Abstract
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 (Fvib) 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 Fvib 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.
Similar content being viewed by others
References
Abbaszadeh Shahri A, Asheghi R (2018) Optimized developed artificial neural network-based models to predict the blast-induced ground vibration. Innov Infrastruct Solut. https://doi.org/10.1007/s41062-018-0137-4
Abbaszadeh Shahri A, Pashamohammadi F, Asheghi R, Abbaszadeh Shahri H (2021) Automated intelligent hybrid computing schemes to predict blasting induced ground vibration. Eng Comput. https://doi.org/10.1007/s00366-021-01444-1
Abbaszadeh Shahri A, Asheghi R, Khorsand Zak M (2021) A hybridized intelligence model to improve the predictability level of strength index parameters of rocks. Neural Comput Appl 33:3841–3854. https://doi.org/10.1007/s00521-020-05223-9
Abbaszadeh Shahri A, Maghsoudi Moud F, Mirfallah Lialestani S (2020) A hybrid computing model to predict rock strength index properties using support vector regression. Eng Comput. https://doi.org/10.1007/s00366-020-01078-9
Abbaszadeh Shahri A, Larsson S, Johansson F (2016) Updated relations for the uniaxial compressive strength of marlstones based on P-wave velocity and point load index test. Innov Infrastruct Solut 1:17. https://doi.org/10.1007/s41062-016-0016-9
Adel-Basset M, Abdel-Fatah L, Sangaiah AK (2018) Metaheuristic algorithms: a comprehensive review. Computational intelligence for multimedia big data on the cloud with engineering applications. Intell Data-Cent Syst. https://doi.org/10.1016/B978-0-12-813314-9.00010-4
Agresti A (1990) Categorical data analysis. Wiley, New York
Alvarez-Vigil AE, Gonzalez-Nicieza C, Lopez Gayarre F, Alvarez-Fernandez MI (2012) Predicting blasting propagation velocity and vibration frequency using artificial neural networks. Int J Rock Mech Min Sci 55:108–116. https://doi.org/10.1016/j.ijrmms.2012.05.002
Arora S, Dey K (2010) Estimation of near-field peak particle velocity. J Geol Min Res 2(4):68–73
Antanasijevic D, Pocajt V, Perić-Grujić A, Ristićb M (2018) Multiple-input–multiple-output general regression neural networks model for the simultaneous estimation of traffic-related air pollutant emissions. Atmos Pollut Res 9(2):388–397. https://doi.org/10.1016/j.apr.2017.10.011
Asheghi R, Abbaszadeh Shahri A, Khorsand Zak M (2019) Prediction of uniaxial compressive strength of different quarried rocks using metaheuristic algorithm. Arab J Sci Eng 44:8645–8659. https://doi.org/10.1007/s13369-019-04046-8
Asheghi R, Hosseini SA, Sanei M, Abbaszadeh Shahri A (2020) Updating the neural network sediment load models using different sensitivity analysis methods: a regional application. J Hydroinf 22(3):562–577. https://doi.org/10.2166/hydro.2020.098
Avellan K, Beloptpcanova E, Puurunen M (2017) Measuring, monitoring and prediction of vibration effects in rock masses in near-structure blasting. Procedia Eng 191:504–511. https://doi.org/10.1016/j.proeng.2017.05.210
Barford NC (1985) Experimental measurements: precision, error, and truth. Wiley, New York
Baykasoglu A, Ozsoydan FB (2014) An improved firefly algorithm for solving dynamic multidimensional knapsack problems. Expert Syst Appl 41(8):3712–3725. https://doi.org/10.1016/j.eswa.2013.11.040
Bielza C, Li G, Larranaga P (2011) Multi-dimensional classification with bayesian networks. Int J Approx Reason 52(6):705–727. https://doi.org/10.1016/j.ijar.2011.01.007
Bochani H, Varando G, Bielza C, Larranaga P (2015) A survey on multi-output regression. WIREs Data Min Knowl Discov 5:216–233. https://doi.org/10.1002/widm.1157
Berk RA (2008) Statistical learning from a regression perspective. Springer, New York. https://doi.org/10.1007/978-3-319-44048-4
Bradley AP (1997) The use of the area under the ROC curve in the evaluation of machine learning algorithms. Pattern Recogn 30(7):1145–1159. https://doi.org/10.1016/S0031-3203(96)00142-2
Broomhead DS, Lowe D (1988) Multivariable functional interpolation and adaptive networks. Complex Syst 2:321–355
Dk B, Nguyen T, Chou JS, Nguyen-Xuan H, Ngo TD (2018) A modified firefly algorithm-artificial neural network expert system for predicting compressive and tensile strength of high-performance concrete. Constr Build Mater 180:320–333. https://doi.org/10.1016/j.conbuildmat.2018.05.201
Chou JS, Ngo NT (2017) Modified firefly algorithm for multidimensional optimization in structural design problems. Struct Multidisc Optim 55:2013–2028. https://doi.org/10.1007/s00158-016-1624-x
Dekking MF, Kraaikamp C, Lopuhaä P, Meester LE (2005) A modern introduction to probability and statistics. Springer, London. https://doi.org/10.1007/1-84628-168-7
Deshamukhya T, Nath R, Hazarika SA, Bhanja D, Nath S (2019) A modified firefly algorithm to maximize heat dissipation of a rectangular porous fin in heat exchangers exposed to both convective and radiative environment. Proc Inst Mech Eng Part E J Process Mech Eng 233(6):1203–1216. https://doi.org/10.1177/0954408919861244
Devore JL, Berk KN (2012) Modern mathematical statistics with applications. Springer, New York. https://doi.org/10.1007/978-1-4614-0391-3
Dowding CH (1985) Blast vibration monitoring and control. Prentice-Hall, Englewoods Cliffs
Dutta R, Ganguli R, Mani V (2011) Exploring isospectral spring-mass systems with firefly algorithm. In Proc R Soc A 467:1–20. https://doi.org/10.1098/rspa.2011.0119
Esmaeilabadi R, Abasszadeh Shahri A, Behzadafshar K, Gheirati A, Nasrabadi JN (2015) Frequency content analysis of the probable earthquake in Kopet Dagh region- Northeast of Iran. Arab J Geosci 8:3833–3844. https://doi.org/10.1007/s12517-014-1446-3
Faritha Banu A, Chandrasekar C (2013) An optimized approach of modified bat algorithm to record deduplication. Int J Comput Appl 62(1):10–15. https://doi.org/10.5120/10043-4627
Fawcett T (2006) An introduction to ROC analysis. Pattern Recogn Lett 27(8):861–874. https://doi.org/10.1016/j.patrec.2005.10.010
Fister I, Yang XS, Brest J (2013) A comprehensive review of firefly algorithms. Swarm Evolut Comput 13:34–46. https://doi.org/10.1016/j.swevo.2013.06.001
Foti S, Comina C, Sambuelli L, Callerio A, Caleffi A (2010) The role of surface waves in prediction of ground vibrations from blasting. In 9th international symposium on rock fragmentation by blasting vibration from blasting, 57–65.
Hu Z (2011) Engineering vibration analysis. Shanghai Jiao Tong University Press, Shanghai
Hustrulid W, Kuchta M, Martin R (2013) Open pit mine planning and design. CRC Press, Taylor & Francis Group, Boca Raton
ISRM (1992) Suggested method for blast vibration monitoring. Int J Rock Mech Min Sci Geomech Abst 29(2):145–146. https://doi.org/10.1016/0148-9062(92)92124-U
Kalra M, Singh S (2015) A review of metaheuristic scheduling techniques in cloud computing. Egypt Informatics J 16(3):275–295. https://doi.org/10.1016/j.eij.2015.07.001
Khan WA, Hamadneh NN, Tilahun SL, Ngnotchouye JMT (2016) A review and comparative study of firefly algorithm and its modified versions. Optim Algorithms Methods Appl Intechopen Press. https://doi.org/10.5772/62472
Khandelwal M, Singh TN (2009) Prediction of blast-induced ground vibration using artificial neural network. Int J Rock Mech Min Sci 46:1214–1222. https://doi.org/10.1016/j.ijrmms.2009.03.004
Khandelwal M, Singh TN (2006) Prediction of blast induced ground vibrations and frequency in opencast mine: a neural network approach. J Sound Vib 289:711–725. https://doi.org/10.1016/j.jsv.2005.02.044
Kordos M, Arnaiz-González A, García-Osorio G (2019) Evolutionary prototype selection for multi-output regression. Neurocomputing 358:309–320. https://doi.org/10.1016/j.neucom.2019.05.055
Leng Z, Fan Y, Gao Q, Hu Y (2020) Evaluation and optimization of blasting approaches to reducing oversize boulders and toes in open-pit mine. Int J Min Sci Technol 30(3):373–380. https://doi.org/10.1016/j.ijmst.2020.03.010
Li H, Li X, Li J, Xia X, Wang X (2016) Application of coupled analysis methods for prediction of blast-induced dominant vibration frequency. Earthq Eng Eng Vib 15(1):153–162. https://doi.org/10.1007/s11803-016-0312-6
Liu B, Chen X (2015) Uncertain multiobjective programming and uncertain goal programming. J Uncertain Anal Appl 3:10. https://doi.org/10.1186/s40467-015-0036-6
Liu C, Gao F, Jin N (2014) Design and simulation of a modified firefly algorithm. In: Proceedings of seventh international joint conference on computational sciences and optimization, IEEE, Beijing, China, 21-25. https://doi.org/10.1109/CSO.2014.13
Mauder T, Sandera C, Stetina J, Seda M (2011) Optimization of the quality of continuously cast steel slabs using the firefly algorithm. Mater Technol 45(4):347–350
Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer Academic Publishers, Springer, Boston. https://doi.org/10.1007/978-1-4615-5563-6
Meyer-Baese A, Schmid V, (2014) Foundations of neural networks. Pattern Recognition and Signal Analysis in Medical Imaging (2nd Eds), 197–243. https://doi.org/10.1016/B978-0-12-409545-8.00007-8
Oliveira PM, Pires EJS, Boaventura-Cunha J, Pinho TM (2020) Review of nature and biologically inspired metaheuristics for greenhouse environment control. Trans Inst Meas Control 42(12):2338–2358. https://doi.org/10.1177/0142331220909010
Pierce WE, Crum SV, Siskind DE (1996) Assessment of low-frequency blast vibrations and potential impacts on structures. US Department of the Interior, Bureau of Mines, Twin Cities Research Center, Interagency Agreement EF68-IA 92–12180.
Rezaeineshat A, Monjezi M, Mehrdanesh A, Khandelwal M (2020) Optimization of blasting design in open pit limestone mines with the aim of reducing ground vibration using robust techniques. Geomech Geophys Geo-Energ Geo-Resour 6:40. https://doi.org/10.1007/s40948-020-00164-y
Savage JC (1966) Thermoelastic attenuation of elastic waves by cracks. J Geophys Res 71(16):3929–3938. https://doi.org/10.1029/JZ071i016p03929
Shi Y, Eberhart R (1998) A modified particle swarm optimizer. IEEE, International conference on evolutionary computation proceedings, IEEE world congress on computational intelligence (Cat. No. 98TH8360), 69–73. https://doi.org/10.1109/ICEC.1998.699146
Singh PK, Roy MP (2010) Damage to surface structures due to blast vibration. Int J Rock Mech Min Sci 47(6):949–961. https://doi.org/10.1016/j.ijrmms.2010.06.010
Stojanovic V, Nedic N, Prsic DDL, Djordjevic V (2016) Application of cuckoo search algorithm to constrained control problem of a parallel robot platform. Int J Adv Manuf Technol 87:2497–2507. https://doi.org/10.1007/s00170-016-8627-z
Stehman S (1997) Selecting and interpreting measures of thematic classification accuracy. Remote Sens Environ 62(1):77–89. https://doi.org/10.1016/S0034-4257(97)00083-7
Wei T, Li X, Stojanovic V (2021) Input-to-state stability of impulsive reaction–diffusion neural networks with infinite distributed delays. Nonlinear Dyn 103:1733–1755. https://doi.org/10.1007/s11071-021-06208-6
Willmott CJ (1981) On the validation of models. Phys Geogr 2:184–194. https://doi.org/10.1080/02723646.1981.10642213
Willmot CJ, Robeson SM, Matsuura K (2011) A refined index of model performance. Int J Climatol 32(13):2088–2094. https://doi.org/10.1002/joc.2419
Wong WK, Ming CI (2019) A review on metaheuristic algorithms: recent trends, benchmarking and applications. IEEE, In proc. 7th ICSCC. https://doi.org/10.1109/ICSCC.2019.8843624
Wu S, Chow TWS (2004) Induction machine fault detection using SOM-based RBF neural networks. IEEE Trans Ind Electron 51(1):183–194. https://doi.org/10.1109/TIE.2003.821897
Wu J, Wang YG, Burrage K, Tian YC, Lawson B, Ding Z (2020) An improved firefly algorithm for global continuous optimization problems. Expert Syst Appl 149:113340. https://doi.org/10.1016/j.eswa.2020.113340
Xu S, Li Y, Liu J, Zhang F (2020) Optimization of blasting parameters for an underground mine through prediction of blasting vibration. J Vib Control 25(9):1585–1595. https://doi.org/10.1177/1077546319829938
Yao K, Gao J (2016) Law of large numbers for uncertain random variables. IEEE Trans Fuzzy Syst 24(3):615–621. https://doi.org/10.1109/TFUZZ.2015.2466080
Yang JH, Lu WB, Jiang QH, Yao C, Zhou CB (2016) Frequency comparison of blast-induced vibration per delay for the full-face millisecond delay blasting in underground opening excavation. Tunn Undergr Space Technol 51:189–201. https://doi.org/10.1016/j.tust.2015.10.036
Yang XS (2008) Nature-inspired metaheuristic algorithms. Luniver Press
Yang XS (2011) Metaheuristic optimization: algorithm analysis and open problems. In: Pardalos PM, Rebennack S (eds), Experimental algorithms, SEA 2011, Lecture notes in computer science, vol 6630, Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20662-7_2
Zhang M, Zhou Z (2014) A review on multi-label learning algorithms. IEEE Trans Knowl Data Eng 26(8):1819–1837. https://doi.org/10.1109/TKDE.2013.39
Zhou JR, Lu WB, Zhong DW, Leng ZD, Wu L, Yan P (2019) Prediction of frequency-dependent attenuation of blast-induced vibration in underground excavation. Eur J Environ Civ Eng. https://doi.org/10.1080/19648189.2019.1620134
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that no conflict of interest exists.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Abbaszadeh Shahri, A., Khorsand Zak, M. & Abbaszadeh Shahri, H. A modified firefly algorithm applying on multi-objective radial-based function for blasting. Neural Comput & Applic 34, 2455–2471 (2022). https://doi.org/10.1007/s00521-021-06544-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-021-06544-z