{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:38:23Z","timestamp":1760240303178,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T00:00:00Z","timestamp":1556841600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation in Xizang Province of China","award":["XZ2018ZR G-64"],"award-info":[{"award-number":["XZ2018ZR G-64"]}]},{"name":"Natural Science Foundation of in Shaanxi Province of China","award":["17JK0826"],"award-info":[{"award-number":["17JK0826"]}]},{"name":"Science Basic Research Program in Xianyang Normal University of China","award":["XSYK18012"],"award-info":[{"award-number":["XSYK18012"]}]},{"name":"Education Scientific Program of 13th Five-year Plan in Shaanxi Province of China","award":["SGH18H373"],"award-info":[{"award-number":["SGH18H373"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>After the teaching\u2013learning-based optimization (TLBO) algorithm was proposed, many improved algorithms have been presented in recent years, which simulate the teaching\u2013learning phenomenon of a classroom to effectively solve global optimization problems. In this paper, a cyclical non-linear inertia-weighted teaching\u2013learning-based optimization (CNIWTLBO) algorithm is presented. This algorithm introduces a cyclical non-linear inertia weighted factor into the basic TLBO to control the memory rate of learners, and uses a non-linear mutation factor to control the learner\u2019s mutation randomly during the learning process. In order to prove the significant performance of the proposed algorithm, it is tested on some classical benchmark functions and the comparison results are provided against the basic TLBO, some variants of TLBO and some other well-known optimization algorithms. The experimental results show that the proposed algorithm has better global search ability and higher search accuracy than the basic TLBO, some variants of TLBO and some other algorithms as well, and can escape from the local minimum easily, while keeping a faster convergence rate.<\/jats:p>","DOI":"10.3390\/a12050094","type":"journal-article","created":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T03:15:46Z","timestamp":1557198946000},"page":"94","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Cyclical Non-Linear Inertia-Weighted Teaching\u2013Learning-Based Optimization Algorithm"],"prefix":"10.3390","volume":"12","author":[{"given":"Zongsheng","family":"Wu","sequence":"first","affiliation":[{"name":"School of Computer Science, Xianyang Normal University, Xianyang 712000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ru","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Xizang Minzu University, Xianyang 712000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/j.jocs.2013.05.005","article-title":"A new genetic algorithm for global optimization of multimodal continuous functions","volume":"5","author":"Thakur","year":"2014","journal-title":"J. Comput. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1140\/epjb\/e2017-80314-2","article-title":"Application of a parallel genetic algorithm to the global optimization of medium-sized Au\u2013Pd sub-nanometre clusters","volume":"91","author":"Hussein","year":"2018","journal-title":"Eur. Phys. J. B"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4618","DOI":"10.1016\/j.eswa.2011.09.076","article-title":"A survey: Ant colony optimization based recent research and implementation on several engineering domain","volume":"39","author":"Baskaran","year":"2012","journal-title":"Expert Syst. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1007\/s10586-017-0793-8","article-title":"Ant colony optimization with different crossover schemes for global optimization","volume":"20","author":"Chen","year":"2017","journal-title":"Clust. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1016\/j.amc.2007.06.020","article-title":"Improved particle swarm algorithms for global optimization","volume":"196","author":"Ali","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.asoc.2017.08.022","article-title":"Multi-leader PSO (MLPSO): A new PSO variant for solving global optimization problems","volume":"61","author":"Liu","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3508","DOI":"10.1016\/j.ins.2011.04.024","article-title":"Rosenbrock artificial bee colony algorithm for accurate global optimization of numerical functions","volume":"181","author":"Kang","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"590","DOI":"10.15837\/ijccc.2018.4.3275","article-title":"An ABC Algorithm with Recombination","volume":"13","author":"You","year":"2018","journal-title":"Int. J. Comput. Commun. Control"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Mohamed, A.K., Mohamed, A.W., Elfeky, E.Z., and Saleh, M. (2019). Solving constrained non-linear integer and mixed-integer global optimization problems using enhanced directed differential evolution algorithm. Machine Learning Paradigms: Theory and Application, Springer.","DOI":"10.1007\/978-3-030-02357-7_16"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s40747-017-0041-0","article-title":"Solving large-scale global optimization problems using enhanced adaptive differential evolution algorithm","volume":"3","author":"Mohamed","year":"2017","journal-title":"Complex Intell. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1007\/s10489-017-0921-4","article-title":"Using differential evolution strategies in chemical reaction optimization for global numerical optimization","volume":"47","author":"Nouioua","year":"2017","journal-title":"Appl. Intell."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.cad.2010.12.015","article-title":"Teaching\u2013learning-based optimization: A novel method for constrained mechanical design optimization problems","volume":"43","author":"Rao","year":"2011","journal-title":"Comput.-Aided Des."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2011.08.006","article-title":"Teaching\u2013learning-based optimization: An optimization method for continuous non-linear large scale problems","volume":"183","author":"Rao","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_15","first-page":"535","article-title":"An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems","volume":"3","author":"Rao","year":"2012","journal-title":"Int. J. Ind. Eng. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1016\/j.engappai.2012.06.007","article-title":"Parameter optimization of modern machining processes using teaching\u2013learning-based optimization algorithm","volume":"26","author":"Kalyankar","year":"2013","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1016\/j.apm.2012.03.043","article-title":"Multi-objective optimization of heat exchangers using a modified teaching-learning-based optimization algorithm","volume":"37","author":"Rao","year":"2013","journal-title":"Appl. Math. Model."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.enconman.2013.09.028","article-title":"A modified teaching\u2013learning based optimization for multi-objective optimal power flow problem","volume":"77","author":"Seifi","year":"2014","journal-title":"Energy Convers. Manag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1016\/j.ijepes.2014.06.031","article-title":"Multi-objective quasi-oppositional teaching learning based optimization for optimal location of distributed generator in radial distribution systems","volume":"63","author":"Sultana","year":"2014","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.ijepes.2014.10.027","article-title":"An improved teaching\u2013learning-based optimization algorithm using L\u00e9vy mutation strategy for non-smooth optimal power flow","volume":"65","author":"Ghasemi","year":"2015","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.knosys.2018.06.004","article-title":"Compact real-valued teaching-learning based optimization with the applications to neural network training","volume":"159","author":"Yang","year":"2018","journal-title":"Knowl.-Based Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.ins.2018.04.083","article-title":"An Improved teaching-learning-based optimization for constrained evolutionary optimization","volume":"456","author":"Wang","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1583","DOI":"10.3233\/JIFS-169453","article-title":"Neighbour teaching learning based optimization for global optimization problems","volume":"34","author":"Singh","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1578","DOI":"10.1016\/j.apenergy.2017.12.115","article-title":"Teaching\u2013learning\u2013based artificial bee colony for solar photovoltaic parameter estimation","volume":"212","author":"Chen","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"429","DOI":"10.4236\/am.2013.43064","article-title":"Weighted Teaching-learning-based optimization for global function optimization","volume":"4","author":"Satapathy","year":"2013","journal-title":"Appl. Math."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.ins.2014.11.001","article-title":"An improved teaching-learning-based optimization algorithm for solving global optimization problem","volume":"297","author":"Chen","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"23","DOI":"10.5267\/j.dsl.2012.10.005","article-title":"Improved teaching learning based optimization for global function optimization","volume":"2","author":"Satapathy","year":"2013","journal-title":"Decis. Sci. Lett."},{"key":"ref_28","first-page":"710","article-title":"An improved teaching-learning-based optimization algorithm for solving unconstrained optimization problems","volume":"20","author":"Rao","year":"2013","journal-title":"Sci. Iran."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"292576","DOI":"10.1155\/2015\/292576","article-title":"Nonlinear Inertia weighted teaching-learning-based optimization for solving global optimization problem","volume":"2015","author":"Wu","year":"2015","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_30","unstructured":"Eberhart, R.C., and Yuhui, S. (2001, January 27\u201330). Tracking and optimizing dynamic systems with particle swarms. Proceedings of the 2001 Congress on Evolutionary Computation, Seoul, Korea."},{"key":"ref_31","unstructured":"Shi, Y., and Eberhart, R.C. (1998, January 4\u20139). A modified particle swarm optimizer. Proceedings of the 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress on Computational Intelligence, Anchorage, AK, USA."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/4235.985692","article-title":"The particle swarm\u2014Explosion, stability, and convergence in a multidimensional complex space","volume":"6","author":"Clerc","year":"2002","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1109\/TEVC.2004.826069","article-title":"A Cooperative approach to particle swarm optimization","volume":"8","author":"Frans","year":"2004","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_34","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. Evolut. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.ins.2010.07.015","article-title":"A modified artificial bee colony algorithm for real-parameter optimization","volume":"192","author":"Akay","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_36","first-page":"445","article-title":"Gbest-guided artificial bee colony algorithm for numerical function","volume":"10","author":"Zhu","year":"2010","journal-title":"Appl. Soft Comput."},{"key":"ref_37","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. Proc. Lett."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/5\/94\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:48:56Z","timestamp":1760186936000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/5\/94"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,3]]},"references-count":37,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,5]]}},"alternative-id":["a12050094"],"URL":"https:\/\/doi.org\/10.3390\/a12050094","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2019,5,3]]}}}