{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T07:42:26Z","timestamp":1771486946055,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T00:00:00Z","timestamp":1544140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Khalid University, Saudi Arabia","award":["."],"award-info":[{"award-number":["."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>Numerous computational algorithms are used to obtain a high performance in solving mathematics, engineering and statistical complexities. Recently, an attractive bio-inspired method\u2014namely the Artificial Bee Colony (ABC)\u2014has shown outstanding performance with some typical computational algorithms in different complex problems. The modification, hybridization and improvement strategies made ABC more attractive to science and engineering researchers. The two well-known honeybees-based upgraded algorithms, Gbest Guided Artificial Bee Colony (GGABC) and Global Artificial Bee Colony Search (GABCS), use the foraging behavior of the global best and guided best honeybees for solving complex optimization tasks. Here, the hybrid of the above GGABC and GABC methods is called the 3G-ABC algorithm for strong discovery and exploitation processes. The proposed and typical methods were implemented on the basis of maximum fitness values instead of maximum cycle numbers, which has provided an extra strength to the proposed and existing methods. The experimental results were tested with sets of fifteen numerical benchmark functions. The obtained results from the proposed approach are compared with the several existing approaches such as ABC, GABC and GGABC, result and found to be very profitable. Finally, obtained results are verified with some statistical testing.<\/jats:p>","DOI":"10.3390\/computers7040069","type":"journal-article","created":{"date-parts":[[2018,12,10]],"date-time":"2018-12-10T03:36:41Z","timestamp":1544413001000},"page":"69","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Global Gbest Guided-Artificial Bee Colony Algorithm for Numerical Function Optimization"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2078-6285","authenticated-orcid":false,"given":"Habib","family":"Shah","sequence":"first","affiliation":[{"name":"College of Computer Science, King Khalid University, Abha 62529, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3957-0508","authenticated-orcid":false,"given":"Nasser","family":"Tairan","sequence":"additional","affiliation":[{"name":"College of Computer Science, King Khalid University, Abha 62529, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9099-8422","authenticated-orcid":false,"given":"Harish","family":"Garg","sequence":"additional","affiliation":[{"name":"School of Mathematics, Thapar Institute of Engineering &amp; Technology (Deemed University) Patiala, Punjab 147004, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rozaida","family":"Ghazali","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science, Universiti Tun Hussein Onn Malaysia, Batu Pahat, Johor 83000, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Shah, H., Tairan, N., Garg, H., and Ghazali, R. (2018). A quick gbest guided artificial bee colony algorithm for stock market prices prediction. Symmetry, 10.","DOI":"10.3390\/sym10070292"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Tairan, N., Algarni, A., Varghese, J., and Jan, M.A. (2015, January 29\u201331). Population-based guided local search for multidimensional knapsack problem. Proceedings of the 2015 Fourth International Conference on Future Generation Communication Technology (FGCT), Luton, UK.","DOI":"10.1109\/FGCT.2015.7300245"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s10489-017-0967-3","article-title":"Improved monarch butterfly optimization for unconstrained global search and neural network training","volume":"48","author":"Faris","year":"2018","journal-title":"Appl. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Shah, H., Ghazali, R., Herawan, T., Khan, N., and Khan, M.S. (2013). Hybrid guided artificial bee colony algorithm for earthquake time series data prediction. International Multi Topic Conference, Springer.","DOI":"10.1007\/978-3-319-10987-9_19"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Shah, H., Herawan, T., Naseem, R., and Ghazali, R. (2014). Hybrid guided artificial bee colony algorithm for numerical function optimization. International Conference in Swarm Intelligence, Springer.","DOI":"10.1007\/978-3-319-11857-4_23"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.amc.2015.11.001","article-title":"A hybrid PSO-GA algorithm for constrained optimization problems","volume":"274","author":"Garg","year":"2016","journal-title":"Appl. Math. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1516271","DOI":"10.1155\/2016\/1516271","article-title":"Hybrid optimization algorithm of particle swarm optimization and cuckoo search for preventive maintenance period optimization","volume":"2016","author":"Guo","year":"2016","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2621","DOI":"10.1016\/j.camwa.2012.06.026","article-title":"Hybrid harmony search and artificial bee colony algorithm for global optimization problems","volume":"64","author":"Wu","year":"2012","journal-title":"Comput. Math. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.1016\/j.asoc.2012.12.025","article-title":"Artificial bee colony algorithm and pattern search hybridized for global optimization","volume":"13","author":"Kang","year":"2013","journal-title":"Appl. Soft Comput."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Shah, H., Tairan, N., Mashwani, W.K., Al-Sewari, A.A., Jan, M.A., and Badshah, G. (2017). Hybrid global crossover bees algorithm for solving boolean function classification task. International Conference on Intelligent Computing, Springer.","DOI":"10.1007\/978-3-319-63315-2_41"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1142\/S012906571000222X","article-title":"A hybrid artificial bee colony optimization and quantum evolutionary algorithm for continuous optimization problems","volume":"20","author":"Duan","year":"2010","journal-title":"Int. J. Neural Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.eswa.2016.08.024","article-title":"Cost and risk aggregation in multi-objective route planning for hazardous materials transportation\u2014A neuro-fuzzy and artificial bee colony approach","volume":"65","author":"Pamucar","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Xu, J., Gang, J., and Lei, X. (2013). Hazmats transportation network design model with emergency response under complex fuzzy environment. Math. Probl. Eng., 2013.","DOI":"10.1155\/2013\/517372"},{"key":"ref_14","first-page":"1","article-title":"ANFIS model for determining the economic order quantity","volume":"1","author":"Sremac","year":"2018","journal-title":"Decis. Making Appl. Manag. Eng."},{"key":"ref_15","first-page":"13","article-title":"Vehicle route selection with an adaptive neuro fuzzy inference system in uncertainty conditions","volume":"1","author":"Pamucar","year":"2018","journal-title":"Decis. Making: Appl. Manag. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8881","DOI":"10.1016\/j.eswa.2015.07.043","article-title":"PS\u2013ABC: A hybrid algorithm based on particle swarm and artificial bee colony for high-dimensional optimization problems","volume":"42","author":"Li","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_17","unstructured":"Yang, X.-S. (2010). Nature-Inspired Metaheuristic Algorithms, Luniver press."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1007\/s00521-014-1577-1","article-title":"An effective hybrid cuckoo search algorithm for constrained global optimization","volume":"25","author":"Long","year":"2014","journal-title":"Neural Comput. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wu, D., Kong, F., Gao, W., Shen, Y., and Ji, Z. (2015, January 8\u201312). Improved chicken swarm optimization. Proceedings of the 2015 IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems (CYBER), Shenyang, China.","DOI":"10.1109\/CYBER.2015.7288023"},{"key":"ref_20","unstructured":"Wang, G.G., Deb, S., and Cui, Z. (2015). Monarch butterfly optimization. Neural Comput. Appl., 1\u201320."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.jocs.2017.06.003","article-title":"A new meta-heuristic butterfly-inspired algorithm","volume":"23","author":"Qi","year":"2017","journal-title":"J. Comput. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s10898-007-9149-x","article-title":"A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm","volume":"39","author":"Karaboga","year":"2007","journal-title":"J. Glob. Optim."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.ins.2018.11.041","article-title":"A hybrid GSA-GA algorithm for constrained optimization problems","volume":"478","author":"Garg","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3166","DOI":"10.1016\/j.amc.2010.08.049","article-title":"Gbest-guided artificial bee colony algorithm for numerical function optimization","volume":"217","author":"Zhu","year":"2010","journal-title":"Appl. Math. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.asoc.2015.03.003","article-title":"Artificial algae algorithm (AAA) for nonlinear global optimization","volume":"31","author":"Uymaz","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Systems, E., Corchado, J.M., and Abraham, A. (2008). Hybrid artificial intelligence systems. Innovations in Hybrid Intelligent, Springer.","DOI":"10.1007\/978-3-540-74972-1"},{"key":"ref_27","first-page":"35","article-title":"Exploration and exploitation in evolutionary algorithms: A survey","volume":"45","author":"Liu","year":"2013","journal-title":"ACM Comput. Surv. (CSUR)"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Guo, P., Cheng, W., and Liang, J. (2011, January 26\u201328). Global artificial bee colony search algorithm for numerical function optimization. Proceedings of the 2011 Seventh International Conference on Natural Computation (ICNC), Shanghai, China.","DOI":"10.1109\/ICNC.2011.6022368"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"19","DOI":"10.4018\/jaec.2012100102","article-title":"Dynamic swarm artificial bee colony algorithm","volume":"3","author":"Sharma","year":"2012","journal-title":"Int. J. Appl. Evol. Comput. (IJAEC)"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1016\/j.asoc.2007.05.007","article-title":"On the performance of artificial bee colony (ABC) algorithm","volume":"8","author":"Karaboga","year":"2008","journal-title":"Appl. Soft Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1016\/j.ipl.2011.06.002","article-title":"Improved artificial bee colony algorithm for global optimization","volume":"111","author":"Gao","year":"2011","journal-title":"Inf. Process. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.cie.2012.09.015","article-title":"Multi-objective reliability-redundancy allocation problem using particle swarm optimization","volume":"64","author":"Garg","year":"2013","journal-title":"Comput. Ind. Eng."},{"key":"ref_33","first-page":"53","article-title":"A simple and global optimization algorithm for engineering problems: Differential evolution algorithm","volume":"12","year":"2004","journal-title":"Turk. J. Electr. Eng. Comput. Sci."},{"key":"ref_34","unstructured":"Shi, Y., and Eberhart, R.C. (1999, January 6\u20139). Empirical study of particle swarm optimization. Proceedings of the 1999 Congress on Evolutionary Computation, Washington, DC, USA."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Ozturk, C., and Karaboga, D. (2011, January 5\u20138). Hybrid artificial bee colony algorithm for neural network training. Proceedings of the 2011 IEEE Congress on Evolutionary Computation (CEC), New Orleans, LA, USA.","DOI":"10.1109\/CEC.2011.5949602"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10462-012-9328-0","article-title":"A comprehensive survey: Artificial bee colony (ABC) algorithm and applications","volume":"42","author":"Karaboga","year":"2014","journal-title":"Artif. Intell. Rev."},{"key":"ref_37","first-page":"137","article-title":"A survey of bio inspired optimization algorithms","volume":"2","author":"Binitha","year":"2012","journal-title":"Int. J. Soft Comput. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.eswa.2016.04.018","article-title":"Bio inspired computing\u2013a review of algorithms and scope of applications","volume":"59","author":"Kar","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1653","DOI":"10.3233\/IFS-151644","article-title":"Multi-objective optimization problem of system reliability under intuitionistic fuzzy set environment using cuckoo search algorithm","volume":"29","author":"Garg","year":"2015","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4018\/jaec.2013040101","article-title":"Comprehensive survey of the hybrid evolutionary algorithms","volume":"4","author":"Mashwani","year":"2013","journal-title":"Int. J. Appl. Evol. Comput. (IJAEC)"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"777","DOI":"10.3934\/jimo.2014.10.777","article-title":"Solving structural engineering design optimization problems using an artificial bee colony algorithm","volume":"10","author":"Garg","year":"2014","journal-title":"J. Ind. Manag. Optim."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.ins.2014.08.040","article-title":"On clarifying misconceptions when comparing variants of the artificial bee colony algorithm by offering a new implementation","volume":"291","author":"Mernik","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s00500-014-1493-4","article-title":"Is a comparison of results meaningful from the inexact replications of computational experiments?","volume":"20","author":"Liu","year":"2016","journal-title":"Soft Comput."},{"key":"ref_44","unstructured":"Vasant, P. (2015). A Hybrid GA\u2014GSA Algorithm for Optimizing the Performance of an Industrial System by Utilizing Uncertain Data. Handbook of Research on Artificial Intelligence Techniques and Algorithms, IGI Global."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1109\/TEVC.2005.857610","article-title":"Comprehensive learning particle swarm optimizer for global optimization of multimodal functions","volume":"10","author":"Liang","year":"2006","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1080\/17445760.2018.1472262","article-title":"Multi-cohort intelligence algorithm: An intra-and inter-group learning behaviour based socio-inspired optimisation methodology","volume":"33","author":"Shastri","year":"2018","journal-title":"Int. J. Parallel Emerg. Distrib. Syst."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1016\/j.asoc.2009.12.025","article-title":"A novel clustering approach: Artificial bee colony (ABC) algorithm","volume":"11","author":"Karaboga","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1007\/s40430-016-0552-4","article-title":"Performance analysis of an industrial systems using soft computing based hybridized technique","volume":"39","author":"Garg","year":"2017","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2015.05.001","article-title":"An efficient biogeography based optimization algorithm for solving reliability optimization problems","volume":"24","author":"Garg","year":"2015","journal-title":"Swarm Evol. Comput."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/j.jmsy.2014.02.008","article-title":"Bi-objective optimization of the reliability-redundancy allocation problem for series-parallel system","volume":"33","author":"Garg","year":"2014","journal-title":"J. Manuf. Syst."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"3157","DOI":"10.1016\/j.eswa.2013.11.014","article-title":"Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment","volume":"41","author":"Garg","year":"2014","journal-title":"Expert Syst. Appl."}],"container-title":["Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-431X\/7\/4\/69\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:32:00Z","timestamp":1760196720000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-431X\/7\/4\/69"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,7]]},"references-count":51,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["computers7040069"],"URL":"https:\/\/doi.org\/10.3390\/computers7040069","relation":{},"ISSN":["2073-431X"],"issn-type":[{"value":"2073-431X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,7]]}}}