{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T07:08:01Z","timestamp":1779174481949,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T00:00:00Z","timestamp":1754870400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Macao Polytechnic University","award":["RP\/FCA-06\/2022"],"award-info":[{"award-number":["RP\/FCA-06\/2022"]}]},{"name":"Macao Polytechnic University","award":["0044\/2023\/ITP2"],"award-info":[{"award-number":["0044\/2023\/ITP2"]}]},{"name":"Macao Science and Technology Development Fund","award":["RP\/FCA-06\/2022"],"award-info":[{"award-number":["RP\/FCA-06\/2022"]}]},{"name":"Macao Science and Technology Development Fund","award":["0044\/2023\/ITP2"],"award-info":[{"award-number":["0044\/2023\/ITP2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>To address the limitations of the Red-billed Blue Magpie Optimization algorithm (RBMO), such as its tendency to get trapped in local optima and its slow convergence rate, an enhanced version called MRBMO was proposed. MRBMO was improved by integrating Good Nodes Set Initialization, an Enhanced Search-for-food Strategy, a newly designed Siege-style Attacking-prey Strategy, and Lens-Imaging Opposition-Based Learning (LIOBL). The experimental results showed that MRBMO demonstrated strong competitiveness on the CEC2005 benchmark. Among a series of advanced metaheuristic algorithms, MRBMO exhibited significant advantages in terms of convergence speed and solution accuracy. On benchmark functions with 30, 50, and 100 dimensions, the average Friedman values of MRBMO were 1.6029, 1.6601, and 1.8775, respectively, significantly outperforming other algorithms. The overall effectiveness of MRBMO on benchmark functions with 30, 50, and 100 dimensions was 95.65%, which confirmed the effectiveness of MRBMO in handling problems of different dimensions. This paper designed two types of simulation experiments to test the practicability of MRBMO. First, MRBMO was used along with other heuristic algorithms to solve four engineering design optimization problems, aiming to verify the applicability of MRBMO in engineering design optimization. Then, to overcome the shortcomings of metaheuristic algorithms in antenna S-parameter optimization problems\u2014such as time-consuming verification processes, cumbersome operations, and complex modes\u2014this paper adopted a test suite specifically designed for antenna S-parameter optimization, with the goal of efficiently validating the effectiveness of metaheuristic algorithms in this domain. The results demonstrated that MRBMO had significant advantages in both engineering design optimization and antenna S-parameter optimization.<\/jats:p>","DOI":"10.3390\/sym17081295","type":"journal-article","created":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T14:32:36Z","timestamp":1754922756000},"page":"1295","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["MRBMO: An Enhanced Red-Billed Blue Magpie Optimization Algorithm for Solving Numerical Optimization Challenges"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-3814-2918","authenticated-orcid":false,"given":"Baili","family":"Lu","sequence":"first","affiliation":[{"name":"College of Animal Science and Technology, Zhongkai University of Agriculture and Engineering, Guangzhou 510225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-0105-6479","authenticated-orcid":false,"given":"Zhanxi","family":"Xie","sequence":"additional","affiliation":[{"name":"Faculty of Humanities and Social Sciences, Macao Polytechnic University, Macao 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-0553-2032","authenticated-orcid":false,"given":"Junhao","family":"Wei","sequence":"additional","affiliation":[{"name":"Faculty of Applied Sciences, Macao Polytechnic University, Macao 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-7162-4927","authenticated-orcid":false,"given":"Yanzhao","family":"Gu","sequence":"additional","affiliation":[{"name":"Faculty of Applied Sciences, Macao Polytechnic University, Macao 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6214-3203","authenticated-orcid":false,"given":"Yuzheng","family":"Yan","sequence":"additional","affiliation":[{"name":"Faculty of Applied Sciences, Macao Polytechnic University, Macao 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-4820-1780","authenticated-orcid":false,"given":"Zikun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Economics and Management, South China Normal University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4655-9675","authenticated-orcid":false,"given":"Shirou","family":"Pan","sequence":"additional","affiliation":[{"name":"College of Animal Science and Technology, Zhongkai University of Agriculture and Engineering, Guangzhou 510225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8068-2368","authenticated-orcid":false,"given":"Ngai","family":"Cheong","sequence":"additional","affiliation":[{"name":"Faculty of Applied Sciences, Macao Polytechnic University, Macao 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Health Economics and Management, Nanjing University of Chinese Medicine, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruishen","family":"Zhou","sequence":"additional","affiliation":[{"name":"Faculty of Applied Sciences, Macao Polytechnic University, Macao 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,11]]},"reference":[{"key":"ref_1","unstructured":"Laarhoven, P.J.M.V., Aarts, E.H.L., and Laarhoven, P.J.M.V. (1987). Simulated Annealing, Springer."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1038\/scientificamerican0792-66","article-title":"Genetic algorithms","volume":"267","author":"Holland","year":"1992","journal-title":"Sci. Am."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MCI.2006.329691","article-title":"Ant colony optimization","volume":"1","author":"Dorigo","year":"2006","journal-title":"IEEE Comput. Intell. Mag."},{"key":"ref_4","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995-International Conference on Neural Networks, Perth, WA, Australia."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/TEVC.2010.2059031","article-title":"Differential evolution: A survey of the state-of-the-art","volume":"15","author":"Das","year":"2010","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","article-title":"The whale optimization algorithm","volume":"95","author":"Mirjalili","year":"2016","journal-title":"Adv. Eng. Softw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/j.future.2019.02.028","article-title":"Harris hawks optimization: Algorithm and applications","volume":"97","author":"Heidari","year":"2019","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"109215","DOI":"10.1016\/j.knosys.2022.109215","article-title":"Beluga whale optimization: A novel nature-inspired metaheuristic algorithm","volume":"251","author":"Zhong","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1007\/s10462-023-10567-4","article-title":"Crayfish optimization algorithm","volume":"56","author":"Jia","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.enconman.2018.08.053","article-title":"Parameter extraction of solar photovoltaic models using an improved whale optimization algorithm","volume":"174","author":"Xiong","year":"2018","journal-title":"Energy Convers. Manag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"119269","DOI":"10.1016\/j.eswa.2022.119269","article-title":"An improved whale optimization algorithm based on multi-population evolution for global optimization and engineering design problems","volume":"215","author":"Shen","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"114649","DOI":"10.1016\/j.measurement.2024.114649","article-title":"Improved sand cat swarm optimization algorithm for enhancing coverage of wireless sensor networks","volume":"233","author":"Li","year":"2024","journal-title":"Measurement"},{"key":"ref_13","unstructured":"Wei, J., Gu, Y., Law, K.L.E., and Cheong, N. (2024, January 21\u201324). Adaptive Position Updating Particle Swarm Optimization for UAV Path Planning. Proceedings of the 2024 22nd International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), Seoul, Republic of Korea, ."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wei, J., Gu, Y., Yan, Y., Li, Z., Lu, B., Pan, S., and Cheong, N. (2025). LSEWOA: An Enhanced Whale Optimization Algorithm with Multi-Strategy for Numerical and Engineering Design Optimization Problems. Sensors, 25.","DOI":"10.20944\/preprints202502.2019.v1"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/s10462-024-10716-3","article-title":"Red-billed blue magpie optimizer: A novel metaheuristic algorithm for 2D\/3D UAV path planning and engineering design problems","volume":"57","author":"Fu","year":"2024","journal-title":"Artif. Intell. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"e21596","DOI":"10.1016\/j.heliyon.2023.e21596","article-title":"Antenna S-parameter optimization based on golden sine mechanism based honey badger algorithm with tent chaos","volume":"9","author":"Adegboye","year":"2023","journal-title":"Heliyon"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2468","DOI":"10.1109\/TWC.2012.051712.110670","article-title":"Antenna placement optimization for distributed antenna systems","volume":"11","author":"Park","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3336","DOI":"10.1109\/TAP.2019.2963588","article-title":"Pixel antenna optimization using NN-port characteristic mode analysis","volume":"68","author":"Jiang","year":"2020","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Karthika, K., Anusha, K., Kavitha, K., and Geetha, D.M. (2024). Optimization algorithms for reconfigurable antenna design: A review. Advances in Microwave Engineering, CRC Press.","DOI":"10.1201\/9781003459880-6"},{"key":"ref_20","first-page":"69","article-title":"Artificial bee colony algorithm-based self-optimization of base station antenna azimuth and down-tilt angle","volume":"1","author":"Cai","year":"2021","journal-title":"Telecommun. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7594","DOI":"10.1109\/TAP.2024.3443411","article-title":"An antenna optimization framework based on deep reinforcement learning","volume":"72","author":"Peng","year":"2024","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Martins, J.R.R.A., and Ning, A. (2021). Engineering Design Optimization, Cambridge University Press.","DOI":"10.1017\/9781108980647"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Salih, S.Q., Alsewari, A.R.A., and Yaseen, Z.M. (2019, January 19\u201321). Pressure vessel design simulation: Implementing of multi-swarm particle swarm optimization. Proceedings of the 2019 8th International Conference on Software and Computer Applications, Penang, Malaysia.","DOI":"10.1145\/3316615.3316643"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7407","DOI":"10.1007\/s13369-019-03767-0","article-title":"Design optimization of rolling element bearings using advanced optimization technique","volume":"44","author":"Dandagwhal","year":"2019","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wei, J., Gu, Y., Lu, B., and Cheong, N. (2025). RWOA: A novel enhanced whale optimization algorithm with multi-strategy for numerical optimization and engineering design problems. PLoS ONE, 20.","DOI":"10.1371\/journal.pone.0320913"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"113917","DOI":"10.1016\/j.eswa.2020.113917","article-title":"An improved grey wolf optimizer for solving engineering problems","volume":"166","author":"Taghian","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"e31629","DOI":"10.1016\/j.heliyon.2024.e31629","article-title":"Greater cane rat algorithm (GCRA): A nature-inspired metaheuristic for optimization problems","volume":"10","author":"Agushaka","year":"2024","journal-title":"Heliyon"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Xiao, C., Cai, Z., and Wang, Y. (2007, January 25\u201328). A good nodes set evolution strategy for constrained optimization. Proceedings of the 2007 IEEE Congress on Evolutionary Computation, Singapore.","DOI":"10.1109\/ICNC.2007.441"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wei, J., Gu, Y., Xie, Z., Yan, Y., Lu, B., Li, Z., and Cheong, N. (2025). TSWOA: An enhanced whale optimization algorithm with Levy flight and Spiral flight for numerical and engineering design optimization problems. PLoS ONE, 20.","DOI":"10.1371\/journal.pone.0320913"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"111211","DOI":"10.1016\/j.asoc.2023.111211","article-title":"Lens imaging opposition-based learning for differential evolution with cauchy perturbation","volume":"152","author":"Yu","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"ref_31","first-page":"2005005","article-title":"Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization","volume":"2005","author":"Suganthan","year":"2005","journal-title":"KanGAL Rep."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"101459","DOI":"10.1016\/j.swevo.2023.101459","article-title":"Attraction-Repulsion Optimization Algorithm for Global Optimization Problems","volume":"84","author":"Cymerys","year":"2024","journal-title":"Swarm Evol. Comput."},{"key":"ref_33","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_34","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.neucom.2023.02.010","article-title":"RIME: A physics-based optimization","volume":"532","author":"Su","year":"2023","journal-title":"Neurocomputing"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"115665","DOI":"10.1016\/j.eswa.2021.115665","article-title":"Remora optimization algorithm","volume":"185","author":"Jia","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"104558","DOI":"10.1016\/j.engappai.2021.104558","article-title":"A Multi-Strategy Whale Optimization Algorithm and Its Application","volume":"108","author":"Wenbiao","year":"2022","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"115003","DOI":"10.1016\/j.eswa.2021.115003","article-title":"An efficient multilevel color image thresholding based on modified whale optimization algorithm","volume":"178","author":"Anitha","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"106761","DOI":"10.1016\/j.asoc.2020.106761","article-title":"MTDE: An effective multi-trial vector-based differential evolution algorithm and its applications for engineering design problems","volume":"97","author":"Shokooh","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"6635","DOI":"10.1109\/TAP.2021.3069524","article-title":"A benchmark test suite for antenna S-parameter optimization","volume":"69","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Antennas Propag."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1295\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:24:47Z","timestamp":1760034287000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1295"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,11]]},"references-count":39,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081295"],"URL":"https:\/\/doi.org\/10.3390\/sym17081295","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,11]]}}}