{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T23:12:33Z","timestamp":1781824353583,"version":"3.54.5"},"reference-count":50,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T00:00:00Z","timestamp":1642032000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100016152","name":"Yayasan Universiti Teknologi PETRONAS","doi-asserted-by":"publisher","award":["YUTP 015LC0-045"],"award-info":[{"award-number":["YUTP 015LC0-045"]}],"id":[{"id":"10.13039\/501100016152","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ajman University\u2019s Internal Research Grant","award":["2021-IRG-ENIT-1"],"award-info":[{"award-number":["2021-IRG-ENIT-1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposes a novel hybrid arithmetic\u2013trigonometric optimization algorithm (ATOA) using different trigonometric functions for complex and continuously evolving real-time problems. The proposed algorithm adopts different trigonometric functions, namely sin, cos, and tan, with the conventional sine cosine algorithm (SCA) and arithmetic optimization algorithm (AOA) to improve the convergence rate and optimal search area in the exploration and exploitation phases. The proposed algorithm is simulated with 33 distinct optimization test problems consisting of multiple dimensions to showcase the effectiveness of ATOA. Furthermore, the different variants of the ATOA optimization technique are used to obtain the controller parameters for the real-time pressure process plant to investigate its performance. The obtained results have shown a remarkable performance improvement compared with the existing algorithms.<\/jats:p>","DOI":"10.3390\/s22020617","type":"journal-article","created":{"date-parts":[[2022,1,14]],"date-time":"2022-01-14T03:14:56Z","timestamp":1642130096000},"page":"617","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":47,"title":["An Arithmetic-Trigonometric Optimization Algorithm with Application for Control of Real-Time Pressure Process Plant"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0231-5113","authenticated-orcid":false,"given":"P. Arun Mozhi","family":"Devan","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1419-9300","authenticated-orcid":false,"given":"Fawnizu Azmadi","family":"Hussin","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1939-0155","authenticated-orcid":false,"given":"Rosdiazli B.","family":"Ibrahim","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7333-7438","authenticated-orcid":false,"given":"Kishore","family":"Bingi","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1984-1817","authenticated-orcid":false,"given":"M.","family":"Nagarajapandian","sequence":"additional","affiliation":[{"name":"Department of Electronics and Instrumentation Engineering, Sri Ramakrishna Engineering College, Coimbatore 641022, Tamil Nadu, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1584-8747","authenticated-orcid":false,"given":"Maher","family":"Assaad","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Ajman University, Ajman 666688, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113609","DOI":"10.1016\/j.cma.2020.113609","article-title":"The arithmetic optimization algorithm","volume":"376","author":"Abualigah","year":"2021","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"61471","DOI":"10.1109\/ACCESS.2020.2983451","article-title":"Rationalized sine cosine optimization with efficient searching patterns","volume":"8","author":"Huang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Devan, P., Hussin, F.A., Ibrahim, R., Bingi, K., and Khanday, F.A. (2021). A Survey on the Application of WirelessHART for Industrial Process Monitoring and Control. Sensors, 21.","DOI":"10.3390\/s21154951"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"50001","DOI":"10.1109\/ACCESS.2021.3067597","article-title":"Grasshopper optimization algorithm: Theory, variants, and applications","volume":"9","author":"Meraihi","year":"2021","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"25993","DOI":"10.1109\/ACCESS.2021.3055292","article-title":"Conventional and metaheuristic optimization algorithms for solving short term hydrothermal scheduling problem: A review","volume":"9","author":"Fakhar","year":"2021","journal-title":"IEEE Access"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2687","DOI":"10.1007\/s13369-017-2740-7","article-title":"Fractional order set-point weighted PID controller for pH neutralization process using accelerated PSO algorithm","volume":"43","author":"Bingi","year":"2018","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Emambocus, B.A.S., Jasser, M.B., Mustapha, A., and Amphawan, A. (2021). Dragonfly Algorithm and Its Hybrids: A Survey on Performance, Objectives and Applications. Sensors, 21.","DOI":"10.3390\/s21227542"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"299","DOI":"10.3390\/s140100299","article-title":"Bio-mimic optimization strategies in wireless sensor networks: A survey","volume":"14","author":"Adnan","year":"2014","journal-title":"Sensors"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yue, Z., Zhang, S., and Xiao, W. (2020). A novel hybrid algorithm based on grey wolf optimizer and fireworks algorithm. Sensors, 20.","DOI":"10.3390\/s20072147"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Devan, P.A.M., Hussin, F.A., Ibrahim, R., Bingi, K., and Abdulrab, H. (2021, January 25\u201326). Design of Fractional-Order Predictive PI Controller for Real-time Pressure Process Plant. Proceedings of the 2021 Australian & New Zealand Control Conference (ANZCC), Gold Coast, Australia.","DOI":"10.1109\/ANZCC53563.2021.9628377"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/s00366-019-00826-w","article-title":"ESA: A hybrid bio-inspired metaheuristic optimization approach for engineering problems","volume":"37","author":"Dhiman","year":"2021","journal-title":"Eng. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106342","DOI":"10.1016\/j.asoc.2020.106342","article-title":"Multi-objective meta-heuristic optimization in intelligent control: A survey on the controller tuning problem","volume":"93","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.conengprac.2014.03.003","article-title":"Controller tuning using evolutionary multi-objective optimisation: Current trends and applications","volume":"28","author":"Blasco","year":"2014","journal-title":"Control Eng. Pract."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1007\/s00521-015-1920-1","article-title":"Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems","volume":"27","author":"Mirjalili","year":"2016","journal-title":"Neural Comput. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1109\/TEVC.2017.2767023","article-title":"Coevolutionary multiobjective evolutionary algorithms: Survey of the state-of-the-art","volume":"22","author":"Antonio","year":"2017","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2017.06.002","article-title":"A survey on multi-objective evolutionary algorithms for the solution of the environmental\/economic dispatch problems","volume":"38","author":"Qu","year":"2018","journal-title":"Swarm Evol. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.knosys.2015.12.022","article-title":"SCA: A sine cosine algorithm for solving optimization problems","volume":"96","author":"Mirjalili","year":"2016","journal-title":"Knowl.-Based Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"012005","DOI":"10.1088\/1757-899X\/366\/1\/012005","article-title":"Optimal operation of cascade hydropower stations based on chaos cultural sine cosine algorithm","volume":"Volume 366","author":"Zou","year":"2018","journal-title":"IOP Conference Series: Materials Science and Engineering"},{"key":"ref_19","first-page":"84","article-title":"Flower pollination algorithm based on sine cosine algorithm","volume":"35","author":"Liu","year":"2018","journal-title":"Microelectron Comput."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"El-Shorbagy, M.A., Farag, M., Mousa, A., and El-Desoky, I. (2019). A hybridization of sine cosine algorithm with steady state genetic algorithm for engineering design problems. International Conference on Advanced Machine Learning Technologies and Applications, Springer.","DOI":"10.1007\/978-3-030-14118-9_15"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1007\/s00521-017-3049-x","article-title":"Multi-objective sine-cosine algorithm (MO-SCA) for multi-objective engineering design problems","volume":"31","author":"Tawhid","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"84263","DOI":"10.1109\/ACCESS.2021.3085529","article-title":"A New Arithmetic Optimization Algorithm for Solving Real-World Multiobjective CEC-2021 Constrained Optimization Problems: Diversity Analysis and Validations","volume":"9","author":"Premkumar","year":"2021","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Panga, N., Sivaramakrishnan, U., Abishek, R., Bingi, K., and Chaudhary, J. (2021). An Improved Arithmetic Optimization Algorithm. 2021 IEEE Madras Section Conference (MASCON), IEEE.","DOI":"10.1109\/MASCON51689.2021.9563579"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"473","DOI":"10.3934\/mbe.2022023","article-title":"An improved arithmetic optimization algorithm with forced switching mechanism for global optimization problems","volume":"19","author":"Zheng","year":"2022","journal-title":"Math. Biosci. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Abualigah, L., Diabat, A., Sumari, P., and Gandomi, A.H. (2021). A novel evolutionary arithmetic optimization algorithm for multilevel thresholding segmentation of covid-19 ct images. Processes, 9.","DOI":"10.3390\/pr9071155"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zheng, R., Jia, H., Abualigah, L., Liu, Q., and Wang, S. (2021). Deep Ensemble of Slime Mold Algorithm and Arithmetic Optimization Algorithm for Global Optimization. Processes, 9.","DOI":"10.3390\/pr9101774"},{"key":"ref_27","first-page":"249","article-title":"Hybridizing sine cosine algorithm with multi-orthogonal search strategy for engineering design problems","volume":"5","year":"2018","journal-title":"J. Comput. Des. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ibrahim, R.A., Abualigah, L., Ewees, A.A., Al-Qaness, M.A., Yousri, D., Alshathri, S., and Abd Elaziz, M. (2021). An Electric Fish-Based Arithmetic Optimization Algorithm for Feature Selection. Entropy, 23.","DOI":"10.3390\/e23091189"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ewees, A.A., Al-qaness, M.A., Abualigah, L., Oliva, D., Algamal, Z.Y., Anter, A.M., Ali Ibrahim, R., Ghoniem, R.M., and Abd Elaziz, M. (2021). Boosting Arithmetic Optimization Algorithm with Genetic Algorithm Operators for Feature Selection: Case Study on Cox Proportional Hazards Model. Mathematics, 9.","DOI":"10.3390\/math9182321"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Tao, L., Yang, X., Zhou, Y., and Yang, L. (2021). A Novel Transformers Fault Diagnosis Method Based on Probabilistic Neural Network and Bio-Inspired Optimizer. Sensors, 21.","DOI":"10.3390\/s21113623"},{"key":"ref_31","first-page":"454","article-title":"An improved sine cosine algorithm to select features for text categorization","volume":"32","author":"Belazzoug","year":"2020","journal-title":"J. King Saud Univ.-Comput. Inf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Elkasem, A.H., Khamies, M., Magdy, G., Taha, I., and Kamel, S. (2021). Frequency Stability of AC\/DC Interconnected Power Systems with Wind Energy Using Arithmetic Optimization Algorithm-Based Fuzzy-PID Controller. Sustainability, 13.","DOI":"10.3390\/su132112095"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.ijepes.2018.01.024","article-title":"Optimal power flow solution in power systems using a novel Sine-Cosine algorithm","volume":"99","author":"Attia","year":"2018","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.eswa.2017.08.038","article-title":"Parameter optimization of support vector regression based on sine cosine algorithm","volume":"91","author":"Li","year":"2018","journal-title":"Expert Syst. Appl."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Izci, D., Ekinci, S., Kayri, M., and Eker, E. (2021). A novel improved arithmetic optimization algorithm for optimal design of PID controlled and Bode\u2019s ideal transfer function based automobile cruise control system. Evol. Syst., 1\u201316.","DOI":"10.1007\/s12530-021-09402-4"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1080\/15325008.2019.1629513","article-title":"Optimal allocation and hourly scheduling of capacitor banks using sine cosine algorithm for maximizing technical and economic benefits","volume":"47","author":"Abdelsalam","year":"2019","journal-title":"Electr. Power Compon. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2018.02.011","article-title":"A synergy of the sine-cosine algorithm and particle swarm optimizer for improved global optimization and object tracking","volume":"43","author":"Nenavath","year":"2018","journal-title":"Swarm Evol. Comput."},{"key":"ref_38","first-page":"101","article-title":"A modified sine cosine algorithm for improving wind plant energy production","volume":"16","author":"Suid","year":"2019","journal-title":"Indones. J. Electr. Eng. Comput. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1007\/s12065-019-00290-x","article-title":"Optimal FOPID\/PID controller parameters tuning for the AVR system based on sine\u2013cosine-algorithm","volume":"12","author":"Bhookya","year":"2019","journal-title":"Evol. Intell."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2567","DOI":"10.1007\/s10462-020-09909-3","article-title":"Advances in sine cosine algorithm: A comprehensive survey","volume":"54","author":"Abualigah","year":"2021","journal-title":"Artif. Intell. Rev."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.comnet.2018.03.023","article-title":"Congestion control in wireless sensor networks by hybrid multi-objective optimization algorithm","volume":"138","author":"Singh","year":"2018","journal-title":"Comput. Netw."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"26901","DOI":"10.1109\/ACCESS.2017.2766453","article-title":"A digital twin-based approach for designing and multi-objective optimization of hollow glass production line","volume":"5","author":"Zhang","year":"2017","journal-title":"Ieee Access"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.future.2020.03.055","article-title":"Slime mould algorithm: A new method for stochastic optimization","volume":"111","author":"Li","year":"2020","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No free lunch theorems for optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"100665","DOI":"10.1016\/j.swevo.2020.100665","article-title":"Recent trends in the use of statistical tests for comparing swarm and evolutionary computing algorithms: Practical guidelines and a critical review","volume":"54","author":"Carrasco","year":"2020","journal-title":"Swarm Evol. Comput."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Devan, P.A.M., Hussin, F.A., Ibrahim, R., Bingi, K., and Abdulrab, H. (2020, January 1\u20133). Fractional-order Predictive PI Controller for Process Plants with Deadtime. Proceedings of the 2020 IEEE 8th R10 Humanitarian Technology Conference (R10-HTC), Kuching, Malaysia.","DOI":"10.1109\/R10-HTC49770.2020.9357000"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"25885","DOI":"10.1109\/ACCESS.2017.2772925","article-title":"Adopting setpoint weighting strategy for WirelessHART networked control systems characterised by stochastic delay","volume":"5","author":"Hassan","year":"2017","journal-title":"IEEE Access"},{"key":"ref_48","first-page":"32","article-title":"Iterative Learning Control Design for a Non-Linear Multivariable System","volume":"23","author":"Mohan","year":"2021","journal-title":"J. Control Eng. Appl. Inform."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Anitha, T., Gopu, G., Nagarajapandian, M., and Devan, P.A.M. (2019, January 15\u201317). Hybrid Fuzzy PID Controller for Pressure Process Control Application. Proceedings of the 2019 IEEE Student Conference on Research and Development (SCOReD), Bandar Seri Iskandar, Malaysia.","DOI":"10.1109\/SCORED.2019.8896276"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"183759","DOI":"10.1109\/ACCESS.2020.3029068","article-title":"Fractional-Order Predictive PI Controller for Dead-Time Processes With Set-Point and Noise Filtering","volume":"8","author":"Devan","year":"2020","journal-title":"IEEE Access"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/2\/617\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:02:20Z","timestamp":1760364140000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/2\/617"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,13]]},"references-count":50,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["s22020617"],"URL":"https:\/\/doi.org\/10.3390\/s22020617","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,13]]}}}