A hybrid metaheuristic approach using random forest and particle swarm optimization to study and evaluate backbreak in open-pit blasting

Backbreak is a rock fracture problem that exceeds the limits of the last row of holes in an explosion operation. Excessive backbreak increases operational costs and also poses a threat to mine safety. In this regard, a new hybrid intelligence approach based on random forest (RF) and particle swarm optimization (PSO) is proposed for predicting backbreak with high accuracy to reduce the unsolicited phenomenon induced by backbreak in open-pit blasting. A data set of 234 samples with six input parameters including special drilling (SD), spacing (S), burden (B), hole length (L), stemming (T) and powder factor (PF) and one output parameter backbreak (BB) is set up in this study. Seven input combinations (one with six parameters, six with five parameters) are built to generate the optimal prediction model. The PSO algorithm is integrated with the RF algorithm to find the optimal hyper-parameters of each model and the fitness function, which is the mean absolute error (MAE) of ten cross-validations. The performance capacities of the optimal models are assessed using MAE, root-mean-square error (RMSE), Pearson correlation coefficient (R2) and mean absolute percentage error (MAPE). Findings demonstrated that the PSO–RF model combining L–S–B–T–PF with MAE of 0.0132 and 0.0568, RMSE of 0.0811 and 0.1686, R2 of 0.9990 and 0.9961 and MAPE of 0.0027 and 0.0116 in training and testing phases, respectively, has optimal prediction performance. The optimal PSO–RF models were compared with the classical artificial neural network, RF, genetic programming, support vector machine and convolutional neural network models and show that the PSO–RF model has superiority in predicting backbreak. The Gini index of each input variable has also been calculated in the RF model, which was 31.2 (L), 23.1 (S), 27.4 (B), 36.6 (T), 23.4 (PF) and 16.9 (SD), respectively.