{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:52:40Z","timestamp":1760237560128,"version":"build-2065373602"},"reference-count":61,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T00:00:00Z","timestamp":1590969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003086","name":"Eusko Jaurlaritza","doi-asserted-by":"publisher","award":["IT1207-19"],"award-info":[{"award-number":["IT1207-19"]}],"id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["RTI2018-094902-B-C21","RTI2018-094902-B-C22 (MCIU\/AEI\/FEDER, UE)"],"award-info":[{"award-number":["RTI2018-094902-B-C21","RTI2018-094902-B-C22 (MCIU\/AEI\/FEDER, UE)"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Global optimization problems are mostly solved using search methods. Therefore, decreasing the search space can increase the efficiency of their solving. A widely exploited technique to reduce the search space is symmetry-breaking, which helps impose constraints on breaking existing symmetries. The present article deals with the airflow control optimization problem in an oscillating-water-column using the Particle Swarm Optimization (PSO). In an effort to ameliorate the efficiency of the PSO search, a symmetry-breaking technique has been implemented. The results of optimization showed that shrinking the search space helped to reduce the search time and ameliorate the efficiency of the PSO algorithm.<\/jats:p>","DOI":"10.3390\/sym12060895","type":"journal-article","created":{"date-parts":[[2020,6,3]],"date-time":"2020-06-03T04:12:09Z","timestamp":1591157529000},"page":"895","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Symmetry-Breaking for Airflow Control Optimization of an Oscillating-Water-Column System"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2935-3830","authenticated-orcid":false,"given":"Fares","family":"M\u2019zoughi","sequence":"first","affiliation":[{"name":"Department of Automatic Control and Systems Engineering, Faculty of Engineering of Bilbao, Automatic Control Group (ACG), Institute of Research and Development of Processes (IIDP), University of the Basque Country (UPV\/EHU), Po Rafael Moreno no3, 48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9801-4130","authenticated-orcid":false,"given":"Izaskun","family":"Garrido","sequence":"additional","affiliation":[{"name":"Department of Automatic Control and Systems Engineering, Faculty of Engineering of Bilbao, Automatic Control Group (ACG), Institute of Research and Development of Processes (IIDP), University of the Basque Country (UPV\/EHU), Po Rafael Moreno no3, 48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aitor J.","family":"Garrido","sequence":"additional","affiliation":[{"name":"Department of Automatic Control and Systems Engineering, Faculty of Engineering of Bilbao, Automatic Control Group (ACG), Institute of Research and Development of Processes (IIDP), University of the Basque Country (UPV\/EHU), Po Rafael Moreno no3, 48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1016\/j.energy.2015.01.099","article-title":"Assessment of the performances of various wave energy converters along the European continental coasts","volume":"82","author":"Rusu","year":"2015","journal-title":"Energy"},{"key":"ref_2","unstructured":"European Parliament (2009). Directive 2009\/28\/EC of the European Parliament and of the Council of 23 April 2009 on the promotion of the use of energy from renewable sources and amending and subsequently repealing Directives 2001\/77\/EC and 2003\/30\/EC. Off. J. Eur. Union, 140, 47."},{"key":"ref_3","unstructured":"UNFCCC (2020, May 12). Adoption of the Paris Agreement FCCC\/CP\/2015\/L. 9\/Rev. 1. 1. United Nations Framework Convention on Climate Change. Paris. December 2015. Available online: http:\/\/unfccc.int\/resource\/docs\/2015\/cop21\/eng\/l09r01.pdf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1016\/j.renene.2018.09.007","article-title":"Energy and socio-economic benefits from the development of wave energy in Greece","volume":"132","author":"Lavidas","year":"2019","journal-title":"Renew. Energy"},{"key":"ref_5","unstructured":"IRENA (2019). Global Energy Transformation: A Roadmap to 2050, International Renewable Energy Agency. [2019th ed.]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1016\/j.rser.2016.11.101","article-title":"Ocean wave energy in the United States: Current status and future perspectives","volume":"74","author":"Lehmann","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Maria-Arenas, A., Garrido, A.J., Rusu, E., and Garrido, I. (2019). Control Strategies Applied to Wave Energy Converters: State of the Art. Energies, 12.","DOI":"10.3390\/en12163115"},{"key":"ref_8","unstructured":"REN21 (2018). Renewables 2018 Global Status Report, REN21."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Soukissian, T.H., Denaxa, D., Karathanasi, F., Prospathopoulos, A., Sarantakos, K., Iona, A., Georgantas, K., and Mavrakos, S. (2017). Marine Renewable Energy in the Mediterranean Sea: Status and Perspectives. Energies, 10.","DOI":"10.3390\/en10101512"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.rser.2017.03.110","article-title":"Wave energy device and breakwater integration: A review","volume":"77","author":"Mustapa","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.renene.2012.05.007","article-title":"Economic modelling of the potential of wave energy","volume":"48","author":"Hayward","year":"2012","journal-title":"Renew. Energy"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Neary, V.S., Ahn, S., Seng, B.E., Allahdadi, M.N., Wang, T., Yang, Z., and He, R. (2020). Characterization of Extreme Wave Conditions for Wave Energy Converter Design and Project Risk Assessment. J. Mar. Sci. Eng., 8.","DOI":"10.3390\/jmse8040289"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Konispoliatis, D.N., and Mavrakos, S.A. (2020). Wave Power Absorption by Arrays of Wave Energy Converters in Front of a Vertical Breakwater: A Theoretical Study. Energies, 13.","DOI":"10.3390\/en13081985"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Aderinto, T., and Li, H. (2020). Conceptual Design and Simulation of a Self-Adjustable Heaving Point Absorber Based Wave Energy Converter. Energies, 13.","DOI":"10.3390\/en13081997"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Lee, H.H., and Chen, C.-H. (2020). Parametric Study for an Oscillating Water Column Wave Energy Conversion System Installed on a Breakwater. Energies, 13.","DOI":"10.3390\/en13081926"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1098\/rsta.2011.0164","article-title":"A review of oscillating water columns","volume":"370","author":"Heath","year":"2012","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1017\/S0001924000096743","article-title":"Performance of the Wells self-rectifying turbine","volume":"89","author":"Raghunathan","year":"1985","journal-title":"Aeronaut. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/0376-0421(95)00001-F","article-title":"The Wells air turbine for wave energy conversion","volume":"31","author":"Raghunathan","year":"1995","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Avery, J. (2012). Symmetry-Adapted Basis Sets: Automatic Generation for Problems in Chemistry and Physics, World Scientific.","DOI":"10.1142\/9789814350471"},{"key":"ref_20","unstructured":"Carter, R.L. (1998). Molecular Symmetry and Group Theory, Wiley."},{"key":"ref_21","unstructured":"Lockwood, E.H., and Macmillan, R.H. (1978). Geometric Symmetry, Cambridge University Press Archive."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0045-7949(98)00158-8","article-title":"A symmetry reduction method for continuum structural topology optimization","volume":"70","author":"Kosaka","year":"1999","journal-title":"Comput. Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1016\/j.cma.2007.04.014","article-title":"Piezoelectric structural acoustic problems: Symmetric variational formulations and finite element results","volume":"197","author":"Larbi","year":"2008","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/S0034-4877(04)90004-3","article-title":"General symmetries in optimal control","volume":"53","year":"2004","journal-title":"Rep. Math. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Kwakernaak, H. (1995). Symmetries in control system design. Trends in Control, Springer.","DOI":"10.1007\/978-1-4471-3061-1_2"},{"key":"ref_26","unstructured":"Hasan, M.A. (2005, January 6\u20139). On Optimization Problems with Symmetric Constraints. Proceedings of the 2005 5th International Conference on Information Communications & Signal Processing, Bangkok, Thailand."},{"key":"ref_27","unstructured":"Walsh, T. (2007, January 23\u201327). Symmetry in constraint optimization. Proceedings of the Seventh International Workshop on Symmetry in Constraint Satisfaction Problems (SymCon\u201907) in Conjunction with the International Conference on Principles and Practice of Constraint Programming (CP\u20192007), Providence, RI, USA."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ji, X., Ma, F., and Zhang, J. (2009, January 1\u20133). Solving global unconstrained optimization problems by symmetry-breaking. Proceedings of the 2009 Eighth IEEE\/ACIS International Conference on Computer and Information Science, Shanghai, China.","DOI":"10.1109\/ICIS.2009.66"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Puget, J.F. (1993, January 15\u201318). On the satisfiability of symmetrical constrained satisfaction problems. Proceedings of the 7th International Symposium on Methodologies for Intelligent Systems (ISMIS\u201993), Trondheim, Norway.","DOI":"10.1007\/3-540-56804-2_33"},{"key":"ref_30","unstructured":"Crawford, J., Ginsberg, M., Luks, E., and Roy, A. (1996). Symmetry-breaking predicates for search problems. Principles of Knowledge Representation and Reasoning: Proceedings of the Fifth International Conference (KR\u201996), Morgan Kaufmann Publishers."},{"key":"ref_31","unstructured":"Puget, J.F. (2006, January 16\u201320). An efficient way of breaking value symmetries. Proceedings of the Twenty-First National Conference on Artificial Intelligence (AAAI-06), Boston, MA, USA."},{"key":"ref_32","unstructured":"Gent, I.P., and Smith, B.M. (2000). Symmetry breaking in constraint programming. Proceedings of ECAI-2000, IOS Press."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Fahle, T., Schamberger, S., and Sellmann, M. (December, January 26). Symmetry breaking. Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming (CP2001), Paphos, Cyprus.","DOI":"10.1007\/3-540-45578-7_7"},{"key":"ref_34","unstructured":"Roney-Dougal, C.M., Gent, I.P., Kelsey, T., and Linton, S. (2004, January 22\u201327). Tractable symmetry breaking using restricted search trees. Proceedings of the 16th European Conference on Artificial Intelligence (ECAI 2004), Valencia, Spain."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Legowski, A., and Niezabitowski, M. (2016, January 27\u201329). Robot path control based on PSO with fractional-order velocity. Proceedings of the International Conference on Robotics and Automation Engineering (ICRAE), Jeju Island, Korea.","DOI":"10.1109\/ICRAE.2016.7738781"},{"key":"ref_36","first-page":"118","article-title":"Water Cycle Algorithm-based Airflow Control for an Oscillating Water Column-based Wave Generation Power Plant","volume":"234","author":"Garrido","year":"2020","journal-title":"Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"M\u2019zoughi, F., Bouall\u00e8gue, S., Ayadi, M., Garrido, A.J., and Garrido, I. (2018, January 22\u201325). Harmony Search Algorithm-based Airflow Control of an Oscillating Water Column-based Wave Generation Power Plants. Proceedings of the 2018 International Conference on Advanced Systems and Electric Technologies (IC_ASET), Hammamet, Tunisia.","DOI":"10.1109\/ASET.2018.8379866"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1109\/TEC.2017.2737657","article-title":"Stalling-free Control Strategies for Oscillating-Water-Column-based Wave Power Generation Plants","volume":"33","author":"Garrido","year":"2018","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"M\u2019zoughi, F., Garrido, I., Bouall\u00e8gue, S., Ayadi, M., and Garrido, A.J. (2019). Intelligent Airflow Controls for a Stalling-Free Operation of an Oscillating Water Column-Based Wave Power Generation Plant. Electronics, 8.","DOI":"10.3390\/electronics8010070"},{"key":"ref_40","unstructured":"Eberhart, R.C., and Kennedy, J. (1995, January 4\u20136). A new optimizer using particle swarm theory. Proceedings of the 6th International Symposium on Micro Machine and Human Science MHS\u201995, Nagoya, Japan."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/4235.985692","article-title":"The Particle Swarm-Explosion, Stability, and Convergence in a Multidimensional Complex Space","volume":"6","author":"Clerc","year":"2002","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1109\/TEVC.2006.880326","article-title":"A survey of particle swarm optimization applications in electric power systems","volume":"13","author":"AlRashidi","year":"2008","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1109\/TAP.2004.823969","article-title":"Particle swarm optimization in electromagnetics","volume":"52","author":"Robinson","year":"2004","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Pandey, S., Wu, L., Guru, S.M., and Buyya, R. (2010, January 20\u201323). A particle swarm optimization-based heuristic for scheduling workflow applications in cloud computing environments. Proceedings of the 2010 24th IEEE International Conference on Advanced Information Networking and Applications, Perth, Australia.","DOI":"10.1109\/AINA.2010.31"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"M\u2019zoughi, F., Garrido, I., Garrido, A.J., and De La Sen, M. (2020). ANN-Based Airflow Control for an Oscillating Water Column Using Surface Elevation Measurements. Sensors, 20.","DOI":"10.3390\/s20051352"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1061\/(ASCE)0733-950X(1987)113:6(565)","article-title":"Application of Stokes, Cnoidal, and Fourier wave theories","volume":"113","author":"Sobey","year":"1987","journal-title":"Waterw. Port Coast. Ocean Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.coastaleng.2007.11.003","article-title":"An extension of the Airy theory for linear waves into shallow water","volume":"55","year":"2008","journal-title":"Coast. Eng."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"727982","DOI":"10.1155\/2015\/727982","article-title":"Mathematical Modeling of Oscillating Water Columns Wave-Structure Interaction in Ocean Energy Plants","volume":"2015","author":"Garrido","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1017\/S0022112085000234","article-title":"Wave generation by an oscillating surface-pressure and its application in wave-energy extraction","volume":"150","author":"Sarmento","year":"1985","journal-title":"J. Fluid Mech."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/S0141-1187(02)00022-6","article-title":"Stochastic modelling of OWC wave power plant performance","volume":"24","author":"Rodrigues","year":"2002","journal-title":"Appl. Ocean Res."},{"key":"ref_51","first-page":"111","article-title":"Air Turbines","volume":"Volume 8","author":"Sayigh","year":"2012","journal-title":"Comprehensive Renewable Energy"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.rser.2013.07.009","article-title":"Review of wave energy technologies and the necessary power-equipment","volume":"27","author":"Andreu","year":"2013","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"2382","DOI":"10.1016\/j.enconman.2005.11.013","article-title":"Current status of self rectifying air turbines for wave energy conversion","volume":"47","author":"Setoguchi","year":"2006","journal-title":"Energy Convers. Manag."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1109\/TEC.2010.2093527","article-title":"Generator selection and comparative performance in offshore oscillating water column","volume":"26","author":"Lewis","year":"2011","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1109\/TEC.2011.2167332","article-title":"Complementary control of oscillating water column-based wave energy conversion plants to improve the instantaneous power output","volume":"26","author":"Alberdi","year":"2011","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Muller, S., Diecke, M., and De Donker, R.W. (2002). Doubly fed induction generator systems for wind turbines. IEEE Ind. Appl. Mag.., 26\u201333.","DOI":"10.1109\/2943.999610"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1109\/TEC.2005.845523","article-title":"Doubly fed induction generator model for transient stability analysis","volume":"20","author":"Ledesma","year":"2005","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.compchemeng.2015.11.004","article-title":"Symmetry breaking in MILP formulations for unit commitment problems","volume":"85","author":"Lima","year":"2016","journal-title":"Comput. Chem. Eng."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s10601-006-7095-8","article-title":"Symmetry breaking constraints for value symmetries in constraint satisfaction","volume":"11","author":"Law","year":"2006","journal-title":"Constraints"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Walsh, T. (2006, January 25\u201329). General symmetry breaking constraints. Proceedings of the International Conference on Principles and Practice of Constraint Programming, Nantes, France.","DOI":"10.1007\/11889205_46"},{"key":"ref_61","unstructured":"Eberhart, R.C., and Shi, Y. (2001, January 27\u201330). Particle Swarm Optimization: Developments, Applications and Resources. Proceedings of the IEEE Congress on Evolutionary Computation, Seoul, Korea."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/6\/895\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:34:32Z","timestamp":1760175272000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/6\/895"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,1]]},"references-count":61,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["sym12060895"],"URL":"https:\/\/doi.org\/10.3390\/sym12060895","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,6,1]]}}}