A modified firefly algorithm applying on multi-objective radial-based function for blasting

Modifying the metaheuristics as a striking alternative of basic algorithms is outstanding and efficient scientific approach in optimization of engineering problems to improve robustness and convergence rate. Firefly algorithm (FA) is one of the new metaheuristics inspired by the flashing behavior of fireflies, where the performance of each randomly generated solution on objective function is evaluated by the brightness. In the current paper, a modified firefly algorithm (MFA) was introduced using expectation value and generalized weighted average of a random brightness and then evaluated with different benchmark functions. Since brightness varies with movements of fireflies, the parameter settings can adaptively be tuned for different problems. The capability of the MFA then in hybridizing with a developed automated multi-objective radial-based function network (MORBF) was examined. In blasting engineering, multi-objective models covering the peak particle velocity (PPV) and the vibration frequency (F-vib) due to providing more insight on safety criteria significantly are essential and great of interested. The hybrid MORBF-MFA then was applied on 78 blasting data comprising stemming, burden, spacing, total charge, distance, and charge per delay to provide more accurate predictive model. Detailed executed analyses through different metrics showed 1.01% and 2.43% improvement in hybrid MORBF-MFA corresponding to PPV and F-vib over MORBF-FA. The observed results approved that the introduced MFA as a reliable and feasible tool with accurate enough response can effectively be applied to multi-objective problems. Implemented sensitivity analyses scored the distance and burden as the most and least influences factors on predicted outputs.

Automated summary

The modified firefly algorithm (MFA) introduced in this paper, along with the hybrid MORBF-MFA, demonstrated excellent performance in engineering optimization problems, showing adaptability, fast convergence speed, and high accuracy. The combination of MFA with MORBF for predictive modeling in blasting engineering resulted in significant improvements and accurate responses to multi-objective problems.