured with 12 countries, 3 imperialists, 20 iterations and a revolution rate of 0.3. Hyperparameter vectors were scaled to [0, 1] and decoded to the ranges in Table 3 (integers rounded). Assimilation moves each colony toward an assigned imperialist; revolution randomly repositions 30% of moves; the search retains the best-so-far solution. (Empire competition and collapse were not implemented in this simplified ICA.) The ICA seed was 10 × repeat + fold in nested CV and 42 for the final fit. Table 3 presents the search spaces and the optimal hyperparameters identified in the final fit on the development set.

Table 3.Regularised base configurations and ICA-identified hyperparameters (final fit on the 80-record development set).

Optimal values are for the λ = 0.3 objective; values from nested-CV folds differ.

The 100 analysis records were first split into a final test set (20 records, 13 slope families) and a development set (80 records) using StratifiedGroupKFold (5 splits, shuffled, random_state = 42; first split), stratified by FOS class and grouped by slope family. The test set was used once, after model selection. On the development set, repeated nested cross-validation was performed: the outer loop used StratifiedGroupKFold (5 folds, random_state = 100 and 101 for two repeats, 10 outer folds); inside every outer training portion the ICA search used 3-fold GroupKFold. Metrics are pooled out-of-fold predictions per repeat, averaged over repeats; 95% confidence intervals come from 1,000 bootstrap resamples of slope families. Paired comparisons use the difference in RMSE with a family-bootstrap interval, a Wilcoxon signed-rank test on the 10 outer-fold RMSEs, and the Nadeau-Bengio corrected resampled t-test. P-values are uncorrected for multiplicity and are exploratory. Seven metrics were computed (R, R², RMSE, MSE, MAE, V A F = [ 1 − Var ( y − y ^ ) / Var ( y ) ] × 100 % , MAPE). A mean-only predictor (training-fold mean FOS) provides a reference. Decision-threshold performance was evaluated at FOS = 1.0 and 1.5 (unstable predicted as stable = missed unstable).

Permutation feature importance [25] was computed on each outer test fold (10 permutations per feature; mean decrease in R² averaged over the 10 outer folds) and on the final test set (20 permutations). Importance values are meaningful only where the model has predictive skill.

Figure 2 shows the best-so-far penalised objective for the final ICA runs. The objectives decline over the first ~10 iterations and are flat thereafter, with ICA-CatBoost and ICA-LightGBM reaching about 0.335 - 0.338; the curves show that the search converged on the training portion but do not show that held-out performance improved. The penalty term was active: in all 10 outer folds the penalty was non-zero at the selected solution for all three learners (mean 0.019, 0.043 and 0.188 RMSE units for XGBoost, LightGBM and CatBoost) and non-zero for 100% of candidate solutions. Table 4 compares the penalised search (λ = 0.3) with an unpenalised search (λ = 0) using the same seeds. The penalty reduced the gap between cross-validated and training RMSE of the selected solution but did not reduce held-out-fold error: the penalised search had equal or slightly higher outer-fold RMSE than the unpenalised search. The study therefore provides no evidence that the proposed objective contributes beyond ordinary cross-validated error minimisation. The choice of λ = 0.3 was not tuned or justified empirically.

Figure 2.Best-so-far penalised group-CV objective for the final ICA runs (development set, λ = 0.3).

Table 4.Overfitting-penalty diagnostic and λ = 0 ablation (nested CV, 10 outer folds). Positive differences mean the penalised search had higher error.

Table 5 gives the primary nested cross-validation results with 95% confidence intervals and a mean-only reference; Table 6 gives the single untouched test evaluation. Figure 3 compares training, cross-validated and held-out RMSE.

Table 5.Repeated group-aware nested cross-validation results (80 development records, 2 × 5 folds). CIs: family bootstrap. Train RMSE: mean over outer-fold training fits.

Table 6. Final untouched test evaluation (20 records; models fitted on the 80-record development set).

Δ = R train 2 − R test 2 . With only 20 test records the 95% CIs are very wide (e.g. CatBoost R² 0.34, CI [−0.39, 0.53]; LightGBM 0.63, CI [0.13, 0.71]); the held-out ranking differs from the nested-CV ranking and should not be used to select a model.

Figure 3.Training, nested-CV and final held-out RMSE for all six models. The dashed line is the nested-CV RMSE of the mean-only predictor.

Under nested group-aware CV, regularised CatBoost had the lowest RMSE (0.336, 95% CI [0.278, 0.386]) and highest R² (0.27, CI [0.11, 0.40]), followed by ICA-CatBoost (R² = 0.23). XGBoost, ICA-XGBoost and ICA-LightGBM were indistinguishable from the mean-only predictor (R² = −0.00), and LightGBM was not significantly better. Paired analysis against the mean-only predictor (Table 7) shows significant RMSE improvements only for CatBoost (ΔRMSE = 0.058, CI [0.023, 0.095]) and ICA-CatBoost (0.048, CI [0.013, 0.086]); absolute errors remain large (MAE ≈ 0.27 - 0.33 FOS units, MAPE ≈ 22% - 27%). The large gap between training and cross-validated RMSE for CatBoost (0.107 vs 0.336) indicates that the fitted models substantially overfit even with regularisation.

These results contrast sharply with the high R² values obtainable when duplicates are present: in a preliminary check on the original 281 records, random shuffled 5-fold CV of a generic gradient boosting model gave R² ≈ 0.87, whereas duplicate-aware CV gave R² ≈ 0.62, and 45 of the 57 test records of a random 80/20 split had an identical-input twin in the training set. Single-split R² values obtained from the raw dataset therefore overstate generalisation.

Figure 4 and Figure 5 present pooled out-of-fold predicted versus observed FOS for the best standalone model (CatBoost) and the best ICA hybrid (ICA-CatBoost). Predictions are compressed toward the centre of the FOS range: low-FOS slopes are over-predicted and high-FOS slopes are under-predicted, consistent with limited skill.

Figure 4.Predicted versus observed FOS for regularised CatBoost (pooled out-of-fold, nested CV).

Figure 5.Predicted versus observed FOS for ICA-CatBoost (pooled out-of-fold, nested CV).

Figure 6 shows residual distributions (pooled out-of-fold) for all six models and Figure 7 the cumulative distribution of absolute errors, including the mean-only reference. CatBoost and ICA-CatBoost have somewhat narrower residual distributions than the other models; the improvement over the mean-only predictor is modest.

Figure 6.Violin plots of residuals (observed-predicted FOS), pooled out-of-fold.

Figure 7.Cumulative distribution of absolute prediction errors (pooled out-of-fold).

Figure 8 shows RMSE with 95% family-bootstrap intervals for nested CV and the final test set; the intervals for most models overlap each other and the mean-only predictor. Table 7 reports paired comparisons. CatBoost has lower RMSE than XGBoost (ΔRMSE = −0.060, CI [−0.084, −0.032], corrected P = 0.019), but its advantage over LightGBM (−0.023, CI [−0.051, 0.002]) and over ICA-CatBoost (−0.009; corrected P = 0.49) is not supported. Figure 9 shows that ICA tuning did not improve held-out RMSE for any base learner. “Best model” statements are therefore limited to CatBoost being the most consistent performer in nested CV; they are not supported by the held-out test, where LightGBM scored highest on 20 records.

Figure 8.RMSE with 95% family-bootstrap CIs: nested CV (n = 80) and final held-out test (n = 20).

Table 7.Paired RMSE comparisons (nested CV, 10 outer folds). Negative ΔRMSE favours A. For “Mean predictor vs model”, positive values favour the model. P-values are uncorrected and exploratory.

Figure 9. Paired RMSE difference, base learner minus ICA-tuned learner (positive favours ICA), with 95% family-bootstrap CIs.

Safety-critical performance is summarised in Figure 10 and Table 8 and Table 9.

Figure 10. Share of slopes below each threshold that were predicted at or above it (missed unstable slopes), nested CV.

Table 8. Decision-threshold performance in nested CV (mean over 2 repeats; 15 of 80 development records have FOS < 1.0 and 60 have FOS < 1.5). “Missed” = true FOS below the threshold but predicted at or above it.

Table 9. Decision-threshold performance on the final held-out test set (n = 20; 4 records with FOS < 1.0, 15 with FOS < 1.5). Counts are very small; no precision should be inferred.

In nested CV, only 15 of the 80 development records have FOS < 1.0; every model missed nearly all of them (predicting FOS ≥ 1.0), with miss rates of 93% (CatBoost) to 100% (XGBoost, ICA-XGBoost, and the mean-only reference). At the FOS = 1.5 threshold, XGBoost and ICA-XGBoost classified almost all slopes as below 1.5, which hides their inability to discriminate (all 20 stable records misclassified); LightGBM missed 19% of slopes below 1.5, and CatBoost and ICA-CatBoost 6% - 8%. On the final test set, 3 - 4 of the 4 unstable slopes were missed by every model. Aggregate regression metrics therefore overstate suitability for stability screening, and the models should not be used as a substitute for LEM analysis.

The evidence supports at most the following: CatBoost (regularised or ICA-tuned) provides small but statistically supported improvements over a mean-only predictor in group-aware nested CV, whereas XGBoost and LightGBM variants do not; ICA tuning with the overfitting penalty did not improve held-out error; and no model is accurate enough to classify unstable slopes. A model ranking scorecard was therefore omitted, because differences between most models are within sampling uncertainty.

Figure 11 and Figure 12 present permutation importance (mean decrease in R² on outer test folds ± SD over 10 folds) for the best standalone model (CatBoost) and the best ICA hybrid (ICA-CatBoost); Table 10 gives all six models. Friction angle has the highest mean importance in all six models (CatBoost 0.27, ICA-CatBoost 0.30), followed by slope angle, slope height and cohesion, whose order differs between models and whose error bars overlap. For XGBoost, ICA-XGBoost and ICA-LightGBM, which show little or no skill, importance values are near zero and should not be interpreted. These importances describe the surrogate models of an LEM calculation; they are not independent evidence of field behaviour.

Figure 11. Permutation importance for regularised CatBoost (nested CV outer folds, mean ± SD).

Figure 12. Permutation importance for ICA-CatBoost (nested CV outer folds, mean ± SD).

Table 10.Mean permutation importance (decrease in R²) over 10 outer test folds.

Because friction angle is the highest-ranked predictor in the surrogate models, characterising friction angle is a reasonable priority for LEM input quality in weathered units; this is a statement about the sensitivity of the modelled FOS to its inputs, not a validated site-risk finding.

1) FOS is computed by Bishop’s method from the same inputs used as predictors; the models are LEM surrogates and were not assessed against observed slope outcomes. 2) The analysis dataset has 100 unique records in 62 slope families; the final test set contains only 20 records (4 with FOS < 1.0), so estimates are imprecise. 3) Identical inputs with different FOS values show that some LEM inputs are not captured. 4) The compiled file has no per-record source identifier or Bishop-analysis settings, so source counts could not be reported and source-level generalisation could not be tested; slope families were used as a conservative grouping proxy. 5) Two repeats of 5-fold nested CV were used; the ICA budget (12 countries, 20 iterations) was fixed. 6) The λ = 0.3 coefficient was not tuned. 7) P-values are uncorrected and exploratory. Comparison with published studies is not made quantitatively, because published datasets, outputs and validation designs differ.