{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:25:23Z","timestamp":1760149523953,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T00:00:00Z","timestamp":1692576000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico\/I. T. La Laguna"},{"name":"CONACYT"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This work presents a comprehensive comparative analysis of four prominent swarm intelligence (SI) optimization algorithms: Ant Lion Optimizer (ALO), Bat Algorithm (BA), Grey Wolf Optimizer (GWO), and Moth Flame Optimization (MFO). When compared under the same conditions with other SI algorithms, the Particle Swarm Optimization (PSO) stands out. First, the Unscented Kalman Filter (UKF) parameters to be optimized are selected, and then each SI optimization algorithm is executed within an off-line simulation. Once the UKF initialization parameters P0, Q0, and R0 are obtained, they are applied in real-time in the decentralized neural block control (DNBC) scheme for the trajectory tracking task of a 2-DOF robot manipulator. Finally, the results are compared according to the criteria performance evaluation using each algorithm, along with CPU cost.<\/jats:p>","DOI":"10.3390\/a16080393","type":"journal-article","created":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T09:07:16Z","timestamp":1692608836000},"page":"393","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Comparative Study of Swarm Intelligence Metaheuristics in UKF-Based Neural Training Applied to the Identification and Control of Robotic Manipulator"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9421-2108","authenticated-orcid":false,"given":"Juan F.","family":"Guerra","sequence":"first","affiliation":[{"name":"Tecnologico Nacional de Mexico, Instituto Tecnologico de La Laguna, Torreon 27000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0602-8795","authenticated-orcid":false,"given":"Ramon","family":"Garcia-Hernandez","sequence":"additional","affiliation":[{"name":"Tecnologico Nacional de Mexico, Instituto Tecnologico de La Laguna, Torreon 27000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6280-0981","authenticated-orcid":false,"given":"Miguel A.","family":"Llama","sequence":"additional","affiliation":[{"name":"Tecnologico Nacional de Mexico, Instituto Tecnologico de La Laguna, Torreon 27000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0870-8615","authenticated-orcid":false,"given":"Victor","family":"Santiba\u00f1ez","sequence":"additional","affiliation":[{"name":"Tecnologico Nacional de Mexico, Instituto Tecnologico de La Laguna, Torreon 27000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yang, X.S., and Karamanoglu, M. (2020). Nature-Inspired Computation and Swarm Intelligence, Elsevier.","DOI":"10.1016\/B978-0-12-819714-1.00010-5"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1109\/JAS.2021.1004129","article-title":"A review on representative swarm intelligence algorithms for solving optimization problems: Applications and trends","volume":"8","author":"Tang","year":"2021","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Alanis, A.Y. (2022). Bioinspired Intelligent Algorithms for Optimization, Modeling and Control: Theory and Applications. Mathematics, 10.","DOI":"10.3390\/math10132334"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Degas, A., Islam, M.R., Hurter, C., Barua, S., Rahman, H., Poudel, M., Ruscio, D., Ahmed, M.U., Begum, S., and Rahman, M.A. (2022). A survey on artificial intelligence (AI) and eXplainable AI in air traffic management: Current trends and development with future research trajectory. Appl. Sci., 12.","DOI":"10.3390\/app12031295"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Cao, X., Yan, H., Huang, Z., Ai, S., Xu, Y., Fu, R., and Zou, X. (2021). A multi-objective particle swarm optimization for trajectory planning of fruit picking manipulator. Agronomy, 11.","DOI":"10.3390\/agronomy11112286"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Malik, A., Henderson, T., and Prazenica, R. (2021). Multi-objective swarm intelligence trajectory generation for a 7 degree of freedom robotic manipulator. Robotics, 10.","DOI":"10.3390\/robotics10040127"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.advengsoft.2015.01.010","article-title":"The ant lion optimizer","volume":"83","author":"Mirjalili","year":"2015","journal-title":"Adv. Eng. Softw."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1504\/IJBIC.2013.055093","article-title":"Bat algorithm: Literature review and applications","volume":"5","author":"Yang","year":"2013","journal-title":"Int. J. Bio-Inspired Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey wolf optimizer","volume":"69","author":"Mirjalili","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.knosys.2015.07.006","article-title":"Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm","volume":"89","author":"Mirjalili","year":"2015","journal-title":"Knowl.-Based Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1942","DOI":"10.1109\/ICNN.1995.488968","article-title":"Particle swarm optimization","volume":"Volume 4","author":"Eberhart","year":"1995","journal-title":"Proceedings of the IEEE International Conference on Neural Networks"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Rao, S.S. (2019). Engineering Optimization: Theory and Practice, John Wiley & Sons.","DOI":"10.1002\/9781119454816"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Oliveira, J., Oliveira, P.M., Boaventura-Cunha, J., and Pinho, T. (2020). Evaluation of hunting-based optimizers for a quadrotor sliding mode flight controller. Robotics, 9.","DOI":"10.3390\/robotics9020022"},{"key":"ref_14","unstructured":"Panda, M., and Das, B. (2019). Proceedings of the Third International Conference on Microelectronics, Computing and Communication Systems: MCCS 2018, Springer."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"William, M.V.A., Ramesh, S., Cep, R., Kumar, M.S., and Elangovan, M. (2022). MFO Tunned SVR Models for Analyzing Dimensional Characteristics of Cracks Developed on Steam Generator Tubes. Appl. Sci., 12.","DOI":"10.3390\/app122312375"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"114501","DOI":"10.1109\/ACCESS.2022.3217816","article-title":"UKF-Based Neural Training for Nonlinear Systems Identification and Control Improvement","volume":"10","author":"Guerra","year":"2022","journal-title":"IEEE Access"},{"key":"ref_17","unstructured":"Wan, E.A., and Van Der Merwe, R. (2000, January 4). The unscented Kalman filter for nonlinear estimation. Proceedings of the Adaptive Systems for Signal Processing, Communications, and Control Symposium 2000, AS-SPCC, the IEEE 2000, Lake Louise, AB, Canada."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/JPROC.2003.823141","article-title":"Unscented filtering and nonlinear estimation","volume":"92","author":"Julier","year":"2004","journal-title":"Proc. IEEE"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Simon, D. (2006). Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, John Wiley & Sons.","DOI":"10.1002\/0470045345"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"S\u00e4rkk\u00e4, S. (2013). Bayesian Filtering and Smoothing, Cambridge University Press.","DOI":"10.1017\/CBO9781139344203"},{"key":"ref_21","first-page":"185","article-title":"Neural network-based nonlinear dynamic modeling for process control","volume":"13","author":"Zhang","year":"2005","journal-title":"Control Eng. Pract."},{"key":"ref_22","unstructured":"Zhang, Z. (2008). Proceedings of the Advances in Neural Networks, Springer."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Alanis, A.Y., Arana-Daniel, N., and Lopez-Franco, C. (2018). Bio-Inspired Algorithms for Engineering, Butterworth-Heinemann.","DOI":"10.1016\/B978-0-12-813788-8.00001-9"},{"key":"ref_24","unstructured":"Kirk, D.E. (2004). Optimal Control Theory: An Introduction, Courier Corporation."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Sethi, S.P., and Sethi, S.P. (2019). What Is Optimal Control Theory?, Springer.","DOI":"10.1007\/978-3-319-98237-3"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Llama, M., Flores, A., Garcia-Hernandez, R., and Santiba\u00f1ez, V. (2020). Heuristic global optimization of an adaptive fuzzy controller for the inverted pendulum system: Experimental comparison. Appl. Sci., 10.","DOI":"10.3390\/app10186158"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Garcia-Hernandez, R., Lopez-Franco, M., Sanchez, E.N., Alanis, A.Y., and Ruz-Hernandez, J.A. (2017). Decentralized Neural Control: Application to Robotics, Springer. Studies in Systems, Decision and Control.","DOI":"10.1007\/978-3-319-53312-4"},{"key":"ref_28","unstructured":"Utkin, V., Guldner, J., and Shi, J. (2009). Sliding Mode Control in Electro-Mechanical Systems, CRC Press."},{"key":"ref_29","unstructured":"Kelly, R., Davila, V.S., and Perez, J.A.L. (2005). Control of Robot Manipulators in Joint Space, Springer Science & Business Media."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2018\/4148975","article-title":"Ls-II: An improved locust search algorithm for solving optimization problems","volume":"2018","author":"Camarena","year":"2018","journal-title":"Math. Probl. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"10744","DOI":"10.1109\/ACCESS.2017.2711484","article-title":"An ant colony optimization approach for the deployment of reliable wireless sensor networks","volume":"5","author":"Deif","year":"2017","journal-title":"IEEE Access"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1397","DOI":"10.1007\/s11831-020-09420-6","article-title":"Ant lion optimizer: A comprehensive survey of its variants and applications","volume":"28","author":"Abualigah","year":"2021","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_33","unstructured":"Chakri, A., Ragueb, H., and Yang, X.S. (2018). Nature-Inspired Algorithms and Applied Optimization, Springer."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Hernandez-Barragan, J., Martinez-Soltero, G., Rios, J.D., Lopez-Franco, C., and Alanis, A.Y. (2022). A Metaheuristic Optimization Approach to Solve Inverse Kinematics of Mobile Dual-Arm Robots. Mathematics, 10.","DOI":"10.3390\/math10214135"},{"key":"ref_35","unstructured":"Mirjalili, S., and Gandomi, A.H. (2023). Comprehensive Metaheuristics: Algorithms and Applications, Elsevier."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Mirjalili, S. (2022). Handbook of Moth-Flame Optimization Algorithm: Variants, Hybrids, Improvements, and Applications, CRC Press.","DOI":"10.1201\/9781003205326"},{"key":"ref_37","unstructured":"Mirjalili, S. (2019). Studies in Computational Intelligence, Springer."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/978-3-030-12127-3_2","article-title":"Nature-inspired optimizers","volume":"811","author":"Mirjalili","year":"2020","journal-title":"Stud. Comput. Intell."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Abdolrasol, M.G., Hussain, S.S., Ustun, T.S., Sarker, M.R., Hannan, M.A., Mohamed, R., Ali, J.A., Mekhilef, S., and Milad, A. (2021). Artificial neural networks based optimization techniques: A review. Electronics, 10.","DOI":"10.3390\/electronics10212689"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"183751","DOI":"10.1109\/ACCESS.2019.2960687","article-title":"A novel heuristic artificial neural network model for urban computing","volume":"7","author":"Na","year":"2019","journal-title":"IEEE Access"},{"key":"ref_41","unstructured":"Heidari, A.A., Faris, H., Mirjalili, S., Aljarah, I., and Mafarja, M. (2020). Nature-Inspired Optimizers: Theories, Literature Reviews and Applications, Springer."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1166\/jmihi.2019.2654","article-title":"Optimization of neural network using improved bat algorithm for data classification","volume":"9","author":"Bangyal","year":"2019","journal-title":"J. Med. Imaging Health Inform."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"109637","DOI":"10.1016\/j.engstruct.2019.109637","article-title":"An efficient artificial neural network for damage detection in bridges and beam-like structures by improving training parameters using cuckoo search algorithm","volume":"199","author":"Khatir","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Zhang, X., Hou, J., Wang, Z., and Jiang, Y. (2022). Joint SOH-SOC estimation model for lithium-ion batteries based on GWO-BP neural network. Energies, 16.","DOI":"10.3390\/en16010132"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"32727","DOI":"10.1109\/ACCESS.2020.2973415","article-title":"Convolutional neural network\u2014Optimized moth flame algorithm for shallow landslide susceptible analysis","volume":"8","author":"Pham","year":"2020","journal-title":"IEEE Access"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.1007\/s10586-021-03235-1","article-title":"A path planning method based on the particle swarm optimization trained fuzzy neural network algorithm","volume":"24","author":"Liu","year":"2021","journal-title":"Clust. Comput."},{"key":"ref_47","first-page":"2551","article-title":"Optimizing connection weights of functional link neural network using APSO algorithm for medical data classification","volume":"34","author":"Khan","year":"2022","journal-title":"J. King Saud Univ.-Comput. Inf. Sci."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Brodzicki, A., Piekarski, M., and Jaworek-Korjakowska, J. (2021). The whale optimization algorithm approach for deep neural networks. Sensors, 21.","DOI":"10.3390\/s21238003"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Pizarro-Lerma, A., Santiba\u00f1ez, V., Garcia-Hernandez, R., and Villalobos-Chin, J. (2021). Sectorial fuzzy controller plus feedforward for the trajectory tracking of robotic arms in joint space. Mathematics, 9.","DOI":"10.3390\/math9060616"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/8\/393\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:38:40Z","timestamp":1760128720000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/8\/393"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,21]]},"references-count":49,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["a16080393"],"URL":"https:\/\/doi.org\/10.3390\/a16080393","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2023,8,21]]}}}