{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T03:38:04Z","timestamp":1779161884985,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,11]],"date-time":"2022-11-11T00:00:00Z","timestamp":1668124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NNSF of China","award":["61640014"],"award-info":[{"award-number":["61640014"]}]},{"name":"NNSF of China","award":["[2022] Yiban017"],"award-info":[{"award-number":["[2022] Yiban017"]}]},{"name":"NNSF of China","award":["[2019] 2152"],"award-info":[{"award-number":["[2019] 2152"]}]},{"name":"NNSF of China","award":["KY [2021]012"],"award-info":[{"award-number":["KY [2021]012"]}]},{"name":"NNSF of China","award":["[2022]043"],"award-info":[{"award-number":["[2022]043"]}]},{"name":"NNSF of China","award":["[2020]1Y266"],"award-info":[{"award-number":["[2020]1Y266"]}]},{"name":"NNSF of China","award":["KCALK201708"],"award-info":[{"award-number":["KCALK201708"]}]},{"name":"NNSF of China","award":["2015"],"award-info":[{"award-number":["2015"]}]},{"name":"Guizhou provincial Science and Technology Projects","award":["61640014"],"award-info":[{"award-number":["61640014"]}]},{"name":"Guizhou provincial Science and Technology Projects","award":["[2022] Yiban017"],"award-info":[{"award-number":["[2022] Yiban017"]}]},{"name":"Guizhou provincial Science and Technology Projects","award":["[2019] 2152"],"award-info":[{"award-number":["[2019] 2152"]}]},{"name":"Guizhou provincial Science and Technology Projects","award":["KY [2021]012"],"award-info":[{"award-number":["KY [2021]012"]}]},{"name":"Guizhou provincial Science and Technology Projects","award":["[2022]043"],"award-info":[{"award-number":["[2022]043"]}]},{"name":"Guizhou provincial Science and Technology Projects","award":["[2020]1Y266"],"award-info":[{"award-number":["[2020]1Y266"]}]},{"name":"Guizhou provincial Science and Technology Projects","award":["KCALK201708"],"award-info":[{"award-number":["KCALK201708"]}]},{"name":"Guizhou provincial Science and Technology Projects","award":["2015"],"award-info":[{"award-number":["2015"]}]},{"name":"Innovation group of Guizhou Education Department","award":["61640014"],"award-info":[{"award-number":["61640014"]}]},{"name":"Innovation group of Guizhou Education Department","award":["[2022] Yiban017"],"award-info":[{"award-number":["[2022] Yiban017"]}]},{"name":"Innovation group of Guizhou Education Department","award":["[2019] 2152"],"award-info":[{"award-number":["[2019] 2152"]}]},{"name":"Innovation group of Guizhou Education Department","award":["KY [2021]012"],"award-info":[{"award-number":["KY [2021]012"]}]},{"name":"Innovation group of Guizhou Education Department","award":["[2022]043"],"award-info":[{"award-number":["[2022]043"]}]},{"name":"Innovation group of Guizhou Education Department","award":["[2020]1Y266"],"award-info":[{"award-number":["[2020]1Y266"]}]},{"name":"Innovation group of Guizhou Education Department","award":["KCALK201708"],"award-info":[{"award-number":["KCALK201708"]}]},{"name":"Innovation group of Guizhou Education Department","award":["2015"],"award-info":[{"award-number":["2015"]}]},{"name":"Engineering Research Center of Guizhou Education Department","award":["61640014"],"award-info":[{"award-number":["61640014"]}]},{"name":"Engineering Research Center of Guizhou Education Department","award":["[2022] Yiban017"],"award-info":[{"award-number":["[2022] Yiban017"]}]},{"name":"Engineering Research Center of Guizhou Education Department","award":["[2019] 2152"],"award-info":[{"award-number":["[2019] 2152"]}]},{"name":"Engineering Research Center of Guizhou Education Department","award":["KY [2021]012"],"award-info":[{"award-number":["KY [2021]012"]}]},{"name":"Engineering Research Center of Guizhou Education Department","award":["[2022]043"],"award-info":[{"award-number":["[2022]043"]}]},{"name":"Engineering Research Center of Guizhou Education Department","award":["[2020]1Y266"],"award-info":[{"award-number":["[2020]1Y266"]}]},{"name":"Engineering Research Center of Guizhou Education Department","award":["KCALK201708"],"award-info":[{"award-number":["KCALK201708"]}]},{"name":"Engineering Research Center of Guizhou Education Department","award":["2015"],"award-info":[{"award-number":["2015"]}]},{"name":"Science and Technology Fund of Guizhou Province","award":["61640014"],"award-info":[{"award-number":["61640014"]}]},{"name":"Science and Technology Fund of Guizhou Province","award":["[2022] Yiban017"],"award-info":[{"award-number":["[2022] Yiban017"]}]},{"name":"Science and Technology Fund of Guizhou Province","award":["[2019] 2152"],"award-info":[{"award-number":["[2019] 2152"]}]},{"name":"Science and Technology Fund of Guizhou Province","award":["KY [2021]012"],"award-info":[{"award-number":["KY [2021]012"]}]},{"name":"Science and Technology Fund of Guizhou Province","award":["[2022]043"],"award-info":[{"award-number":["[2022]043"]}]},{"name":"Science and Technology Fund of Guizhou Province","award":["[2020]1Y266"],"award-info":[{"award-number":["[2020]1Y266"]}]},{"name":"Science and Technology Fund of Guizhou Province","award":["KCALK201708"],"award-info":[{"award-number":["KCALK201708"]}]},{"name":"Science and Technology Fund of Guizhou Province","award":["2015"],"award-info":[{"award-number":["2015"]}]},{"name":"CASE Library of IOT","award":["61640014"],"award-info":[{"award-number":["61640014"]}]},{"name":"CASE Library of IOT","award":["[2022] Yiban017"],"award-info":[{"award-number":["[2022] Yiban017"]}]},{"name":"CASE Library of IOT","award":["[2019] 2152"],"award-info":[{"award-number":["[2019] 2152"]}]},{"name":"CASE Library of IOT","award":["KY [2021]012"],"award-info":[{"award-number":["KY [2021]012"]}]},{"name":"CASE Library of IOT","award":["[2022]043"],"award-info":[{"award-number":["[2022]043"]}]},{"name":"CASE Library of IOT","award":["[2020]1Y266"],"award-info":[{"award-number":["[2020]1Y266"]}]},{"name":"CASE Library of IOT","award":["KCALK201708"],"award-info":[{"award-number":["KCALK201708"]}]},{"name":"CASE Library of IOT","award":["2015"],"award-info":[{"award-number":["2015"]}]},{"name":"IOT platform of Guiyang National High technology industry development zone","award":["61640014"],"award-info":[{"award-number":["61640014"]}]},{"name":"IOT platform of Guiyang National High technology industry development zone","award":["[2022] Yiban017"],"award-info":[{"award-number":["[2022] Yiban017"]}]},{"name":"IOT platform of Guiyang National High technology industry development zone","award":["[2019] 2152"],"award-info":[{"award-number":["[2019] 2152"]}]},{"name":"IOT platform of Guiyang National High technology industry development zone","award":["KY [2021]012"],"award-info":[{"award-number":["KY [2021]012"]}]},{"name":"IOT platform of Guiyang National High technology industry development zone","award":["[2022]043"],"award-info":[{"award-number":["[2022]043"]}]},{"name":"IOT platform of Guiyang National High technology industry development zone","award":["[2020]1Y266"],"award-info":[{"award-number":["[2020]1Y266"]}]},{"name":"IOT platform of Guiyang National High technology industry development zone","award":["KCALK201708"],"award-info":[{"award-number":["KCALK201708"]}]},{"name":"IOT platform of Guiyang National High technology industry development zone","award":["2015"],"award-info":[{"award-number":["2015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The black widow spider optimization algorithm (BWOA) had the problems of slow convergence speed and easily to falling into local optimum mode. To address these problems, this paper proposes a multi-strategy black widow spider optimization algorithm (IBWOA). First, Gauss chaotic mapping is introduced to initialize the population to ensure the diversity of the algorithm at the initial stage. Then, the sine cosine strategy is introduced to perturb the individuals during iteration to improve the global search ability of the algorithm. In addition, the elite opposition-based learning strategy is introduced to improve convergence speed of algorithm. Finally, the mutation method of the differential evolution algorithm is integrated to reorganize the individuals with poor fitness values. Through the analysis of the optimization results of 13 benchmark test functions and a part of CEC2017 test functions, the effectiveness and rationality of each improved strategy are verified. Moreover, it shows that the proposed algorithm has significant improvement in solution accuracy, performance and convergence speed compared with other algorithms. Furthermore, the IBWOA algorithm is used to solve six practical constrained engineering problems. The results show that the IBWOA has excellent optimization ability and scalability.<\/jats:p>","DOI":"10.3390\/e24111640","type":"journal-article","created":{"date-parts":[[2022,11,14]],"date-time":"2022-11-14T02:32:01Z","timestamp":1668393121000},"page":"1640","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Improved Black Widow Spider Optimization Algorithm Integrating Multiple Strategies"],"prefix":"10.3390","volume":"24","author":[{"given":"Chenxin","family":"Wan","sequence":"first","affiliation":[{"name":"Electrical Engineering College, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bitao","family":"He","sequence":"additional","affiliation":[{"name":"Power China Guizhou Engineering Co., Ltd., Guiyang 550001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuancheng","family":"Fan","sequence":"additional","affiliation":[{"name":"Power China Guizhou Engineering Co., Ltd., Guiyang 550001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Tan","sequence":"additional","affiliation":[{"name":"College of Forestry, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Qin","sequence":"additional","affiliation":[{"name":"Electrical Engineering College, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6407-1276","authenticated-orcid":false,"given":"Jing","family":"Yang","sequence":"additional","affiliation":[{"name":"Electrical Engineering College, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,11]]},"reference":[{"key":"ref_1","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995-International Conference on Neural Networks, Perth, WA, Australia."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1007\/s00500-018-3102-4","article-title":"Butterflfly optimization algorithm: A novel approach for global optimization","volume":"23","author":"Arora","year":"2019","journal-title":"Soft Comput."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s00366-011-0241-y","article-title":"Cuckoo search algorithm: A metaheuristic approach to solve structural optimization problems","volume":"29","author":"Gandomi","year":"2013","journal-title":"Eng. Comput."},{"key":"ref_6","first-page":"3271","article-title":"Whale optimization algorithm based on Gauss map and small hole imaging learning strategy","volume":"37","author":"Xu","year":"2020","journal-title":"Appl. Res. Comput."},{"key":"ref_7","unstructured":"Liu, R., and Mo, Y.B. (2021). Enhanced Sparrow Search Algorithm and its Application in Engineering Optimization. J. Chin. Comput. Syst., Available online: https:\/\/kns.cnki.net\/kcms\/detail\/21.1106.TP.20211106.1227.006.html."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"108695","DOI":"10.1016\/j.cie.2022.108695","article-title":"Sequential clustering and classification using deep learning technique and multi-objective sine-cosine algorithm","volume":"173","author":"Kuo","year":"2022","journal-title":"Comput. Ind. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"13193","DOI":"10.1007\/s00500-022-07133-5","article-title":"Color image segmentation based on improved sine cosine optimization algorithm","volume":"26","author":"Mookiah","year":"2022","journal-title":"Soft Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"108947","DOI":"10.1016\/j.asoc.2022.108947","article-title":"Optimization of an auto drum fashioned brake using the elite opposition-based learning and chaotic k-best gravitational search strategy based grey wolf optimizer algorithm","volume":"123","author":"Yuan","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.neucom.2015.01.110","article-title":"Elite opposition-based flower pollination algorithm","volume":"188","author":"Zhou","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_12","first-page":"8856040","article-title":"A Novel Bio-Inspired Algorithm Applied to Selective Harmonic Elimination in a Three-Phase Eleven-Level Inverter","volume":"2020","year":"2020","journal-title":"Math. Probl. Eng."},{"key":"ref_13","first-page":"893","article-title":"Gravitational search algorithm based on improved Tent chaos","volume":"35","author":"Zhang","year":"2020","journal-title":"Control. Decis."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.knosys.2015.12.022","article-title":"A Sine Cosine Algorithm for Solving Optimization Problems","volume":"96","author":"Mirjalili","year":"2016","journal-title":"Knowl-Based Syst."},{"key":"ref_15","unstructured":"Tizhoosh, H.R. (2005, January 28\u201330). Opposition-based learning: A new scheme for machine intelligence. Proceedings of the International Conference on Intelligent Agent, Web Technologies and Internet Commerce (CIMCA-IAWTIC\u201906), Vienna, Austria."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4699","DOI":"10.1016\/j.ins.2011.03.016","article-title":"Enhancing particle swarm optimization using generalized opposition-based on learning","volume":"181","author":"Wang","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_17","first-page":"111","article-title":"A Hybrid Differential Evolution with Elite Opposition-Based Learning","volume":"59","author":"Wang","year":"2013","journal-title":"J. Wuhan Univ. (Nat. Sci. Ed.)"},{"key":"ref_18","unstructured":"Storn, R., and Price, K. (2006). Differential Evolution\u2014A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces, University of California."},{"key":"ref_19","first-page":"1584","article-title":"Ions motion optimization algorithm based on diversity optimal guidance and opposition-based learning","volume":"35","author":"Wang","year":"2020","journal-title":"Control. Decis."},{"key":"ref_20","first-page":"1480","article-title":"Cuckoo Search Algorithm with Gravity Acceleration Mechanism","volume":"32","author":"Fu","year":"2021","journal-title":"J. Softw."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.engappai.2006.03.003","article-title":"An effective co-evolutionary particle swarm optimization for constrained engineering design problems","volume":"20","author":"He","year":"2007","journal-title":"Eng. Appl. Artif. Intel."},{"key":"ref_22","unstructured":"Awad, N.H., Ali, M.Z., Liang, J.J., Qu, B.Y., and Suganthan, P.N. (2016). Problem Definitions and Evaluation Criteria for the CEC 2017 Special Session and Competition on Single Objective Real-Parameter Optimization, Nanyang Technological University. Technical Report."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Naruei, I., and Keynia, F. (2021). Wild horse optimizer: A new meta-heuristic algorithm for solving. Eng. Comput.-Ger., Available online: https:\/\/link.springer.com\/article\/10.1007\/s00366-021-01438-z.","DOI":"10.1007\/s00366-021-01438-z"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1007\/s00366-020-01233-2","article-title":"SChoA: A newly fusion of sine and cosine with chimp optimization algorithm for HLS of datapaths in digital filters and engineering applications","volume":"38","author":"Kaur","year":"2022","journal-title":"Eng. Comput.-Ger."},{"key":"ref_25","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_26","doi-asserted-by":"crossref","unstructured":"Zhang, M.J., Wang, D.G., and Yang, J. (2022). Hybrid-Flash Butterfly Optimization Algorithm with Logistic Mapping for Solving the Engineering Constrained Optimization Problems. Entropy, 24.","DOI":"10.3390\/e24040525"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2232","DOI":"10.1016\/j.ins.2009.03.004","article-title":"GSA: A gravitational search algorithm","volume":"179","author":"Rashedi","year":"2009","journal-title":"Inf. Sci."},{"key":"ref_28","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. Comp. SY"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2592","DOI":"10.1016\/j.asoc.2012.11.026","article-title":"Mine blast algorithm: A new population based algorithm for solving constrained engineering optimization problems","volume":"13","author":"Sadollah","year":"2013","journal-title":"Appl. Soft Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.compstruc.2014.03.007","article-title":"Symbiotic organisms search: A new metaheuristic optimization algorithm","volume":"139","author":"Cheng","year":"2014","journal-title":"Comput. Struct."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1002\/(SICI)1097-0207(19960315)39:5<829::AID-NME884>3.0.CO;2-U","article-title":"Structural optimization using a new local approximation method","volume":"39","author":"Chickermane","year":"1996","journal-title":"Int. J. Numer. Meth. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"106734","DOI":"10.1016\/j.asoc.2020.106734","article-title":"Cooperation search algorithm: A novel metaheuristic evolutionary intelligence algorithm for numerical optimization and engineering optimization problems","volume":"98","author":"Feng","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"302","DOI":"10.3846\/13923730.2014.897986","article-title":"An introduction of krill herd algorithm for engineering optimization","volume":"22","author":"Gandomi","year":"2013","journal-title":"J. Civ. Eng. Manag."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/11\/1640\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:14:37Z","timestamp":1760145277000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/11\/1640"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,11]]},"references-count":33,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["e24111640"],"URL":"https:\/\/doi.org\/10.3390\/e24111640","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,11]]}}}