## 1 Introduction
### Hybrid Metaheuristic and Advanced Machine Learning Models  
Given the inherent complexity of blasting processes, many researchers have turned to hybrid models that integrate machine learning with evolutionary or swarm optimization techniques. The motivation is two-fold: (1) to optimize model parameters/architecture for better accuracy, and (2) to possibly find optimal blasting designs that minimize flyrock. A common strategy is coupling an ANN or other learner with an optimizer to fine-tune its weights or hyperparameters. For example, [PERSON] et al. [39] combined particle swarm optimization with an ANN (PSO-ANN) to improve convergence and avoid local minima in training. Applied to 44 blast cases in Malaysian quarries, the PSO-ANN was able to predict flyrock distance with \"a high degree of accuracy\", better than a standard back-propagation ANN, and the authors reported that powder factor and charge per delay were the most influential inputs on the model. [PERSON] et al. [40] used a different evolutionary algorithm (imperialist competitive algorithm, ICA) to optimize an ANN and showed that this ICA-ANN hybrid outperformed a conventional ANN as well as two newly developed empirical equations on a dataset of 113 blasts. Likewise, [PERSON] et al. [24] had earlier demonstrated a GA-optimized ANN (neuro-genetic model) with superior performance to an unoptimized network, underscoring the value of such hybridization. Beyond ANN enhancements, researchers have also explored hybrid models with alternative learning algorithms. Extreme learning machine (ELM) is a fast neural network variant, and [PERSON] et al. [41] optimized it using biogeography-based optimization (BBO). Their BBO-ELM achieved a testing R\({}^{2}\approx 0.94\), compared to R\({}^{2}\approx 0.79\) for a plain ELM on the same data (262 blast samples). In fact, the hybrid BBO-ELM slightly outperformed a PSO-tuned ELM as well (which had R\({}^{2}\approx 0.93\)), making BBO-ELM the top model in that study [40]. A recent study by [PERSON] et al. [42] introduced an equilibrium optimizer coupled ELM (EO-ELM) and benchmarked it against PSO-ELM and PSO-ANN models. Using 114 blast records for training/testing, the EO-ELM attained an impressive R\({}^{2}\approx 0.97\) (RMSE \(\sim 32\) m) on the test set, whereas the PSO-ANN yielded R\({}^{2}\sim 0.87\) (RMSE \(\sim 64\) m) and PSO-ELM \(\sim 0.88\) (RMSE \(\sim 49\) m). This huge accuracy gain (EO-ELM reducing error by \(\sim\)50% relative to the ANN model) demonstrates how modern metaheuristic optimizers can dramatically improve model performance [41]. It is worth noting that such hybrids also often include a sensitivity analysis component; for instance, [PERSON] et al. [42] identified powder factor and blastability index as the most sensitive inputs (each with a normalized sensitivity of 0.98) in their EO-ELM model. Another category of hybrid models aims to combine predictive modeling with optimization of blasting parameters. [PERSON] et al. [43] took a two-stage approach, first training an ANN to predict flyrock, then using a PSO algorithm to search for optimal blast design parameters that minimize the predicted flyrock. In a case study, they showed that by adjusting the pattern (within practical limits), the anticipated flyrock distance could be reduced to \(\sim\)34 m under ideal conditions (or \(\sim\)109 m under typical field conditions), whereas the baseline scenario had much greater flyrock throw. This highlights the potential of AI not just to predict outcomes, but to actively improve blasting practices. Similarly, [PERSON] et al. [44] combined an ANN with an ant colony optimization (ACO) procedure. Their trained network predicted flyrock and back-break with high accuracy (for the ANN alone, \(\text{Ea}\approx 0.014\) and RMSE \(\approx 0.063\) in scaled units), and then the ACO algorithm was used to optimize the blast layout.