{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T13:44:37Z","timestamp":1771335877257,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,15]],"date-time":"2018-03-15T00:00:00Z","timestamp":1521072000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Cuckoo Search (CS) is a Meta-heuristic method, which exhibits several advantages such as easier to application and fewer tuning parameters. However, it has proven to very easily fall into local optimal solutions and has a slow rate of convergence. Therefore, we propose Modified cuckoo search algorithm with variational parameter and logistic map (VLCS) to ameliorate these defects. To balance the exploitation and exploration of the VLCS algorithm, we not only use the coefficient function to change step size \u03b1 and probability of detection p a at next generation, but also use logistic map of each dimension to initialize host nest location and update the location of host nest beyond the boundary. With fifteen benchmark functions, the simulations demonstrate that the VLCS algorithm can over come the disadvantages of the CS algorithm.In addition, the VLCS algorithm is good at dealing with high dimension problems and low dimension problems.<\/jats:p>","DOI":"10.3390\/a11030030","type":"journal-article","created":{"date-parts":[[2018,3,15]],"date-time":"2018-03-15T16:07:17Z","timestamp":1521130037000},"page":"30","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Modified Cuckoo Search Algorithm with Variational Parameters and Logistic Map"],"prefix":"10.3390","volume":"11","author":[{"given":"Liping","family":"Liu","sequence":"first","affiliation":[{"name":"School of Software, Central South University, Changsha 410075, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5767-3044","authenticated-orcid":false,"given":"Xiaobo","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Software, Central South University, Changsha 410075, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9053-9012","authenticated-orcid":false,"given":"Ning","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Software, Central South University, Changsha 410075, China"}]},{"given":"Peijun","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Software, Central South University, Changsha 410075, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,15]]},"reference":[{"key":"ref_1","first-page":"754","article-title":"Optimization Problem Formulation for Multidisciplinary Design","volume":"4","author":"Shubin","year":"1993","journal-title":"Siam J. Optim."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1109\/TEVC.2012.2196800","article-title":"A Survey on Multiobjective Evolutionary Algorithms for the Solution of the Portfolio Optimization Problem and Other Finance and Economics Applications","volume":"17","author":"Ponsich","year":"2013","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gaobo, Y., Xingming, S., and Xiaojing, W. (2006, January 3\u20136). A Genetic Algorithm based Video Watermarking in the DWT Domain. Proceedings of the International Conference on Computational Intelligence and Security, Guangzhou, China.","DOI":"10.1109\/ICCIAS.2006.295247"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"016209","DOI":"10.1103\/PhysRevE.76.016209","article-title":"Estimating system parameters from chaotic time series with synchronization optimized by a genetic algorithm","volume":"76","author":"Tao","year":"2007","journal-title":"Phys. Rev. E Stat. Nonlinear Soft Matter Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2557","DOI":"10.1103\/PhysRevE.55.2557","article-title":"Forecasting chaotic time series with genetic algorithms","volume":"55","author":"Szpiro","year":"1997","journal-title":"Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1109\/ACCESS.2014.2352261","article-title":"A Rule-Based Dynamic Decision-Making Stock Trading System Based on Quantum-Inspired Tabu Search Algorithm","volume":"2","author":"Chou","year":"2014","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4711","DOI":"10.1007\/s11227-017-2041-7","article-title":"Reconstructing permutation table to improve the Tabu Search for the PFSP on GPU","volume":"73","author":"Wei","year":"2017","journal-title":"J. Supercomput."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Alidaee, B., Ramalingam, V.P., Wang, H., and Kethley, B. (2017). Computational experiment of critical event tabu search for the general integer multidimensional knapsack problem. Ann. Oper. Res., 1\u201317.","DOI":"10.1007\/s10479-017-2675-0"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/TEVC.2007.900837","article-title":"A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA","volume":"12","author":"Bandyopadhyay","year":"2008","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2156","DOI":"10.1093\/bioinformatics\/btx090","article-title":"SANA: Simulated annealing far outperforms many other search algorithms for biological network alignment","volume":"33","author":"Mamano","year":"2017","journal-title":"Bioinformatics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103510","DOI":"10.1063\/1.4991511","article-title":"Angular filter refractometry analysis using simulated annealing","volume":"88","author":"Angland","year":"2017","journal-title":"Rev. Sci. Instrum."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"577","DOI":"10.7498\/aps.55.577","article-title":"Parameter estimation for chaotic system based on particle swarm optimization","volume":"55","author":"Fei","year":"2006","journal-title":"Acta Phys. Sin."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1109\/TEVC.2013.2260755","article-title":"Optimal Cycle Program of Traffic Lights With Particle Swarm Optimization","volume":"17","author":"Olivera","year":"2013","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2101","DOI":"10.1007\/s00521-012-1158-0","article-title":"Global minimization of multi-funnel functions using particle swarm optimization","volume":"23","author":"Salahi","year":"2013","journal-title":"Neural Comput. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1109\/TEVC.2006.890229","article-title":"Classification with Ant Colony Optimization","volume":"11","author":"Martens","year":"2007","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1109\/TEVC.2016.2591064","article-title":"Adaptive Multimodal Continuous Ant Colony Optimization","volume":"21","author":"Yang","year":"2017","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.ins.2017.04.016","article-title":"Ant-colony algorithm with a strengthened negative-feedback mechanism for constraint-satisfaction problems","volume":"406\u2013407","author":"Ye","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Yang, X.S., and Deb, S. (2010, January 9\u201311). Cuckoo Search via L\u00e9vy Flights. Proceedings of the World Congress on Nature & Biologically Inspired Computing, 2009 (NaBIC 2009), Coimbatore, India.","DOI":"10.1109\/NABIC.2009.5393690"},{"key":"ref_19","first-page":"138","article-title":"Cuckoo Search Approach for Cutting Stock Problem","volume":"5","author":"Shair","year":"2015","journal-title":"Int. J. Inf. Electron. Eng."},{"key":"ref_20","first-page":"1","article-title":"Binary cuckoo search algorithm for band selection in hyperspectral image classification","volume":"42","author":"Medjahed","year":"2015","journal-title":"IAENG Int. J. Comput. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1016\/j.chaos.2011.06.004","article-title":"Modified cuckoo search: A new gradient free optimisation algorithm","volume":"44","author":"Walton","year":"2011","journal-title":"Chaos Solitons Fractals"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.ins.2014.11.042","article-title":"Modified cuckoo search algorithm with self adaptive parameter method","volume":"298","author":"Li","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, G.G., Deb, S., Gandomi, A.H., Zhang, Z., and Alavi, A.H. (2015, January 26\u201327). A Novel Cuckoo Search with Chaos Theory and Elitism Scheme. Proceedings of the International Conference on Soft Computing and Machine Intelligence, New Delhi, India.","DOI":"10.1109\/ISCMI.2014.8"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3860","DOI":"10.1016\/j.apm.2015.10.052","article-title":"Chaos-enhanced Cuckoo search optimization algorithms for global optimization","volume":"40","author":"Huang","year":"2016","journal-title":"Appl. Math. Model."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1016\/j.amc.2015.06.041","article-title":"Cuckoo search algorithm based on frog leaping local search and chaos theory","volume":"266","author":"Liu","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_26","first-page":"4193","article-title":"A novel Cuckoo Search optimization algorithm base on gauss distribution","volume":"8","author":"Zheng","year":"2012","journal-title":"J. Comput. Inf. Syst."},{"key":"ref_27","first-page":"57","article-title":"Hybrid optimization algorithm of Cuckoo Search and DE","volume":"49","author":"Li","year":"2013","journal-title":"Comput. Eng. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.asoc.2017.07.053","article-title":"Bio-Inspired Computation: Recent Development on the Modifications of the Cuckoo Search Algorithm","volume":"61","author":"Chiroma","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s00521-013-1367-1","article-title":"Cuckoo search: Recent advances and applications","volume":"24","author":"Yang","year":"2014","journal-title":"Neural Comput. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.scriptamat.2016.12.022","article-title":"Cuckoo searching optimal composition of multicomponent alloys by molecular simulations","volume":"130","author":"Sharma","year":"2017","journal-title":"Scr. Mater."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/S0375-9601(01)00609-0","article-title":"Logistic map as a block encryption algorithm","volume":"289","author":"Kocarev","year":"2001","journal-title":"Phys. Lett. A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s11071-013-1065-7","article-title":"Discrete fractional logistic map and its chaos","volume":"75","author":"Wu","year":"2013","journal-title":"Nonlinear Dyn."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.knosys.2016.07.039","article-title":"Adaptive affinity propagation method based on improved cuckoo search","volume":"111","author":"Jia","year":"2016","journal-title":"Knowl.-Based Syst."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/BF00932471","article-title":"A study of test functions for optimization algorithms","volume":"8","author":"Chattopadhyay","year":"1971","journal-title":"J. Optim. Theory Appl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1162\/evco.2006.14.1.119","article-title":"A Note on the Extended Rosenbrock Function","volume":"14","author":"Shang","year":"2006","journal-title":"Evolut. Comput."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/BF01096734","article-title":"A wide class of test functions for global optimization","volume":"3","author":"Schoen","year":"1993","journal-title":"J. Glob. Optim."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/11\/3\/30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:57:16Z","timestamp":1760194636000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/11\/3\/30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,15]]},"references-count":36,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,3]]}},"alternative-id":["a11030030"],"URL":"https:\/\/doi.org\/10.3390\/a11030030","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,15]]}}}