Metaheuristic-based broad learning systems for compressive strength prediction of concrete structures

Abstract

The Broad Learning System (BLS) provides an effective framework for nonlinear mapping, offering advantages over traditional deep neural networks through its expanded input node architecture. While BLS has demonstrated improved classification accuracy and reduced computational cost, its performance can be compromised by randomly initialized input weights and biases. To address this limitation, this study proposes an integration of metaheuristic optimization algorithms with BLS (termed MBLS). Five metaphor-free optimization methods and four algorithm-specific, parameter-free methods are independently employed to optimize BLS parameters, yielding nine hybrid models. These models are applied to four benchmark datasets for predicting the compressive strength (CS) of concrete structures. Although various machine learning (ML) and deep learning (DL) methods have been explored for this task, their practical utility is constrained by structural and computational complexity. In contrast, the proposed MBLS framework achieves both structural simplicity and computational efficiency. The predictive performance of the nine hybrid MBLS models, along with a multilayer perceptron artificial neural network (MLPANN), is evaluated on four real-world datasets using four performance metrics: mean absolute percentage error (MAPE), root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). To further enhance prediction accuracy, the training data are augmented with interpolated samples. Extensive experimental results, comparative analyses, and statistical tests confirm the effectiveness of the MBLS methods. Among them, the BL-BMR model consistently achieves the best overall performance, evidenced by the lowest average MAPE, RMSE, and MAE, and the highest R² across datasets. Specifically, adopting BL-BMR forecasts yields MAPE improvements ranging from 8% to 84.98% for Dataset 1, 57.50% to 78.55% for Dataset 2, 7.82% to 62.74% for Dataset 3, and 27.24% to 42.76% for Dataset 4. The strong nonlinear input–output mapping capability of BLS, combined with effective parameter search via the BMR algorithm, renders the hybrid model highly effective for precise CS prediction.

Keywords

Compressive strength prediction / Broad learning systems / Metaphor-less optimization algorithm / Best-mean-random optimization technique / Chemical reaction optimization

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