{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T10:58:03Z","timestamp":1784026683389,"version":"3.55.0"},"reference-count":94,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T00:00:00Z","timestamp":1639094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The moth-flame optimization (MFO) algorithm is an effective nature-inspired algorithm based on the chemical effect of light on moths as an animal with bilateral symmetry. Although it is widely used to solve different optimization problems, its movement strategy affects the convergence and the balance between exploration and exploitation when dealing with complex problems. Since movement strategies significantly affect the performance of algorithms, the use of multi-search strategies can enhance their ability and effectiveness to solve different optimization problems. In this paper, we propose a multi-trial vector-based moth-flame optimization (MTV-MFO) algorithm. In the proposed algorithm, the MFO movement strategy is substituted by the multi-trial vector (MTV) approach to use a combination of different movement strategies, each of which is adjusted to accomplish a particular behavior. The proposed MTV-MFO algorithm uses three different search strategies to enhance the global search ability, maintain the balance between exploration and exploitation, and prevent the original MFO\u2019s premature convergence during the optimization process. Furthermore, the MTV-MFO algorithm uses the knowledge of inferior moths preserved in two archives to prevent premature convergence and avoid local optima. The performance of the MTV-MFO algorithm was evaluated using 29 benchmark problems taken from the CEC 2018 competition on real parameter optimization. The gained results were compared with eight metaheuristic algorithms. The comparison of results shows that the MTV-MFO algorithm is able to provide competitive and superior results to the compared algorithms in terms of accuracy and convergence rate. Moreover, a statistical analysis of the MTV-MFO algorithm and other compared algorithms was conducted, and the effectiveness of our proposed algorithm was also demonstrated experimentally.<\/jats:p>","DOI":"10.3390\/sym13122388","type":"journal-article","created":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T01:29:33Z","timestamp":1639358973000},"page":"2388","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":44,"title":["MTV-MFO: Multi-Trial Vector-Based Moth-Flame Optimization Algorithm"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0135-1115","authenticated-orcid":false,"given":"Mohammad H.","family":"Nadimi-Shahraki","sequence":"first","affiliation":[{"name":"Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran"},{"name":"Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8872-8455","authenticated-orcid":false,"given":"Shokooh","family":"Taghian","sequence":"additional","affiliation":[{"name":"Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran"},{"name":"Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1443-9458","authenticated-orcid":false,"given":"Seyedali","family":"Mirjalili","sequence":"additional","affiliation":[{"name":"Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Fortitude Valley, QLD 4006, Australia"},{"name":"Yonsei Frontier Lab, Yonsei University, Seodaemun-gu, Seoul 03722, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ahmed A.","family":"Ewees","sequence":"additional","affiliation":[{"name":"Department of Computer, Damietta University, Damietta 34511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2203-4549","authenticated-orcid":false,"given":"Laith","family":"Abualigah","sequence":"additional","affiliation":[{"name":"Faculty of Computer Sciences and Informatics, Amman Arab University, Amman 11953, Jordan"},{"name":"School of Computer Sciences, Universiti Sains Malaysia, Pulau Pinang 11800, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7682-6269","authenticated-orcid":false,"given":"Mohamed","family":"Abd Elaziz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt"},{"name":"Artificial Intelligence Research Center (AIRC), Ajman University, Ajman 346, United Arab Emirates"},{"name":"Department of Artificial Intelligence Science & Engineering, Galala University, Suze 435611, Egypt"},{"name":"School of Computer Science and Robotics, Tomsk Polytechnic University, 634050 Tomsk, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Du, K.-L., and Swamy, M. (2016). Search and optimization by metaheuristics. Techniques and Algorithms Inspired by Nature, Birkh\u00e4user.","DOI":"10.1007\/978-3-319-41192-7_3"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Talbi, E.-G. (2009). Metaheuristics: From Design to Implementation, John Wiley & Sons.","DOI":"10.1002\/9780470496916"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"101104","DOI":"10.1016\/j.jocs.2020.101104","article-title":"Nature-inspired optimization algorithms: Challenges and open problems","volume":"46","author":"Yang","year":"2020","journal-title":"J. Comput. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No free lunch theorems for optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_5","unstructured":"Eberhart, R., and Kennedy, J. (1995, January 4\u20136). A new optimizer using particle swarm theory. Proceedings of the MHS\u201995 Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1023\/A:1022602019183","article-title":"Genetic algorithms and machine learning","volume":"3","author":"Goldberg","year":"1988","journal-title":"Mach. Learn."},{"key":"ref_7","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_8","doi-asserted-by":"crossref","unstructured":"Po\u0142ap, D. (2017). Polar bear optimization algorithm: Meta-heuristic with fast population movement and dynamic birth and death mechanism. Symmetry, 9.","DOI":"10.3390\/sym9100203"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.advengsoft.2017.07.002","article-title":"Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems","volume":"114","author":"Mirjalili","year":"2017","journal-title":"Adv. Eng. Softw."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"114107","DOI":"10.1016\/j.eswa.2020.114107","article-title":"Red fox optimization algorithm","volume":"166","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"104314","DOI":"10.1016\/j.engappai.2021.104314","article-title":"QANA: Quantum-based avian navigation optimizer algorithm","volume":"104","author":"Zamani","year":"2021","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zeybek, S., Pham, D.T., Ko\u00e7, E., and Se\u00e7er, A. (2021). An Improved Bees Algorithm for Training Deep Recurrent Networks for Sentiment Classification. Symmetry, 13.","DOI":"10.3390\/sym13081347"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Dey, N., Rajinikanth, V., Ashour, A.S., and Tavares, J.M.R. (2018). Social group optimization supported segmentation and evaluation of skin melanoma images. Symmetry, 10.","DOI":"10.3390\/sym10020051"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s00366-017-0523-0","article-title":"Enhanced IGMM optimization algorithm based on vibration for numerical and engineering problems","volume":"34","author":"Ghasemi","year":"2018","journal-title":"Eng. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Shen, Y., Liang, Z., Kang, H., Sun, X., and Chen, Q. (2021). A Modified jSO Algorithm for Solving Constrained Engineering Problems. Symmetry, 13.","DOI":"10.3390\/sym13010063"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"120211","DOI":"10.1016\/j.energy.2021.120211","article-title":"A high-performance crisscross search based grey wolf optimizer for solving optimal power flow problem","volume":"225","author":"Meng","year":"2021","journal-title":"Energy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"32169","DOI":"10.1007\/s11042-020-09639-2","article-title":"An improved artificial bee colony algorithm based on whale optimization algorithm for data clustering","volume":"79","author":"Rahnema","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"56066","DOI":"10.1109\/ACCESS.2021.3072336","article-title":"An improved tunicate swarm algorithm for global optimization and image segmentation","volume":"9","author":"Houssein","year":"2021","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"105583","DOI":"10.1016\/j.asoc.2019.105583","article-title":"CCSA: Conscious Neighborhood-based Crow Search Algorithm for Solving Global Optimization Problems","volume":"85","author":"Zamani","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"107218","DOI":"10.1016\/j.asoc.2021.107218","article-title":"Opposition-based JAYA with population reduction for parameter estimation of photovoltaic solar cells and modules","volume":"104","author":"Yang","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.eswa.2018.10.050","article-title":"A hybrid self-adaptive sine cosine algorithm with opposition based learning","volume":"119","author":"Gupta","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.asoc.2014.06.034","article-title":"A novel particle swarm optimization algorithm with Levy flight","volume":"23","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"116078","DOI":"10.1109\/ACCESS.2019.2936254","article-title":"Levy flight shuffle frog leaping algorithm based on differential perturbation and quasi-Newton search","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.ins.2019.04.022","article-title":"Enhanced Moth-flame optimizer with mutation strategy for global optimization","volume":"492","author":"Xu","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.jocs.2018.11.002","article-title":"Improved self-adaptive bat algorithm with step-control and mutation mechanisms","volume":"30","author":"Lyu","year":"2019","journal-title":"J. Comput. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.compag.2017.02.026","article-title":"An improved moth flame optimization algorithm based on rough sets for tomato diseases detection","volume":"136","author":"Hassanien","year":"2017","journal-title":"Comput. Electron. Agric."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.patrec.2006.09.003","article-title":"Feature selection based on rough sets and particle swarm optimization","volume":"28","author":"Wang","year":"2007","journal-title":"Pattern Recognit. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.asoc.2018.10.044","article-title":"\u03b2-chaotic map enabled grey wolf optimizer","volume":"75","author":"Saxena","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.neucom.2017.04.060","article-title":"Toward an optimal kernel extreme learning machine using a chaotic moth-flame optimization strategy with applications in medical diagnoses","volume":"267","author":"Wang","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.knosys.2015.07.006","article-title":"Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm","volume":"89","author":"Mirjalili","year":"2015","journal-title":"Knowl.-Based Syst."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, Y., Zhu, X., and Liu, J. (2020). An improved moth-flame optimization algorithm for engineering problems. Symmetry, 12.","DOI":"10.3390\/sym12081234"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Nadimi-Shahraki, M.H., Banaie-Dezfouli, M., Zamani, H., Taghian, S., and Mirjalili, S. (2021). B-MFO: A Binary Moth-Flame Optimization for Feature Selection from Medical Datasets. Computers, 10.","DOI":"10.3390\/computers10110136"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zhang, X., Zhang, C., and Wei, Z. (2019). Carbon price forecasting based on multi-resolution singular value decomposition and extreme learning machine optimized by the moth\u2013flame optimization algorithm considering energy and economic factors. Energies, 12.","DOI":"10.3390\/en12224283"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Sheng, H., Li, C., Wang, H., Yan, Z., Xiong, Y., Cao, Z., and Kuang, Q. (2019). Parameters extraction of photovoltaic models using an improved moth-flame optimization. Energies, 12.","DOI":"10.3390\/en12183527"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Kamalapathi, K., Priyadarshi, N., Padmanaban, S., Holm-Nielsen, J.B., Azam, F., Umayal, C., and Ramachandaramurthy, V.K. (2018). A hybrid moth-flame fuzzy logic controller based integrated cuk converter fed brushless DC motor for power factor correction. Electronics, 7.","DOI":"10.20944\/preprints201809.0462.v1"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3063","DOI":"10.3390\/en13123063","article-title":"An assessment of onshore and offshore wind energy potential in India using moth flame optimization","volume":"13","author":"Raju","year":"2020","journal-title":"Energies"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"107193","DOI":"10.1016\/j.asoc.2021.107193","article-title":"Design of moth flame optimization heuristics for integrated power plant system containing stochastic wind","volume":"104","author":"Khan","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"115436","DOI":"10.1016\/j.eswa.2021.115436","article-title":"Death mechanism-based moth\u2013flame optimization with improved flame generation mechanism for global optimization tasks","volume":"183","author":"Li","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1016\/j.energy.2018.06.088","article-title":"An enhanced moth-flame optimizer for solving non-smooth economic dispatch problems with emissions","volume":"157","author":"Elsakaan","year":"2018","journal-title":"Energy"},{"key":"ref_40","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":"Taghian","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_41","unstructured":"Awad, N., Ali, M., Liang, J., Qu, B., and Suganthan, P. (2016). Problem Definitions and Evaluation Criteria for the cec 2017 Special Sessionand Competition on Single Objective Real-Parameter Numerical Optimization, Nanyang Technological University. Technical Report."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"4831","DOI":"10.1016\/j.cnsns.2012.05.010","article-title":"Krill herd: A new bio-inspired optimization algorithm","volume":"17","author":"Gandomi","year":"2012","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_43","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_44","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1007\/s00500-018-3102-4","article-title":"Butterfly optimization algorithm: A novel approach for global optimization","volume":"23","author":"Arora","year":"2019","journal-title":"Soft Comput."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1016\/j.future.2019.07.015","article-title":"Henry gas solubility optimization: A novel physics-based algorithm","volume":"101","author":"Hashim","year":"2019","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1531","DOI":"10.1007\/s10489-020-01893-z","article-title":"Archimedes optimization algorithm: A new metaheuristic algorithm for solving optimization problems","volume":"51","author":"Hashim","year":"2021","journal-title":"Appl. Intell."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Gandomi, A.H., Yang, X.-S., Talatahari, S., and Alavi, A.H. (2013). Metaheuristic algorithms in modeling and optimization. Metaheuristic Applications in Structures and Infrastructures, Elsevier Oxford.","DOI":"10.1016\/B978-0-12-398364-0.00001-2"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential evolution\u2013a simple and efficient heuristic for global optimization over continuous spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_49","unstructured":"Rechenberg, I. (1973). Evolution Strategy: Optimization of Technical systems by means of biological evolution. Rechenberg I. Evolution Strategy: Optimization of Technical Systems by Means of Biological Evolution, Fromman-Holzboog."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/4235.771163","article-title":"Evolutionary programming made faster","volume":"3","author":"Yao","year":"1999","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_51","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_52","doi-asserted-by":"crossref","first-page":"6374","DOI":"10.1016\/j.eswa.2013.05.041","article-title":"A swarm optimization algorithm inspired in the behavior of the social-spider","volume":"40","author":"Cuevas","year":"2013","journal-title":"Expert Syst. Appl."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"107250","DOI":"10.1016\/j.cie.2021.107250","article-title":"Aquila Optimizer: A novel meta-heuristic optimization Algorithm","volume":"157","author":"Abualigah","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by simulated annealing","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"425","DOI":"10.2528\/PIER07082403","article-title":"Central force optimization","volume":"77","author":"Formato","year":"2007","journal-title":"Prog. Electromagn. Res."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.knosys.2018.08.030","article-title":"Atom search optimization and its application to solve a hydrogeologic parameter estimation problem","volume":"163","author":"Zhao","year":"2019","journal-title":"Knowl.-Based Syst."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"114522","DOI":"10.1016\/j.eswa.2020.114522","article-title":"Lichtenberg algorithm: A novel hybrid physics-based meta-heuristic for global optimization","volume":"170","author":"Pereira","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Pichai, S., Sunat, K., and Chiewchanwattana, S. (2020). An asymmetric chaotic competitive swarm optimization algorithm for feature selection in high-dimensional data. Symmetry, 12.","DOI":"10.3390\/sym12111782"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1142\/S0219622020500546","article-title":"Feature Selection with Binary Symbiotic Organisms Search Algorithm for Email Spam Detection","volume":"20","author":"Mohammadzadeh","year":"2021","journal-title":"Int. J. Inf. Technol. Decis. Mak."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Gharehchopogh, F.S., Maleki, I., and Dizaji, Z.A. (2021). Chaotic vortex search algorithm: Metaheuristic algorithm for feature selection. Evol. Intell., 1\u201332. In press.","DOI":"10.1007\/s12065-021-00590-1"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"9102","DOI":"10.1007\/s11227-021-03626-6","article-title":"An efficient binary chaotic symbiotic organisms search algorithm approaches for feature selection problems","volume":"77","author":"Mohmmadzadeh","year":"2021","journal-title":"J. Supercomput."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1007\/s00170-009-2363-6","article-title":"Using bees algorithm for material handling equipment planning in manufacturing systems","volume":"48","author":"Sayarshad","year":"2010","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.eswa.2017.02.042","article-title":"Cross entropy based thresholding for magnetic resonance brain images using Crow Search Algorithm","volume":"79","author":"Oliva","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Li, G., Shuang, F., Zhao, P., and Le, C. (2019). An improved butterfly optimization algorithm for engineering design problems using the cross-entropy method. Symmetry, 11.","DOI":"10.3390\/sym11081049"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.energy.2014.05.011","article-title":"Parameter identification of solar cells using artificial bee colony optimization","volume":"72","author":"Oliva","year":"2014","journal-title":"Energy"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.apenergy.2017.05.029","article-title":"Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm","volume":"200","author":"Oliva","year":"2017","journal-title":"Appl. Energy"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"7015","DOI":"10.1016\/j.egyr.2021.10.067","article-title":"An enhanced exploratory whale optimization algorithm for dynamic economic dispatch","volume":"7","author":"Yang","year":"2021","journal-title":"Energy Rep."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s00366-016-0485-7","article-title":"A fast multi-objective optimization using an efficient ideal gas molecular movement algorithm","volume":"33","author":"Ghasemi","year":"2017","journal-title":"Eng. Comput."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2019.03.004","article-title":"A comprehensive survey: Whale Optimization Algorithm and its applications","volume":"48","author":"Gharehchopogh","year":"2019","journal-title":"Swarm Evol. Comput."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Yang, W., Xia, K., Li, T., Xie, M., and Zhao, Y. (2021). An Improved Transient Search Optimization with Neighborhood Dimensional Learning for Global Optimization Problems. Symmetry, 13.","DOI":"10.3390\/sym13020244"},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Pizzuti, C. (2009, January 2\u20134). A multi-objective genetic algorithm for community detection in networks. Proceedings of the 2009 21st IEEE International Conference on Tools with Artificial Intelligence, Newark, NJ, USA.","DOI":"10.1109\/ICTAI.2009.58"},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Li, Y.-H., Wang, J.-Q., Wang, X.-J., Zhao, Y.-L., Lu, X.-H., and Liu, D.-L. (2017). Community detection based on differential evolution using social spider optimization. Symmetry, 9.","DOI":"10.3390\/sym9090183"},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Nadimi-Shahraki, M.H., Moeini, E., Taghian, S., and Mirjalili, S. (2021). DMFO-CD: A Discrete Moth-Flame Optimization Algorithm for Community Detection. Algorithms, 14.","DOI":"10.3390\/a14110314"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.ins.2012.02.014","article-title":"On fast and accurate block-based motion estimation algorithms using particle swarm optimization","volume":"197","author":"Cai","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1016\/j.engappai.2012.08.003","article-title":"Block-matching algorithm based on differential evolution for motion estimation","volume":"26","author":"Cuevas","year":"2013","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Yamany, W., Fawzy, M., Tharwat, A., and Hassanien, A.E. (2015, January 29\u201330). Moth-flame optimization for training multi-layer perceptrons. Proceedings of the 2015 11th International Computer Engineering Conference (ICENCO), Cairo, Egypt.","DOI":"10.1109\/ICENCO.2015.7416360"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.asoc.2017.05.057","article-title":"Optimal reactive power dispatch solution by loss minimization using moth-flame optimization technique","volume":"59","author":"Mei","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_78","first-page":"47","article-title":"Modified moth-flame optimization algorithms for terrorism prediction","volume":"5","author":"Soliman","year":"2016","journal-title":"Int. J. Appl. Or Innov. Eng. Manag."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.yofte.2017.05.018","article-title":"Optical network unit placement in Fiber-Wireless (FiWi) access network by Moth-Flame optimization algorithm","volume":"36","author":"Singh","year":"2017","journal-title":"Opt. Fiber Technol."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"112105","DOI":"10.1016\/j.enconman.2019.112105","article-title":"A demand response-centred approach to the long-term equipment capacity planning of grid-independent micro-grids optimized by the moth-flame optimization algorithm","volume":"200","author":"Mohseni","year":"2019","journal-title":"Energy Convers. Manag."},{"key":"ref_81","first-page":"206","article-title":"Dynamic performance enhancement for wind energy conversion system using Moth-Flame Optimization based blade pitch controller","volume":"27","author":"Ebrahim","year":"2018","journal-title":"Sustain. Energy Technol. Assess."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"3096","DOI":"10.1016\/j.ins.2008.01.020","article-title":"Multi-strategy ensemble particle swarm optimization for dynamic optimization","volume":"178","author":"Du","year":"2008","journal-title":"Inf. Sci."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.engappai.2014.08.002","article-title":"Multi-strategy adaptive particle swarm optimization for numerical optimization","volume":"37","author":"Tang","year":"2015","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.cor.2015.02.008","article-title":"Multiple strategies based orthogonal design particle swarm optimizer for numerical optimization","volume":"60","author":"Qin","year":"2015","journal-title":"Comput. Oper. Res."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.ins.2020.06.027","article-title":"Heterogeneous comprehensive learning and dynamic multi-swarm particle swarm optimizer with two mutation operators","volume":"540","author":"Wang","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.ins.2014.02.104","article-title":"Enhancing artificial bee colony algorithm using more information-based search equations","volume":"270","author":"Gao","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.asoc.2018.11.047","article-title":"Multi-strategy ensemble grey wolf optimizer and its application to feature selection","volume":"76","author":"Tu","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_88","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_89","first-page":"1","article-title":"A multi-strategy enhanced salp swarm algorithm for global optimization","volume":"10","author":"Zhang","year":"2020","journal-title":"Eng. Comput."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1109\/TEVC.2008.927706","article-title":"Differential evolution algorithm with strategy adaptation for global numerical optimization","volume":"13","author":"Qin","year":"2008","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TEVC.2010.2087271","article-title":"Differential evolution with composite trial vector generation strategies and control parameters","volume":"15","author":"Wang","year":"2011","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.ins.2016.01.068","article-title":"An adaptive multi-population differential evolution algorithm for continuous multi-objective optimization","volume":"348","author":"Wang","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_93","unstructured":"Cordeschi, R. (2002). The Discovery of the Artificial: Behavior, Mind and Machines before and beyond Cybernetics, Springer."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.swevo.2011.02.002","article-title":"A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms","volume":"1","author":"Derrac","year":"2011","journal-title":"Swarm Evol. Comput."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2388\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:45:16Z","timestamp":1760168716000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2388"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,10]]},"references-count":94,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["sym13122388"],"URL":"https:\/\/doi.org\/10.3390\/sym13122388","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,10]]}}}