{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:04:28Z","timestamp":1760148268382,"version":"build-2065373602"},"reference-count":114,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T00:00:00Z","timestamp":1681689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>Artificial neural networks are machine learning models widely used in many sciences as well as in practical applications. The basic element of these models is a vector of parameters; the values of these parameters should be estimated using some computational method, and this process is called training. For effective training of the network, computational methods from the field of global minimization are often used. However, for global minimization techniques to be effective, the bounds of the objective function should also be clearly defined. In this paper, a two-stage global optimization technique is presented for efficient training of artificial neural networks. In the first stage, the bounds for the neural network parameters are estimated using Particle Swarm Optimization and, in the following phase, the parameters of the network are optimized within the bounds of the first phase using global optimization techniques. The suggested method was used on a series of well-known problems in the literature and the experimental results were more than encouraging.<\/jats:p>","DOI":"10.3390\/computers12040082","type":"journal-article","created":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T04:45:32Z","timestamp":1681706732000},"page":"82","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Bound the Parameters of Neural Networks Using Particle Swarm Optimization"],"prefix":"10.3390","volume":"12","author":[{"given":"Ioannis G.","family":"Tsoulos","sequence":"first","affiliation":[{"name":"Department of Informatics and Telecommunications, University of Ioannina, 45110 Ioannina, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9043-1290","authenticated-orcid":false,"given":"Alexandros","family":"Tzallas","sequence":"additional","affiliation":[{"name":"Department of Informatics and Telecommunications, University of Ioannina, 45110 Ioannina, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6243-3755","authenticated-orcid":false,"given":"Evangelos","family":"Karvounis","sequence":"additional","affiliation":[{"name":"Department of Informatics and Telecommunications, University of Ioannina, 45110 Ioannina, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dimitrios","family":"Tsalikakis","sequence":"additional","affiliation":[{"name":"Department of Engineering Informatics and Telecommunications, University of Western Macedonia, 50100 Kozani, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bishop, C. (1995). Neural Networks for Pattern Recognition, Oxford University Press.","DOI":"10.1201\/9781420050646.ptb6"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02551274","article-title":"Approximation by superpositions of a sigmoidal function","volume":"2","author":"Cybenko","year":"1989","journal-title":"Math. Control. Signals Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjc\/s10052-016-4099-4","article-title":"Parameterized neural networks for high-energy physics","volume":"76","author":"Baldi","year":"2016","journal-title":"Eur. Phys. J. C"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.neunet.2006.01.006","article-title":"Time dependent neural network models for detecting changes of state in complex processes: Applications in earth sciences and astronomy","volume":"19","author":"Valdas","year":"2006","journal-title":"Neural Netw."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1126\/science.aag2302","article-title":"Solving the quantum many-body problem with artificial neural networks","volume":"355","author":"Carleo","year":"2017","journal-title":"Science"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4934","DOI":"10.1021\/acs.jctc.6b00663","article-title":"Multiscale Quantum Mechanics\/Molecular Mechanics Simulations with Neural Networks","volume":"12","author":"Shen","year":"2016","journal-title":"J. Chem. Theory Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1002\/qua.24795","article-title":"Neural network-based approaches for building high dimensional and quantum dynamics-friendly potential energy surfaces","volume":"115","author":"Manzhos","year":"2015","journal-title":"Int. J. Quantum Chem."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1021\/acscentsci.6b00219","article-title":"Neural Networks for the Prediction of Organic Chemistry Reactions","volume":"2","author":"Wei","year":"2016","journal-title":"ACS Cent. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1080\/17460441.2016.1201262","article-title":"A renaissance of neural networks in drug discovery","volume":"11","author":"Baskin","year":"2016","journal-title":"Expert Opin. Drug Discov."},{"key":"ref_10","first-page":"16","article-title":"Prediction of Novel Anti-Ebola Virus Compounds Utilizing Artificial Neural Network (ANN)","volume":"49","author":"Bartzatt","year":"2018","journal-title":"Chem. Fac."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/S2212-5671(15)01619-6","article-title":"Quantitative Modelling in Economics with Advanced Artificial Neural Networks","volume":"34","author":"Falat","year":"2015","journal-title":"Procedia Econ. Financ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1801","DOI":"10.1016\/j.jbusres.2015.10.059","article-title":"Detecting and ranking cash flow risk factors via artificial neural networks technique","volume":"69","author":"Namazi","year":"2016","journal-title":"J. Bus. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/S0169-2070(00)00063-7","article-title":"Neural network forecasting of Canadian GDP growth","volume":"17","author":"Tkacz","year":"2001","journal-title":"Int. J. Forecast."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.asoc.2008.02.003","article-title":"Multilayer perceptron neural networks with novel unsupervised training method for numerical solution of the partial differential equations","volume":"9","author":"Shirvany","year":"2009","journal-title":"Appl. Soft Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.amc.2006.05.068","article-title":"Numerical solution for high order differential equations using a hybrid neural network\u2014Optimization method","volume":"183","author":"Malek","year":"2006","journal-title":"Appl. Math. Comput."},{"key":"ref_16","first-page":"464","article-title":"Predicting moisture content of agricultural products using artificial neural networks","volume":"41","author":"Topuz","year":"2010","journal-title":"Adv. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Escamilla-Garc\u00eda, A., Soto-Zaraz\u00faa, G.M., Toledano-Ayala, M., Rivas-Araiza, E., and Gast\u00e9lum-Barrios, A. (2020). Applications of Artificial Neural Networks in Greenhouse Technology and Overview for Smart Agriculture Development. Appl. Sci., 10.","DOI":"10.3390\/app10113835"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1007\/s11042-014-2322-6","article-title":"Facial expression recognition based on a mlp neural network using constructive training algorithm","volume":"75","author":"Boughrara","year":"2016","journal-title":"Multimed Tools Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.enconman.2014.12.053","article-title":"Comparison of four Adaboost algorithm based artificial neural networks in wind speed predictions","volume":"92","author":"Liu","year":"2015","journal-title":"Energy Convers. Manag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.energy.2015.03.084","article-title":"Forecasting of natural gas consumption with artificial neural networks","volume":"85","author":"Szoplik","year":"2015","journal-title":"Energy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.icte.2018.01.014","article-title":"Intrusion detection for cloud computing using neural networks and artificial bee colony optimization algorithm","volume":"5","author":"Bahram","year":"2019","journal-title":"ICT Express"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.1109\/TNN.2009.2026902","article-title":"Privacy-Preserving Backpropagation Neural Network Learning","volume":"20","author":"Chen","year":"2009","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_24","unstructured":"Riedmiller, M., and Braun, H. (April, January 28). A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP algorithm. Proceedings of the IEEE International Conference on Neural Networks, San Francisco, CA, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1109\/TII.2014.2359620","article-title":"Neural Speed Controller Trained Online by Means of Modified RPROP Algorithm","volume":"11","author":"Pajchrowski","year":"2015","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.procs.2018.08.147","article-title":"Waiting-Time Estimation in Bank Customer Queues using RPROP Neural Networks","volume":"135","author":"Hermanto","year":"2018","journal-title":"Procedia Comput. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1016\/0098-1354(95)00228-6","article-title":"Modified quasi-Newton methods for training neural networks","volume":"20","author":"Robitaille","year":"1996","journal-title":"Comput. Chem. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1109\/TVLSI.2018.2820016","article-title":"Fast Neural Network Training on FPGA Using Quasi-Newton Optimization Method","volume":"26","author":"Liu","year":"2018","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Yamazaki, A., and de Souto, M.C.P. (2002, January 12\u201317). Optimization of neural network weights and architectures for odor recognition using simulated annealing. Proceedings of the 2002 International Joint Conference on Neural Networks, IJCNN\u201902 1, Honolulu, HI, USA.","DOI":"10.1109\/IJCNN.2002.1005531"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1016\/j.neucom.2004.07.002","article-title":"An improved PSO-based ANN with simulated annealing technique","volume":"63","author":"Da","year":"2005","journal-title":"Neurocomputing"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1109\/TNN.2002.804317","article-title":"Tuning of the structure and parameters of a neural network using an improved genetic algorithm","volume":"14","author":"Leung","year":"2003","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1109\/5.784219","article-title":"Evolving artificial neural networks","volume":"87","author":"Yao","year":"1999","journal-title":"Proc. IEEE"},{"key":"ref_33","unstructured":"Zhang, C., Shao, H., and Li, Y. (2000, January 8\u201311). Particle swarm optimisation for evolving artificial neural network. Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, Nashville, TN, USA."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1016\/j.neucom.2007.10.013","article-title":"Evolving artificial neural networks using an improved PSO and DPSO","volume":"71","author":"Yu","year":"2008","journal-title":"Neurocomputing"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1023\/A:1022995128597","article-title":"Differential Evolution Training Algorithm for Feed-Forward Neural Networks","volume":"17","author":"Ilonen","year":"2003","journal-title":"Neural Process. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2809","DOI":"10.1016\/j.neucom.2006.05.023","article-title":"Evolution of neural networks for classification and regression","volume":"70","author":"Rocha","year":"2007","journal-title":"Neurocomputing"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00500-016-2442-1","article-title":"Optimizing connection weights in neural networks using the whale optimization algorithm","volume":"22","author":"Aljarah","year":"2018","journal-title":"Soft Comput."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Gedeon, T., Wong, K., and Lee, M. (2019). Neural Information Processing. ICONIP 2019, Springer. Lecture Notes in Computer Science.","DOI":"10.1007\/978-3-030-36711-4"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/0950-7051(96)81917-4","article-title":"Initialization of neural networks by means of decision trees","volume":"8","author":"Ivanova","year":"1995","journal-title":"Knowl. Based Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/S0925-2312(99)00127-7","article-title":"A weight initialization method for improving training speed in feedforward neural network","volume":"30","author":"Yam","year":"2000","journal-title":"Neurocomputing"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Itano, F., de Abreu de Sousa, M.A., and Del-Moral-Hernandez, E. (2018, January 8\u201313). Extending MLP ANN hyper-parameters Optimization by using Genetic Algorithm. Proceedings of the 2018 International Joint Conference on Neural Networks (IJCNN), Rio de Janeiro, Brazil.","DOI":"10.1109\/IJCNN.2018.8489520"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.neunet.2021.11.020","article-title":"Feedforward neural networks initialization based on discriminant learning","volume":"146","author":"Chumachenko","year":"2022","journal-title":"Neural Netw."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2865","DOI":"10.1162\/089976601317098565","article-title":"Feedforward Neural Network Construction Using Cross Validation","volume":"13","author":"Setiono","year":"2001","journal-title":"Neural Comput."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/4235.942529","article-title":"Grammatical evolution","volume":"5","author":"Ryan","year":"2001","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.neucom.2008.01.017","article-title":"Neural network construction and training using grammatical evolution","volume":"72","author":"Tsoulos","year":"2008","journal-title":"Neurocomputing"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2193","DOI":"10.1016\/j.neucom.2005.07.013","article-title":"Evolved neural networks based on cellular automata for sensory-motor controller","volume":"69","author":"Kim","year":"2006","journal-title":"Neurocomputing"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Sandoval, F., Prieto, A., Cabestany, J., and Gra\u00f1a, M. (2007). Computational and Ambient Intelligence. IWANN 2007, Springer. Lecture Notes in Computer Science.","DOI":"10.1007\/978-3-540-73007-1"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.procs.2013.05.198","article-title":"Multicore and GPU Parallelization of Neural Networks for Face Recognition","volume":"18","author":"Huqqani","year":"2013","journal-title":"Procedia Comput. Sci."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1162\/neco.1992.4.4.473","article-title":"Simplifying neural networks by soft weight sharing","volume":"4","author":"Nowlan","year":"1992","journal-title":"Neural Comput."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Kim, J.K., Lee, M.Y., Kim, J.Y., Kim, B.J., and Lee, J.H. (2016, January 26\u201328). An efficient pruning and weight sharing method for neural network. Proceedings of the 2016 IEEE International Conference on Consumer Electronics-Asia (ICCE-Asia), Seoul, Republic of Korea.","DOI":"10.1109\/ICCE-Asia.2016.7804738"},{"key":"ref_51","unstructured":"Touretzky, D.S. (1989). Comparing biases for minimal network construction with back propagation, In Advances in Neural Information Processing Systems, Morgan Kaufmann."},{"key":"ref_52","first-page":"107","article-title":"Skeletonization: A technique for trimming the fat from a network via relevance assesment","volume":"Volume 1","author":"Touretzky","year":"1989","journal-title":"Advances in Neural Processing Systems"},{"key":"ref_53","first-page":"105","article-title":"Pruning algorithms of neural networks\u2014A comparative study","volume":"3","author":"Augasta","year":"2003","journal-title":"Cent. Eur. Comput. Sci."},{"key":"ref_54","first-page":"1929","article-title":"Dropout: A simple way to prevent neural networks from overfitting","volume":"15","author":"Srivastava","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.neucom.2015.04.006","article-title":"DropELM: Fast neural network regularization with Dropout and DropConnect","volume":"162","author":"Iosifidis","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1016\/S0893-6080(98)00046-X","article-title":"Weight decay backpropagation for noisy data","volume":"11","author":"Gupta","year":"1998","journal-title":"Neural Netw."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Carvalho, M., and Ludermir, T.B. (2006, January 13\u201315). Particle Swarm Optimization of Feed-Forward Neural Networks with Weight Decay. Proceedings of the 2006 Sixth International Conference on Hybrid Intelligent Systems (HIS\u201906), Rio de Janeiro, Brazil.","DOI":"10.1109\/HIS.2006.264888"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1109\/72.701179","article-title":"Simulated annealing and weight decay in adaptive learning: The SARPROP algorithm","volume":"9","author":"Treadgold","year":"1998","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"2399","DOI":"10.1093\/ietisy\/e88-d.10.2399","article-title":"Neural network training algorithm with possitive correlation","volume":"88","author":"Shahjahan","year":"2005","journal-title":"IEEE Trans. Inf. Syst."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/neco.1992.4.1.1","article-title":"Neural networks and the bias\/variance dilemma","volume":"4","author":"Geman","year":"1992","journal-title":"Neural Comput."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1021\/ci0342472","article-title":"The Problem of Overfitting","volume":"44","author":"Hawkins","year":"2004","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.chemolab.2015.08.020","article-title":"Particle swarm optimization (PSO). A tutorial","volume":"149","author":"Marini","year":"2015","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.pnucene.2008.07.002","article-title":"Particle Swarm Optimization applied to the nuclear reload problem of a Pressurized Water Reactor","volume":"51","author":"Machado","year":"2009","journal-title":"Progress Nucl. Energy"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"F75","DOI":"10.1190\/1.2432481","article-title":"Particle swarm optimization: A new tool to invert geophysical data","volume":"72","author":"Shaw","year":"2007","journal-title":"Geophysics"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.1016\/S0098-1354(02)00153-9","article-title":"The use of particle swarm optimization for dynamical analysis in chemical processes","volume":"26","author":"Ourique","year":"2002","journal-title":"Comput. Chem. Eng."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1007\/s11705-021-2043-0","article-title":"Hybrid method integrating machine learning and particle swarm optimization for smart chemical process operations","volume":"16","author":"Fang","year":"2022","journal-title":"Front. Chem. Sci. Eng."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1109\/TEVC.2004.826068","article-title":"An approach to multimodal biomedical image registration utilizing particle swarm optimization","volume":"8","author":"Wachowiak","year":"2004","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1016\/j.eswa.2007.08.089","article-title":"Particle swarm optimization for pap-smear diagnosis","volume":"35","author":"Marinaki","year":"2008","journal-title":"Expert Syst. Appl."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1109\/TPWRS.2009.2030293","article-title":"An Improved Particle Swarm Optimization for Nonconvex Economic Dispatch Problems","volume":"25","author":"Park","year":"2010","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1080\/01621459.1997.10474027","article-title":"Prediction Intervals for Artificial Neural Networks","volume":"92","author":"Hwang","year":"1997","journal-title":"J. Am. Stat."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.jhydrol.2013.06.043","article-title":"Constructing prediction interval for artificial neural network rainfall runoff models based on ensemble simulations","volume":"499","author":"Kasiviswanathan","year":"2013","journal-title":"J. Hydrol."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.aasri.2014.05.004","article-title":"Interval based Weight Initialization Method for Sigmoidal Feedforward Artificial Neural Networks","volume":"6","author":"Sodhi","year":"2014","journal-title":"AASRI Procedia"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s10462-021-10033-z","article-title":"A review on weight initialization strategies for neural networks","volume":"55","author":"Narkhede","year":"2022","journal-title":"Artif. Intell. Rev."},{"key":"ref_74","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995\u2014International Conference on Neural Networks, Perth, Australia."},{"key":"ref_75","unstructured":"Eberhart, R.C., and Shi, Y.H. (2001, January 27\u201330). Tracking and optimizing dynamic systems with particle swarms. Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546), Seoul, Republic of Korea."},{"key":"ref_76","unstructured":"Shi, Y.H., and Eberhart, R.C. (1999, January 6\u20139). Empirical study of particle swarm optimization. Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), Washington, DC, USA."},{"key":"ref_77","unstructured":"Shi, Y.H., and Eberhart, R.C. (May, January 30). Experimental study of particle swarm optimization. Proceedings of the SCI2000 Conference, Orlando, FL, USA."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1007\/BF01589118","article-title":"A Tolerant Algorithm for Linearly Constrained Optimization Calculations","volume":"45","author":"Powell","year":"1989","journal-title":"Math. Program."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1093\/comjnl\/13.3.317","article-title":"A new approach to variable metric algorithms","volume":"13","author":"Fletcher","year":"1970","journal-title":"Comput. J."},{"key":"ref_80","first-page":"255","article-title":"KEEL Data-Mining Software Tool: Data Set Repository, Integration of Algorithms and Experimental Analysis Framework","volume":"17","author":"Fernandez","year":"2011","journal-title":"J. Mult. Valued Log. Soft Comput."},{"key":"ref_81","unstructured":"Weiss, S.M., and Kulikowski, C.A. (1991). Computer Systems That Learn: Classification and Prediction Methods from Statistics, Neural Nets, Machine Learning, and Expert Systems, Morgan Kaufmann Publishers Inc."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0020-7373(87)80053-6","article-title":"Simplifying Decision Trees","volume":"27","author":"Quinlan","year":"1987","journal-title":"Int. Man Mach. Stud."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/BF00993174","article-title":"Schmidt, Modeling Cognitive Development on Balance Scale Phenomena","volume":"16","author":"Shultz","year":"1994","journal-title":"Mach. Learn."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1109\/TKDE.2004.11","article-title":"NeC4.5: Neural ensemble based C4.5","volume":"16","author":"Zhou","year":"2004","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1023\/A:1008307919726","article-title":"FERNN: An Algorithm for Fast Extraction of Rules from Neural Networks","volume":"12","author":"Setiono","year":"2000","journal-title":"Appl. Intell."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0933-3657(98)00028-1","article-title":"Learning Differential Diagnosis of Eryhemato-Squamous Diseases using Voting Feature Intervals","volume":"13","author":"Demiroz","year":"1998","journal-title":"Artif. Intell. Med."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1023\/A:1008280620621","article-title":"Overcoming the Myopia of Inductive Learning Algorithms with RELIEFF","volume":"7","author":"Kononenko","year":"1997","journal-title":"Appl. Intell."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/S0022-5371(77)80054-6","article-title":"Concept learning and the recognition and classification of exemplars","volume":"16","year":"1977","journal-title":"J. Verbal Learning Verbal Behav."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"1755","DOI":"10.1162\/08997660260028700","article-title":"Using noise to compute error surfaces in connectionist networks: A novel means of reducing catastrophic forgetting","volume":"14","author":"French","year":"2002","journal-title":"Neural Comput."},{"key":"ref_90","first-page":"45","article-title":"Feature Selection for Unsupervised Learning","volume":"5","author":"Dy","year":"2004","journal-title":"J. Mach. Learn. Res."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1023\/A:1018792728057","article-title":"Input Feature Extraction for Multilayered Perceptrons Using Supervised Principal Component Analysis","volume":"10","author":"Perantonis","year":"1999","journal-title":"Neural Process. Lett."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"483","DOI":"10.3233\/IDA-2002-6602","article-title":"Classification with sparse grids using simplicial basis functions","volume":"6","author":"Garcke","year":"2002","journal-title":"Intell. Data Anal."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"4164","DOI":"10.1118\/1.2786864","article-title":"The prediction of breast cancer biopsy outcomes using two CAD approaches that both emphasize an intelligible decision process","volume":"34","author":"Elter","year":"2007","journal-title":"Med. Phys."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1080\/08839519408945432","article-title":"Multistrategy Learning for Document Recognition","volume":"8","author":"Esposito","year":"1994","journal-title":"Appl. Artif. Intell."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1109\/TBME.2008.2005954","article-title":"Suitability of dysphonia measurements for telemonitoring of Parkinson\u2019s disease","volume":"56","author":"Little","year":"2009","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_96","unstructured":"Smith, J.W., Everhart, J.E., Dickson, W.C., Knowler, W.C., and Johannes, R.S. (1988, January 8\u201310). Using the ADAP learning algorithm to forecast the onset of diabetes mellitus. Proceedings of the Symposium on Computer Applications and Medical Care IEEE Computer Society Press, Minneapolis, MN, USA."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.5194\/gmd-6-1157-2013","article-title":"Failure analysis of parameter-induced simulation crashes in climate models","volume":"6","author":"Lucas","year":"2013","journal-title":"Geosci. Model Dev."},{"key":"ref_98","doi-asserted-by":"crossref","unstructured":"Giannakeas, N., Tsipouras, M.G., Tzallas, A.T., Kyriakidi, K., Tsianou, Z.E., Manousou, P., Hall, A., Karvounis, E.C., Tsianos, V., and Tsianos, E. (2015, January 25\u201329). A clustering based method for collagen proportional area extraction in liver biopsy images. Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS, Milan, Italy.","DOI":"10.1109\/EMBC.2015.7319047"},{"key":"ref_99","first-page":"260","article-title":"Non-parametric logistic and proportional odds regression","volume":"36","author":"Hastie","year":"1987","journal-title":"JRSS-C (Appl. Stat.)"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/S0169-023X(02)00138-6","article-title":"Fast hierarchical clustering and its validation","volume":"44","author":"Dash","year":"2003","journal-title":"Data Knowl. Eng."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"9193","DOI":"10.1073\/pnas.87.23.9193","article-title":"Multisurface method of pattern separation for medical diagnosis applied to breast cytology","volume":"87","author":"Wolberg","year":"1990","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/TSMCB.2003.816922","article-title":"Knowledge discovery in medical and biological datasets using a hybrid Bayes classifier\/evolutionary algorithm","volume":"33","author":"Raymer","year":"2003","journal-title":"IEEE Trans. Syst. Man Cybern. Part B"},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1080\/10556780600834745","article-title":"Regularized nonsmooth Newton method for multi-class support vector machines","volume":"22","author":"Zhong","year":"2007","journal-title":"Optim. Methods Softw."},{"key":"ref_104","first-page":"549","article-title":"Exact Bayesian Structure Discovery in Bayesian Networks","volume":"5","author":"Koivisto","year":"2004","journal-title":"J. Mach. Learn. Res."},{"key":"ref_105","unstructured":"Nash, W.J., Sellers, T.L., Talbot, S.R., Cawthor, A.J., and Ford, W.B. (1994). The Population Biology of Abalone (_Haliotis_ species) in Tasmania. I. Blacklip Abalone (_H. rubra_) from the North Coast and Islands of Bass Strait, Sea Fisheries Division, Department of Primary Industry and Fisheries, Tasmania. Technical Report No. 48 (ISSN 1034-3288)."},{"key":"ref_106","unstructured":"Brooks, T.F., Pope, D.S., and Marcolini, A.M. (1989). Airfoil Self-Noise and Prediction, National Aeronautics and Space Administration. Technical Report, NASA RP-1218."},{"key":"ref_107","doi-asserted-by":"crossref","unstructured":"Simonoff, J.S. (1996). Smooting Methods in Statistics, Springer.","DOI":"10.1007\/978-1-4612-4026-6"},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"1797","DOI":"10.1016\/S0008-8846(98)00165-3","article-title":"Modeling of strength of high performance concrete using artificial neural networks","volume":"28","author":"Yeh","year":"1998","journal-title":"Cem. Concr. Res."},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0095-0696(78)90006-2","article-title":"Hedonic prices and the demand for clean ai","volume":"5","author":"Harrison","year":"1978","journal-title":"J. Environ. Econ. Manag."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"11322","DOI":"10.1073\/pnas.89.23.11322","article-title":"Drug design by machine learning: The use of inductive logic programming to model the structure-activity relationships of trimethoprim analogues binding to dihydrofolate reductase","volume":"89","author":"King","year":"1992","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1162\/neco.1991.3.2.246","article-title":"Universal Approximation Using Radial-Basis-Function Networks","volume":"3","author":"Park","year":"1991","journal-title":"Neural Comput."},{"key":"ref_112","unstructured":"Kingma, D.P., and Ba, J.L. (2015, January 7\u20139). ADAM: A method for stochastic optimization. Proceedings of the 3rd International Conference on Learning Representations (ICLR 2015), San Diego, CA, USA."},{"key":"ref_113","unstructured":"Klima, G. (2023, April 14). Fast Compressed Neural Networks. Available online: http:\/\/fcnn.sourceforge.net\/."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1162\/106365602320169811","article-title":"Evolving Neural Networks through Augmenting Topologies","volume":"10","author":"Stanley","year":"2002","journal-title":"Evol. Comput."}],"container-title":["Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-431X\/12\/4\/82\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:17:13Z","timestamp":1760123833000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-431X\/12\/4\/82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,17]]},"references-count":114,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["computers12040082"],"URL":"https:\/\/doi.org\/10.3390\/computers12040082","relation":{},"ISSN":["2073-431X"],"issn-type":[{"type":"electronic","value":"2073-431X"}],"subject":[],"published":{"date-parts":[[2023,4,17]]}}}