{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:02:11Z","timestamp":1785402131484,"version":"3.56.0"},"reference-count":51,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T00:00:00Z","timestamp":1782950400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Wenzhou University of Technology Research Project","award":["ky202504"],"award-info":[{"award-number":["ky202504"]}]},{"award":["ky202504"],"award-info":[{"award-number":["ky202504"]}],"id":[{"id":"https:\/\/ror.org\/03dd7qj98","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Wenzhou Applied Basic Research Project","award":["GC20250014"],"award-info":[{"award-number":["GC20250014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>The Horned Lizard Optimization Algorithm (HLOA) is a newly proposed swarm intelligence optimizer mimicking the defensive and survival behaviors of horned lizards. The original HLOA suffers evident drawbacks when tackling high-dimensional, multimodal and heavily constrained complicated optimization problems. Rapid decline in population diversity in late iterations and insufficient local optimum escape strategies further trigger premature convergence and unsatisfactory optimization precision. To systematically address the above deficiencies and boost the global optimization and engineering applicability of HLOA, this paper proposes a hybrid-strategy improved Horned Lizard Optimization Algorithm (HSHLOA). First, an improved uniform Logistic chaotic mapping replaces conventional random initialization. It enhances the ergodicity and uniformity of initial populations across search spaces and upgrades the quality of initial solutions and population diversity. Second, an adaptive optimal guidance strategy is constructed via nonlinear dynamic adjustment factors. It prioritizes global exploration in early iterations and strengthens local exploitation in later iterations to accelerate convergence and raise optimization accuracy. Third, a lens imaging learning strategy is embedded. It generates adaptive opposite solutions following dynamic convex lens optical imaging rules, strengthens the capability to escape local optima and mitigates premature convergence. To verify the optimization performance of the proposed algorithm, comparative experiments are conducted on the CEC 2017 benchmark test suite under 30-dimensional and 100-dimensional high-dimensional settings. Seven mainstream swarm intelligence algorithms are selected for benchmark comparison. Quantitative analyses cover convergence rate, optimization precision, numerical stability and local optimum escaping ability. Experimental results reveal that HSHLOA outperforms all peer competitors on unimodal, multimodal, hybrid and composite functions with remarkable superiority. The proposed HSHLOA is further applied to three typical constrained engineering optimization cases, including reinforced concrete beam design, three-bar truss design and pressure vessel design. Application results prove that HSHLOA satisfies all engineering constraints steadily and obtains superior structural schemes with higher efficiency. The reliability and superiority of HSHLOA for practical engineering problems are therefore verified.<\/jats:p>","DOI":"10.3390\/biomimetics11070463","type":"journal-article","created":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T14:43:14Z","timestamp":1783003394000},"page":"463","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hybrid Strategy Improved Horned Lizard Optimization Algorithm for Advanced Global Optimization and Engineering Applications"],"prefix":"10.3390","volume":"11","author":[{"given":"Zhenkun","family":"Lu","sequence":"first","affiliation":[{"name":"School of Robot Engineering, Wenzhou University of Technology, Wenzhou 325035, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mingbin","family":"Tang","sequence":"additional","affiliation":[{"name":"Engineering Technology Department, Shanghai Caoyang Vocational School, Shanghai 200333, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Meng","family":"Li","sequence":"additional","affiliation":[{"name":"Zhejiang Quality Inspection Center of High and Low-Voltage Electrical Products, Yueqing 325603, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiangyun","family":"Meng","sequence":"additional","affiliation":[{"name":"School of Robot Engineering, Wenzhou University of Technology, Wenzhou 325035, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hanjin","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Robot Engineering, Wenzhou University of Technology, Wenzhou 325035, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rui","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Robot Engineering, Wenzhou University of Technology, Wenzhou 325035, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zihao","family":"Cheng","sequence":"additional","affiliation":[{"name":"College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"120887","DOI":"10.1016\/j.ins.2024.120887","article-title":"Multi-subswarm cooperative particle swarm optimization algorithm and its application","volume":"677","author":"Tang","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"110016","DOI":"10.1016\/j.engappai.2025.110016","article-title":"Parameters identification of magnetorheological damper based on particle swarm optimization algorithm","volume":"143","author":"Guo","year":"2025","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.comcom.2023.12.040","article-title":"Path planning of unmanned vehicles based on adaptive particle swarm optimization algorithm","volume":"216","author":"Zhao","year":"2024","journal-title":"Comput. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"125411","DOI":"10.1016\/j.eswa.2024.125411","article-title":"A multi-stage competitive swarm optimization algorithm for solving large-scale multi-objective optimization problems","volume":"260","author":"Shang","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_5","first-page":"101012","article-title":"Improved synergistic swarm optimization algorithm to optimize task scheduling problems in cloud computing","volume":"43","author":"Abualigah","year":"2024","journal-title":"Sustain. Comput. Inform. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Qin, S., Zeng, H., Sun, W., Wu, J., and Yang, J. (2024). Multi-strategy improved particle swarm optimization algorithm and gazelle optimization algorithm and application. Electronics, 13.","DOI":"10.3390\/electronics13081580"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1007\/s10462-024-10786-3","article-title":"A comprehensive survey on the chicken swarm optimization algorithm and its applications: State-of-the-art and research challenges","volume":"57","author":"Chen","year":"2024","journal-title":"Artif. Intell. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wang, S., Deng, Y., Lan, N., Cao, L., Cheng, Z., and Xiong, M. (2026). Coverage Optimization Strategy for Wireless Sensor Networks Based on Improved Northern Goshawk Optimization Algorithm. Biomimetics, 11.","DOI":"10.3390\/biomimetics11060378"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.jmsy.2024.03.002","article-title":"Flexible job shop scheduling with stochastic machine breakdowns by an improved tuna swarm optimization algorithm","volume":"74","author":"Fan","year":"2024","journal-title":"J. Manuf. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Yue, Y., Cao, L., Chen, C., Chen, Y., and Chen, B. (2025). Snake Optimization Algorithm Augmented by Adaptive t-Distribution Mixed Mutation and Its Application in Energy Storage System Capacity Optimization. Biomimetics, 10.","DOI":"10.3390\/biomimetics10040244"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1089\/ten.teb.2024.0022","article-title":"Application of artificial intelligence in tissue engineering","volume":"31","author":"Bagherpour","year":"2025","journal-title":"Tissue Eng. Part B Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"321","DOI":"10.3390\/biomimetics11050321","article-title":"Chaos-Integrated Difference-Enhanced Greater Cane Rat Algorithm and Its Application","volume":"11","author":"Cheng","year":"2026","journal-title":"Biomimetics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"113555","DOI":"10.1016\/j.knosys.2025.113555","article-title":"Particle swarm optimization algorithm based on teaming behavior","volume":"318","author":"Yu","year":"2025","journal-title":"Knowl.-Based Syst."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Cao, L., Yue, Y., Chen, Y., Chen, C., and Chen, B. (2025). Sailfish optimization algorithm integrated with the osprey optimization algorithm and cauchy mutation and its engineering applications. Symmetry, 17.","DOI":"10.3390\/sym17060938"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wu, N., Jia, D., Li, Z., and He, Z. (2024). Trajectory planning of robotic arm based on particle swarm optimization algorithm. Appl. Sci., 14.","DOI":"10.3390\/app14188234"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"287","DOI":"10.3390\/biomimetics11040287","article-title":"Multi-Strategy Improved Red-Billed Blue Magpie Optimization Algorithm and Its Engineering Applications","volume":"11","author":"Ni","year":"2026","journal-title":"Biomimetics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"111280","DOI":"10.1016\/j.asoc.2024.111280","article-title":"A particle swarm optimization algorithm based on modified crowding distance for multimodal multi-objective problems","volume":"152","author":"Feng","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"ref_18","first-page":"81","article-title":"Coverage optimization strategy for 3D wireless sensor network based on adaptive inertia weight Arctic Puffin Optimization Algorithm","volume":"12","author":"Wang","year":"2025","journal-title":"J. Comput. Des. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"101890","DOI":"10.1016\/j.swevo.2025.101890","article-title":"Adaptive distance-based multi-objective particle swarm optimization algorithm with simple position update","volume":"94","author":"Wang","year":"2025","journal-title":"Swarm Evol. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3076","DOI":"10.1007\/s42235-024-00578-4","article-title":"An opposition-based learning adaptive chaotic particle swarm optimization algorithm","volume":"21","author":"Jiao","year":"2024","journal-title":"J. Bionic Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Cao, L., Li, M., Chen, K., Yue, Y., Qiu, Y., and Cheng, Z. (2026). Multi-Strategy Enhanced White Shark Optimizer for Solving Job Shop Scheduling Problem. Biomimetics, 11.","DOI":"10.3390\/biomimetics11060372"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"200198","DOI":"10.1016\/j.sasc.2025.200198","article-title":"Application of improved particle swarm optimization algorithm combined with genetic algorithm in shear wall design","volume":"7","author":"Gao","year":"2025","journal-title":"Syst. Soft Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1109\/TCYB.2024.3524457","article-title":"Kriging surrogate model-based constraint multiobjective particle swarm optimization algorithm","volume":"55","author":"Wang","year":"2025","journal-title":"IEEE Trans. Cybern."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"112884","DOI":"10.1016\/j.ymssp.2025.112884","article-title":"Efficient predictive model for high-frequency fatigue life of high-speed railway fastening clips using particle swarm optimization algorithm","volume":"235","author":"Luo","year":"2025","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s10462-023-10653-7","article-title":"A novel metaheuristic inspired by horned lizard defense tactics","volume":"57","author":"Sinha","year":"2024","journal-title":"Artif. Intell. Rev."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1007\/s44196-025-00824-5","article-title":"A multi-strategy improved horned lizard optimization algorithm and its application in engineering optimization","volume":"18","author":"Li","year":"2025","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"e70011","DOI":"10.1002\/fuce.70011","article-title":"Horned Lizard defense tactics optimization algorithm for precise identification of PEMFC parameters","volume":"25","author":"Kanouni","year":"2025","journal-title":"Fuel Cells"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Yin, B., Lu, H., Dai, L., and Ding, H. (2026). Multi-Strategy-Enhanced Improved Horned Lizard Optimization Algorithm for Path Planning in Mobile Robots. Algorithms, 19.","DOI":"10.3390\/a19040272"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Alfawaz, O., Mostafa, R.R., and Khedr, A.M. (2025). Localization in Wireless Sensor Networks Based Enhanced Horned Lizard Optimization Algorithm. 2025 IEEE 22nd International Multi-Conference on Systems, Signals & Devices (SSD), IEEE.","DOI":"10.1109\/SSD64182.2025.10989813"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"104386","DOI":"10.1016\/j.jnca.2025.104386","article-title":"Task scheduling of cloud computing system by frilled lizard optimization with time varying expansion mixed function oscillation and horned lizard camouflage strategy","volume":"245","author":"Song","year":"2025","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Geng, Y., Du, Q., and Ma, W. (2025). An Improved Horned Lizard Optimization Algorithm. 2025 IEEE 6th International Seminar on Artificial Intelligence, Networking and Information Technology (AINIT), IEEE.","DOI":"10.1109\/AINIT65432.2025.11036030"},{"key":"ref_32","first-page":"200478","article-title":"A novel improved horned lizard optimization algorithm to identify optimal parameters of adaptive fuzzy logic MPPT for performance boosting of PEM fuel cell","volume":"25","author":"Rezk","year":"2025","journal-title":"Intell. Syst. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"115865","DOI":"10.1016\/j.knosys.2026.115865","article-title":"A Novel Dynamic Horned Lizard Algorithm with Advanced Strategies for High-Dimensional Optimization and Pathology Lung Cancer Image Segmentation","volume":"342","author":"Tarek","year":"2026","journal-title":"Knowl.-Based Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"012022","DOI":"10.1088\/1742-6596\/3201\/1\/012022","article-title":"Tuning a Proportional-Integral-Derivative (PID) controller by the HLOA Algorithm for the Sloshing Dynamics Problem","volume":"3201","author":"Cortez","year":"2026","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"111349","DOI":"10.1016\/j.patcog.2025.111349","article-title":"Deep intelligent technique for person Re-identification system in surveillance images","volume":"162","author":"Pandeeswari","year":"2025","journal-title":"Pattern Recognit."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2867","DOI":"10.1007\/s11071-024-10331-5","article-title":"A novel 2D Log-Logistic\u2013Sine chaotic map for image encryption","volume":"113","author":"Wang","year":"2025","journal-title":"Nonlinear Dyn."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"9649","DOI":"10.1038\/s41598-024-60402-1","article-title":"A logistic-tent chaotic mapping Levenberg Marquardt algorithm for improving positioning accuracy of grinding robot","volume":"14","author":"Liu","year":"2024","journal-title":"Sci. Rep."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1007\/s40747-023-01186-1","article-title":"A novel adaptive parameter strategy differential evolution algorithm and its application in midcourse guidance maneuver decision-making","volume":"10","author":"Xie","year":"2024","journal-title":"Complex Intell. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"122032","DOI":"10.1016\/j.apenergy.2023.122032","article-title":"Multi-strategy adaptive guidance differential evolution algorithm using fitness-distance balance and opposition-based learning for constrained global optimization of photovoltaic cells and modules","volume":"353","author":"Liu","year":"2024","journal-title":"Appl. Energy"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"103284","DOI":"10.1016\/j.adhoc.2023.103284","article-title":"A novel self-adaptive multi-strategy artificial bee colony algorithm for coverage optimization in wireless sensor networks","volume":"150","author":"Wang","year":"2023","journal-title":"Ad Hoc Netw."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"5059","DOI":"10.1007\/s10639-024-12973-9","article-title":"The effects of an augmented reality lens imaging learning system on students\u2019 science achievement, learning motivation, and inquiry skills in physics inquiry activities","volume":"30","author":"Liao","year":"2025","journal-title":"Educ. Inf. Technol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"13724","DOI":"10.1109\/ACCESS.2023.3243081","article-title":"Parameter estimation of fractional-order chaotic power system based on lens imaging learning strategy state transition algorithm","volume":"11","author":"Ai","year":"2023","journal-title":"IEEE Access"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"6168","DOI":"10.1007\/s11227-022-04916-3","article-title":"Multifactorial brain storm optimization algorithm based on direct search transfer mechanism and concave lens imaging learning strategy","volume":"79","author":"Li","year":"2023","journal-title":"J. Supercomput."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"7305","DOI":"10.1007\/s11227-022-04959-6","article-title":"Dung beetle optimizer: A new meta-heuristic algorithm for global optimization","volume":"79","author":"Xue","year":"2023","journal-title":"J. Supercomput."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/s10462-024-10723-4","article-title":"Black-winged kite algorithm: A nature-inspired meta-heuristic for solving benchmark functions and engineering problems","volume":"57","author":"Wang","year":"2024","journal-title":"Artif. Intell. Rev."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"4113","DOI":"10.1007\/s11831-023-09928-7","article-title":"A systematic review of the whale optimization algorithm: Theoretical foundation, improvements, and hybridizations","volume":"30","author":"Zamani","year":"2023","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Trojovsk\u00fd, P., and Dehghani, M. (2022). Pelican optimization algorithm: A novel nature-inspired algorithm for engineering applications. Sensors, 22.","DOI":"10.3390\/s22030855"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"485","DOI":"10.35378\/gujs.820885","article-title":"Application of grey wolf optimization algorithm: Recent trends, issues, and possible horizons","volume":"35","author":"Dada","year":"2022","journal-title":"Gazi Univ. J. Sci."},{"key":"ref_49","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_50","doi-asserted-by":"crossref","unstructured":"Agushaka, J.O., Akinola, O., Ezugwu, A.E., Oyelade, O.N., and Saha, A. (2022). Advanced dwarf mongoose optimization for solving CEC 2011 and CEC 2017 benchmark problems. PLoS ONE, 17.","DOI":"10.1371\/journal.pone.0275346"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"27593","DOI":"10.1007\/s00521-025-11678-5","article-title":"Enhancing differential evolution algorithm for CEC 2014, CEC 2017, CEC 2021, and CEC 2022 test suites","volume":"37","author":"Salgotra","year":"2025","journal-title":"Neural Comput. Appl."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/7\/463\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T15:34:07Z","timestamp":1783006447000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/11\/7\/463"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,2]]},"references-count":51,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7]]}},"alternative-id":["biomimetics11070463"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics11070463","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,2]]}}}