{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T10:36:07Z","timestamp":1768991767090,"version":"3.49.0"},"reference-count":66,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T00:00:00Z","timestamp":1575504000000},"content-version":"vor","delay-in-days":338,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71841054"],"award-info":[{"award-number":["71841054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2572018BM07"],"award-info":[{"award-number":["2572018BM07"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005046","name":"Natural Science Foundation of Heilongjiang Province","doi-asserted-by":"publisher","award":["LH2019G014"],"award-info":[{"award-number":["LH2019G014"]}],"id":[{"id":"10.13039\/501100005046","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004027","name":"Postdoctoral Foundation of Hei Long Jiang Province","doi-asserted-by":"publisher","award":["LBH-Z18015"],"award-info":[{"award-number":["LBH-Z18015"]}],"id":[{"id":"10.13039\/501100004027","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006579","name":"Ministry of Industry and Information Technology of the People's Republic of China","doi-asserted-by":"publisher","award":["19GZY411"],"award-info":[{"award-number":["19GZY411"]}],"id":[{"id":"10.13039\/501100006579","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>The grey wolf optimizer (GWO) algorithm is a recently developed, novel, population\u2010based optimization technique that is inspired by the hunting mechanism of grey wolves. The GWO algorithm has some distinct advantages, such as few algorithm parameters, strong global optimization ability, and ease of implementation on a computer. However, the paramount challenge is that there are some cases where the GWO is prone to stagnation in local optima. This drawback of the GWO algorithm may be attributed to an insufficiency in its position\u2010updated equation, which disregards the positional interaction information about the three best grey wolves (i.e., the three leaders). This paper proposes an improved version of the GWO algorithm that is based on a dynamically dimensioned search, spiral walking predation technique, and positional interaction information (referred to as the DGWO). In addition, a nonlinear control parameter strategy, i.e., the control parameter that is nonlinearly increased with an increase in iterations, is designed to balance the exploration and exploitation of the GWO algorithm. The experimental results for 23 general benchmark functions and 3 well\u2010known engineering optimization design applications validate the effectiveness and feasibility of the proposed DGWO algorithm. The comparison results for the 23 benchmark functions show that the proposed DGWO algorithm performs significantly better than the GWO and its improved variant for most benchmarks. The DGWO provides the highest solution precision, strongest robustness, and fastest convergence rate among the compared algorithms in almost all cases.<\/jats:p>","DOI":"10.1155\/2019\/7189653","type":"journal-article","created":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T23:31:28Z","timestamp":1575588688000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Dynamically Dimensioned Search Grey Wolf Optimizer Based on Positional Interaction Information"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7749-7922","authenticated-orcid":false,"given":"Fu","family":"Yan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6526-6825","authenticated-orcid":false,"given":"Jianzhong","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5380-2467","authenticated-orcid":false,"given":"Kumchol","family":"Yun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,12,5]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.02.041"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-014-1771-7"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1081\/drt-120004044"},{"key":"e_1_2_9_4_2","first-page":"20","article-title":"Based on micro canonical annealing and improved FCM algorithm for remote sensing image segmentation","volume":"32","author":"Jia Z. H.","year":"2011","journal-title":"Laser Journal"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2018.05.019"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.phycom.2017.12.006"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1029\/2005wr004723"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11269-016-1520-6"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/7919324"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1029\/2008wr007673"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/2401818"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2018.04.012"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.02.008"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1080\/0305215x.2017.1302438"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2018.07.303"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13369-018-3536-0"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11277-017-5024-3"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.12989\/sem.2015.55.3.535"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1002\/tal.1151"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1080\/0952813x.2016.1266037"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.soildyn.2015.04.004"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2013.12.007"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2018.01.001"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2018.07.022"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-017-3272-5"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1155\/2016\/7950348"},{"key":"e_1_2_9_27_2","doi-asserted-by":"crossref","unstructured":"KishorA.andSinghP. K. PantM. DeepK. BansalJ. NagarA. andDasK. Empirical study of grey wolf optimizer 436 Proceedings of Fifth International Conference on Soft Computing for Problem Solving 2015 Singapore Springer 1037\u20131049.","DOI":"10.1007\/978-981-10-0448-3_87"},{"key":"e_1_2_9_28_2","doi-asserted-by":"publisher","DOI":"10.3390\/a9010004"},{"key":"e_1_2_9_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2016.10.062"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.3233\/jifs-182706"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/2981282"},{"key":"e_1_2_9_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2015.03.011"},{"key":"e_1_2_9_33_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-13572-4_1"},{"key":"e_1_2_9_34_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-014-0645-7"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1049\/iet-smt.2017.0486"},{"key":"e_1_2_9_36_2","doi-asserted-by":"publisher","DOI":"10.1515\/jisys-2014-0137"},{"key":"e_1_2_9_37_2","doi-asserted-by":"publisher","DOI":"10.3390\/en12122274"},{"key":"e_1_2_9_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2016.05.015"},{"key":"e_1_2_9_39_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48490-7_20"},{"key":"e_1_2_9_40_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11277-017-5161-8"},{"key":"e_1_2_9_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2015.07.003"},{"key":"e_1_2_9_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2017.10.024"},{"key":"e_1_2_9_43_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-62398-6_9"},{"key":"e_1_2_9_44_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2016.01.008"},{"key":"e_1_2_9_45_2","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/481360"},{"key":"e_1_2_9_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2011.02.002"},{"key":"e_1_2_9_47_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-014-1806-7"},{"key":"e_1_2_9_48_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13369-014-1156-x"},{"key":"e_1_2_9_49_2","doi-asserted-by":"crossref","unstructured":"CuiZ. ZengJ. andYinY. An improved PSO with time-varying accelerator coefficients Proceedings of the Eighth International Conference on Intelligent Systems Design and Applications November 2008 Kaohsiung Taiwan 638\u2013643 https:\/\/doi.org\/10.1109\/isda.2008.86 2-s2.0-67449123340.","DOI":"10.1109\/ISDA.2008.86"},{"key":"e_1_2_9_50_2","doi-asserted-by":"crossref","unstructured":"BaoG. Q.andMaoK. F. Particle swarm optimization algorithm with asymmetric time varying acceleration coefficients Proceedings of the IEEE International Conference on Robotics and Biomimetics December 2009 Guilin China 2134\u20132139 https:\/\/doi.org\/10.1109\/robio.2009.5420504 2-s2.0-77951457175.","DOI":"10.1109\/ROBIO.2009.5420504"},{"key":"e_1_2_9_51_2","doi-asserted-by":"crossref","unstructured":"ZiyuT.andDingxueZ. A modified particle swarm optimization with an adaptive acceleration coefficients Proceedings of the Asia-Pacific Conference on Information Processing July 2009 Shenzhen China 330\u2013332 https:\/\/doi.org\/10.1109\/apcip.2009.217 2-s2.0-70450201988.","DOI":"10.1109\/APCIP.2009.217"},{"key":"e_1_2_9_52_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-010-0591-1"},{"key":"e_1_2_9_53_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2017.04.053"},{"key":"e_1_2_9_54_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2017.07.002"},{"key":"e_1_2_9_55_2","doi-asserted-by":"publisher","DOI":"10.1155\/s1048953389000201"},{"key":"e_1_2_9_56_2","volume-title":"Applied Nonlinear Programming","author":"Himmelblau D. M.","year":"1972"},{"key":"e_1_2_9_57_2","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2014.10.777"},{"key":"e_1_2_9_58_2","doi-asserted-by":"publisher","DOI":"10.1177\/003754979406200405"},{"key":"e_1_2_9_59_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.2912596"},{"key":"e_1_2_9_60_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00366-011-0241-y"},{"key":"e_1_2_9_61_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.11.041"},{"key":"e_1_2_9_62_2","first-page":"30","article-title":"A combined genetic adaptive search (GeneAS) for engineering design","volume":"26","author":"Deb K.","year":"1996","journal-title":"Computer Science and Informatics"},{"key":"e_1_2_9_63_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.2919393"},{"key":"e_1_2_9_64_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0166-3615(99)00046-9"},{"key":"e_1_2_9_65_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2006.03.003"},{"key":"e_1_2_9_66_2","first-page":"611","article-title":"Engineering optimization with hybrid particle swarm and ant colony optimization","volume":"10","author":"Kaveh A.","year":"2009","journal-title":"Asian Journal of Civil Engineering"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/7189653.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/7189653.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2019\/7189653","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T12:32:37Z","timestamp":1723033957000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2019\/7189653"}},"subtitle":[],"editor":[{"given":"Ra\u00fal","family":"Ba\u00f1os","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":66,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1155\/2019\/7189653"],"URL":"https:\/\/doi.org\/10.1155\/2019\/7189653","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]},"assertion":[{"value":"2019-06-22","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-10-21","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-12-05","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"7189653"}}