{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T16:20:12Z","timestamp":1771950012018,"version":"3.50.1"},"reference-count":70,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T00:00:00Z","timestamp":1683763200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T00:00:00Z","timestamp":1683763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["20A460"],"award-info":[{"award-number":["20A460"]}]},{"name":"Scientific Research Start-up Fund for High-level Talents in Xiangnan University"},{"name":"the Applied Characteristic Disciplines of Electronic Science and Technology of Xiangnan University","award":["2020-3667"],"award-info":[{"award-number":["2020-3667"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>To develop a high performance and widely applicable particle swarm optimization (PSO) algorithm, a heterogeneous differential evolution particle swarm optimization (HeDE-PSO) is proposed in this study. HeDE-PSO adopts two differential evolution (DE) mutants to construct different characteristics of learning exemplars for PSO, one DE mutant is for enhancing exploration and the other is for enhance exploitation. To further improve search accuracy in the late stage of optimization, the BFGS (Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno) local search is employed. To assess the performance of HeDE-PSO, it is tested on the CEC2017 test suite and the industrial refrigeration system design problem. The test results are compared with seven recent PSO algorithms, JADE (adaptive differential evolution with optional external archive) and four meta-heuristics. The comparison results show that with two DE mutants to construct learning exemplars, HeDE-PSO can balance exploration and exploitation and obtains strong adaptability on different kinds of optimization problems. On 10-dimensional functions and 30-dimensional functions, HeDE-PSO is only outperformed by the most competitive PSO algorithm on seven and six functions, respectively. HeDE-PSO obtains the best performance on sixteen 10-dimensional functions and seventeen-30 dimensional functions. Moreover, HeDE-PSO outperforms other compared PSO algorithms on the industrial refrigeration system design problem.<\/jats:p>","DOI":"10.1007\/s40747-023-01082-8","type":"journal-article","created":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T06:02:13Z","timestamp":1686117733000},"page":"6905-6925","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Heterogeneous differential evolution particle swarm optimization with local search"],"prefix":"10.1007","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5219-4378","authenticated-orcid":false,"given":"Anping","family":"Lin","sequence":"first","affiliation":[]},{"given":"Dong","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Zhongqi","family":"Li","sequence":"additional","affiliation":[]},{"given":"Hany M.","family":"Hasanien","sequence":"additional","affiliation":[]},{"given":"Yaoting","family":"Shi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,11]]},"reference":[{"key":"1082_CR1","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1137\/0202009","volume":"2","author":"JH Holland","year":"1973","unstructured":"Holland JH (1973) Erratum: genetic algorithms and the optimal allocation of trials. SIAM J Comput 2:88\u2013105","journal-title":"SIAM J Comput"},{"key":"1082_CR2","doi-asserted-by":"crossref","unstructured":"Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the 6th international symposium on micro machine and human science, pp 39\u201343","DOI":"10.1109\/MHS.1995.494215"},{"key":"1082_CR3","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/TEVC.2004.826071","volume":"8","author":"A Ratnaweera","year":"2004","unstructured":"Ratnaweera A, Halgamuge SK, Watson HC (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evol Comput 8:240\u2013255","journal-title":"IEEE Trans Evol Comput"},{"key":"1082_CR4","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1109\/TCYB.2019.2925015","volume":"51","author":"W Liu","year":"2019","unstructured":"Liu W, Wang Z, Yuan Y, Zeng N, Hone K, Liu X (2019) A novel sigmoid-function-based adaptive weighted particle swarm optimizer. IEEE Trans Cybern 51:1085\u20131093","journal-title":"IEEE Trans Cybern"},{"key":"1082_CR5","unstructured":"Shi Y, Eberhart RC (2001) Fuzzy adaptive particle swarm optimization. In: IEEE congress on evolutionary computation, pp 101\u2013106"},{"key":"1082_CR6","unstructured":"Xia X, Song H, Zhang Y, Gui L, Xu X, Li K et al (2022) A particle swarm optimization with adaptive learning weights tuned by a multiple-input multiple-output fuzzy logic controller. IEEE Trans Fuzzy Syst, pp 1\u201315"},{"key":"1082_CR7","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1016\/j.chaos.2007.09.063","volume":"40","author":"B Alatas","year":"2009","unstructured":"Alatas B, Akin E, Ozer AB (2009) Chaos embedded particle swarm optimization algorithms. Chaos Solitons Fractals 40:1715\u20131734","journal-title":"Chaos Solitons Fractals"},{"key":"1082_CR8","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1109\/TSMCB.2009.2015956","volume":"39","author":"Z-H Zhan","year":"2009","unstructured":"Zhan Z-H, Zhang J, Li Y, Chung HS-H (2009) Adaptive particle swarm optimization. IEEE Trans Syst Man Cybern Part B Cybern 39:1362\u20131381","journal-title":"IEEE Trans Syst Man Cybern Part B Cybern"},{"key":"1082_CR9","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.ins.2019.08.065","volume":"508","author":"X Xia","year":"2020","unstructured":"Xia X, Gui L, He G, Wei B, Zhang Y, Yu F et al (2020) An expanded particle swarm optimization based on multi-exemplar and forgetting ability. Inf Sci 508:105\u2013120","journal-title":"Inf Sci"},{"key":"1082_CR10","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1109\/TEVC.2004.826074","volume":"8","author":"R Mendes","year":"2004","unstructured":"Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: simpler, maybe better. IEEE Trans Evol Comput 8:204\u2013210","journal-title":"IEEE Trans Evol Comput"},{"key":"1082_CR11","first-page":"124","volume":"2005","author":"JJ Liang","year":"2005","unstructured":"Liang JJ, Suganthan PN (2005) Dynamic multi-swarm particle swarm optimizer. IEEE Swarm Intell Symp 2005:124\u2013129","journal-title":"IEEE Swarm Intell Symp"},{"key":"1082_CR12","volume":"121","author":"T Li","year":"2022","unstructured":"Li T, Shi J, Deng W, Hu Z (2022) Pyramid particle swarm optimization with novel strategies of competition and cooperation. Appl Soft Comput 121:108731","journal-title":"Appl Soft Comput"},{"key":"1082_CR13","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.engappai.2013.09.011","volume":"27","author":"WH Lim","year":"2014","unstructured":"Lim WH, Isa NAM (2014) Particle swarm optimization with increasing topology connectivity. Eng Appl Artif Intell 27:80\u2013102","journal-title":"Eng Appl Artif Intell"},{"key":"1082_CR14","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1016\/j.asoc.2016.07.041","volume":"48","author":"L Wang","year":"2016","unstructured":"Wang L, Yang B, Orchard J (2016) Particle swarm optimization using dynamic tournament topology. Appl Soft Comput 48:584\u2013596","journal-title":"Appl Soft Comput"},{"key":"1082_CR15","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/j.eij.2022.04.003","volume":"23","author":"A Lin","year":"2022","unstructured":"Lin A, Li S, Liu R (2022) Mutual learning differential particle swarm optimization. Egypt Inform J 23:469\u2013481","journal-title":"Egypt Inform J"},{"key":"1082_CR16","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1016\/j.asoc.2017.07.023","volume":"60","author":"F Javidrad","year":"2017","unstructured":"Javidrad F, Nazari M (2017) A new hybrid particle swarm and simulated annealing stochastic optimization method. Appl Soft Comput 60:634\u2013654","journal-title":"Appl Soft Comput"},{"key":"1082_CR17","doi-asserted-by":"crossref","first-page":"2277","DOI":"10.1109\/TCYB.2015.2475174","volume":"46","author":"YJ Gong","year":"2016","unstructured":"Gong YJ, Li JJ, Zhou Y, Li Y, Chung HSH, Shi YH et al (2016) Genetic learning particle swarm optimization. IEEE Trans Cybern 46:2277\u20132290","journal-title":"IEEE Trans Cybern"},{"key":"1082_CR18","volume":"6","author":"A Adamu","year":"2021","unstructured":"Adamu A, Abdullahi M, Junaidu SB, Hassan IH (2021) An hybrid particle swarm optimization with crow search algorithm for feature selection. Mach Learn Appl 6:100108","journal-title":"Mach Learn Appl"},{"key":"1082_CR19","doi-asserted-by":"crossref","first-page":"5446","DOI":"10.1016\/j.egyr.2021.08.120","volume":"7","author":"R Yang","year":"2021","unstructured":"Yang R, Liu Y, Yu Y, He X, Li H (2021) Hybrid improved particle swarm optimization-cuckoo search optimized fuzzy PID controller for micro gas turbine. Energy Rep 7:5446\u20135454","journal-title":"Energy Rep"},{"key":"1082_CR20","first-page":"6432","volume":"34","author":"A G\u00fcm\u00fc\u015f\u00e7\u00fc","year":"2021","unstructured":"G\u00fcm\u00fc\u015f\u00e7\u00fc A, Kaya S, Tenekeci ME, Kara\u00e7izmeli \u0130H, Aydilek \u0130B (2021) The impact of local search strategies on chaotic hybrid firefly particle swarm optimization algorithm in flow-shop scheduling. J King Saud Univ Comput Inf Sci 34:6432\u20136440","journal-title":"J King Saud Univ Comput Inf Sci"},{"key":"1082_CR21","doi-asserted-by":"crossref","unstructured":"Bashath S, Ismail AR (2019) Improved particle swarm optimization by fast simulated annealing algorithm. In: 2019 international conference of artificial intelligence and information technology (ICAIIT), pp 297\u2013301","DOI":"10.1109\/ICAIIT.2019.8834515"},{"key":"1082_CR22","doi-asserted-by":"crossref","first-page":"29354","DOI":"10.1109\/ACCESS.2020.2972826","volume":"8","author":"L Zhen","year":"2020","unstructured":"Zhen L, Liu Y, Dongsheng W, Wei Z (2020) Parameter estimation of software reliability model and prediction based on hybrid wolf pack algorithm and particle swarm optimization. IEEE Access 8:29354\u201329369","journal-title":"IEEE Access"},{"key":"1082_CR23","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1109\/TEVC.2005.857610","volume":"10","author":"JJ Liang","year":"2006","unstructured":"Liang JJ, Qin AK, Member S, Suganthan PN, Member S, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10:281\u2013295","journal-title":"IEEE Trans Evol Comput"},{"key":"1082_CR24","doi-asserted-by":"crossref","first-page":"2238","DOI":"10.1109\/TCYB.2015.2474153","volume":"46","author":"QD Qin","year":"2016","unstructured":"Qin QD, Cheng S, Zhang QY, Li L, Shi YH (2016) Particle swarm optimization with inter swarm interactive learning strategy. IEEE Trans Cybern 46:2238\u20132251","journal-title":"IEEE Trans Cybern"},{"key":"1082_CR25","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.ins.2014.08.039","volume":"291","author":"R Cheng","year":"2015","unstructured":"Cheng R, Jin Y (2015) A social learning particle swarm optimization algorithm for scalable optimization. Inf Sci 291:43\u201360","journal-title":"Inf Sci"},{"key":"1082_CR26","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.swevo.2018.12.009","volume":"45","author":"G Xu","year":"2019","unstructured":"Xu G, Cui Q, Shi X, Ge H, Zhan Z-H, Lee HP et al (2019) Particle swarm optimization based on dimensional learning strategy. Swarm Evol Comput 45:33\u201351","journal-title":"Swarm Evol Comput"},{"key":"1082_CR27","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.ins.2018.01.027","volume":"436","author":"F Wang","year":"2018","unstructured":"Wang F, Zhang H, Li KS, Lin ZY, Yang J, Shen XL (2018) A hybrid particle swarm optimization algorithm using adaptive learning strategy. Inf Sci 436:162\u2013177","journal-title":"Inf Sci"},{"key":"1082_CR28","doi-asserted-by":"crossref","unstructured":"Kaucic M, Piccotto F (2022) A level-based learning swarm optimizer with a hybrid constraint-handling technique for large-scale portfolio selection problems. In: 2022 IEEE congress on evolutionary computation (CEC), pp 1\u20138","DOI":"10.1109\/CEC55065.2022.9870358"},{"key":"1082_CR29","volume":"60","author":"D Li","year":"2021","unstructured":"Li D, Guo W, Lerch A, Li Y, Wang L, Wu Q (2021) An adaptive particle swarm optimizer with decoupled exploration and exploitation for large scale optimization. Swarm Evol Comput 60:100789","journal-title":"Swarm Evol Comput"},{"key":"1082_CR30","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2022.108382","volume":"242","author":"M Sheng","year":"2022","unstructured":"Sheng M, Wang Z, Liu W, Wang X, Chen S, Liu X (2022) A particle swarm optimizer with multi-level population sampling and dynamic p-learning mechanisms for large-scale optimization. Knowl Based Syst 242:108382","journal-title":"Knowl Based Syst"},{"key":"1082_CR31","unstructured":"Liang JJ, Suganthan PN (2005) Dynamic multi-swarm particle swarm optimizer with local search. In: IEEE congress on evolutionary computation, pp 522\u2013528"},{"key":"1082_CR32","doi-asserted-by":"crossref","first-page":"7536","DOI":"10.1016\/j.eswa.2014.06.005","volume":"41","author":"G Wu","year":"2014","unstructured":"Wu G, Qiu D, Yu Y, Pedrycz W, Ma M, Li H (2014) Superior solution guided particle swarm optimization combined with local search techniques. Expert Syst Appl 41:7536\u20137548","journal-title":"Expert Syst Appl"},{"key":"1082_CR33","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.swevo.2017.10.004","volume":"39","author":"Y Chen","year":"2017","unstructured":"Chen Y, Li L, Peng H, Xiao J, Wu QT (2017) Dynamic multi-swarm differential learning particle swarm optimizer. Swarm Evol Comput 39:209\u2013221","journal-title":"Swarm Evol Comput"},{"key":"1082_CR34","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1109\/TEVC.2012.2232931","volume":"17","author":"M Hu","year":"2013","unstructured":"Hu M, Wu T, Weir JD (2013) An adaptive particle swarm optimization with multiple adaptive methods. IEEE Trans Evol Comput 17:705\u2013720","journal-title":"IEEE Trans Evol Comput"},{"key":"1082_CR35","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1109\/TEVC.2018.2885075","volume":"23","author":"Y Cao","year":"2019","unstructured":"Cao Y, Zhang H, Li W, Zhou M, Zhang Y, Chaovalitwongse WA (2019) Comprehensive learning particle swarm optimization algorithm with local search for multimodal functions. IEEE Trans Evol Comput 23:718\u2013731","journal-title":"IEEE Trans Evol Comput"},{"key":"1082_CR36","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.ins.2022.07.067","volume":"609","author":"F Yu","year":"2022","unstructured":"Yu F, Tong L, Xia X (2022) Adjustable driving force based particle swarm optimization algorithm. Inf Sci 609:60\u201378","journal-title":"Inf Sci"},{"key":"1082_CR37","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.asoc.2017.07.020","volume":"61","author":"Y Chen","year":"2017","unstructured":"Chen Y, Li L, Peng H, Xiao J, Yang Y, Shi Y (2017) Particle swarm optimizer with two differential mutation. Appl Soft Comput 61:314\u2013330","journal-title":"Appl Soft Comput"},{"key":"1082_CR38","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/j.asoc.2017.02.007","volume":"55","author":"N Lynn","year":"2017","unstructured":"Lynn N, Suganthan PN (2017) Ensemble particle swarm optimizer. Appl Soft Comput 55:533\u2013548","journal-title":"Appl Soft Comput"},{"key":"1082_CR39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40747-020-00148-1","volume":"7","author":"H Wang","year":"2021","unstructured":"Wang H, Liang M, Sun C, Zhang G, Xie L (2021) Multiple-strategy learning particle swarm optimization for large-scale optimization problems. Complex Intell Syst 7:1\u201316","journal-title":"Complex Intell Syst"},{"key":"1082_CR40","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s10489-018-1258-3","volume":"49","author":"Y Ning","year":"2018","unstructured":"Ning Y, Peng Z, Dai Y, Bi D, Wang J (2018) Enhanced particle swarm optimization with multi-swarm and multi-velocity for optimizing high-dimensional problems. Appl Intell 49:335\u2013351","journal-title":"Appl Intell"},{"key":"1082_CR41","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.swevo.2015.05.002","volume":"24","author":"N Lynn","year":"2015","unstructured":"Lynn N, Suganthan PN (2015) Heterogeneous comprehensive learning particle swarm optimization with enhanced exploration and exploitation. Swarm Evol Comput 24:11\u201324","journal-title":"Swarm Evol Comput"},{"key":"1082_CR42","volume-title":"A modified particle swarm optimizer","author":"YH Shi","year":"1998","unstructured":"Shi YH, Eberhart R (1998) A modified particle swarm optimizer. IEEE, New York"},{"key":"1082_CR43","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.swevo.2018.07.002","volume":"44","author":"A Lin","year":"2018","unstructured":"Lin A, Sun W, Yu H, Wu G, Tang H (2018) Global genetic learning particle swarm optimization with diversity enhancement by ring topology. Swarm Evol Comput 44:571\u2013583","journal-title":"Swarm Evol Comput"},{"key":"1082_CR44","doi-asserted-by":"crossref","first-page":"7519","DOI":"10.1007\/s00500-016-2307-7","volume":"21","author":"X Chen","year":"2017","unstructured":"Chen X, Tianfield H, Mei CL, Du WL, Liu GH (2017) Biogeography-based learning particle swarm optimization. Soft Comput 21:7519\u20137541","journal-title":"Soft Comput"},{"key":"1082_CR45","doi-asserted-by":"crossref","first-page":"2199","DOI":"10.1007\/s40747-021-00395-w","volume":"7","author":"L Lu","year":"2021","unstructured":"Lu L, Zheng H, Jie J, Zhang M, Dai R (2021) Reinforcement learning-based particle swarm optimization for sewage treatment control. Complex Intell Syst 7:2199\u20132210","journal-title":"Complex Intell Syst"},{"key":"1082_CR46","volume":"103","author":"X Zhang","year":"2021","unstructured":"Zhang X, Sun W, Xue M, Lin A (2021) Probability-optimal leader comprehensive learning particle swarm optimization with Bayesian iteration. Appl Soft Comput 103:107132","journal-title":"Appl Soft Comput"},{"key":"1082_CR47","volume":"130","author":"D Zhang","year":"2022","unstructured":"Zhang D, Ma G, Deng Z, Wang Q, Zhang G, Zhou W (2022) A self-adaptive gradient-based particle swarm optimization algorithm with dynamic population topology. Appl Soft Comput 130:109660","journal-title":"Appl Soft Comput"},{"key":"1082_CR48","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s40747-018-0071-2","volume":"4","author":"S Cheng","year":"2018","unstructured":"Cheng S, Lu H, Lei X, Shi Y (2018) A quarter century of particle swarm optimization. Complex Intell Syst 4:227\u2013239","journal-title":"Complex Intell Syst"},{"key":"1082_CR49","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2016.01.004","volume":"27","author":"S Das","year":"2016","unstructured":"Das S, Mullick SS, Suganthan PN (2016) Recent advances in differential evolution\u2014an updated survey. Swarm Evol Comput 27:1\u201330","journal-title":"Swarm Evol Comput"},{"key":"1082_CR50","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1109\/TEVC.2009.2014613","volume":"13","author":"JQ Zhang","year":"2009","unstructured":"Zhang JQ, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13:945\u2013958","journal-title":"IEEE Trans Evol Comput"},{"key":"1082_CR51","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.ins.2017.09.053","volume":"423","author":"G Wu","year":"2017","unstructured":"Wu G, Shen X, Li H, Chen H, Lin A (2017) Ensemble of differential evolution variants. Inf Sci 423:172\u2013186","journal-title":"Inf Sci"},{"key":"1082_CR52","doi-asserted-by":"crossref","first-page":"3831","DOI":"10.1016\/j.aej.2021.09.013","volume":"61","author":"MF Ahmad","year":"2022","unstructured":"Ahmad MF, Isa NAM, Lim WH, Ang KM (2022) Differential evolution: a recent review based on state-of-the-art works. Alex Eng J 61:3831\u20133872","journal-title":"Alex Eng J"},{"key":"1082_CR53","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.actaastro.2018.04.045","volume":"148","author":"RG Melton","year":"2018","unstructured":"Melton RG (2018) Differential evolution\/particle swarm optimizer for constrained slew maneuvers. Acta Astronaut 148:246\u2013259","journal-title":"Acta Astronaut"},{"key":"1082_CR54","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.jweia.2017.10.032","volume":"172","author":"M Song","year":"2018","unstructured":"Song M, Chen K, Wang J (2018) Three-dimensional wind turbine positioning using Gaussian particle swarm optimization with differential evolution. J Wind Eng Ind Aerodyn 172:317\u2013324","journal-title":"J Wind Eng Ind Aerodyn"},{"key":"1082_CR55","volume":"81","author":"S Wang","year":"2019","unstructured":"Wang S, Li Y, Yang H (2019) Self-adaptive mutation differential evolution algorithm based on particle swarm optimization. Appl Soft Comput 81:105496","journal-title":"Appl Soft Comput"},{"key":"1082_CR56","doi-asserted-by":"crossref","DOI":"10.1016\/j.catena.2020.105024","volume":"198","author":"B Mohammadi","year":"2021","unstructured":"Mohammadi B, Guan Y, Moazenzadeh R, Safari MJS (2021) Implementation of hybrid particle swarm optimization-differential evolution algorithms coupled with multi-layer perceptron for suspended sediment load estimation. CATENA 198:105024","journal-title":"CATENA"},{"key":"1082_CR57","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1016\/j.asoc.2015.10.041","volume":"38","author":"A Moharam","year":"2016","unstructured":"Moharam A, El-Hosseini MA, Ali HA (2016) Design of optimal PID controller using hybrid differential evolution and particle swarm optimization with an aging leader and challengers. Appl Soft Comput 38:727\u2013737","journal-title":"Appl Soft Comput"},{"key":"1082_CR58","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.neucom.2015.03.119","volume":"174","author":"L Deng","year":"2016","unstructured":"Deng L, Lu G, Shao Y, Fei M, Hu H (2016) A novel camera calibration technique based on differential evolution particle swarm optimization algorithm. Neurocomputing 174:456\u2013465","journal-title":"Neurocomputing"},{"key":"1082_CR59","volume":"44","author":"C Wang","year":"2021","unstructured":"Wang C, Xu M, Zhang Q, Feng J, Jiang R, Wei Y et al (2021) Parameters identification of Thevenin model for lithium-ion batteries using self-adaptive particle swarm optimization differential evolution algorithm to estimate state of charge. J Energy Storage 44:103244","journal-title":"J Energy Storage"},{"key":"1082_CR60","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.swevo.2018.04.006","volume":"44","author":"XW Xia","year":"2019","unstructured":"Xia XW, Xing Y, Wei B, Zhang YL, Li X, Deng XL et al (2019) A fitness-based multi-role particle swarm optimization. Swarm Evol Comput 44:349\u2013364","journal-title":"Swarm Evol Comput"},{"key":"1082_CR61","doi-asserted-by":"crossref","first-page":"9701","DOI":"10.1007\/s00500-018-3536-8","volume":"23","author":"M Ghasemi","year":"2019","unstructured":"Ghasemi M, Akbari E, Rahimnejad A, Razavi SE, Ghavidel S, Li L (2019) Phasor particle swarm optimization: a simple and efficient variant of PSO. Soft Comput 23:9701\u20139718","journal-title":"Soft Comput"},{"key":"1082_CR62","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.matcom.2021.08.013","volume":"192","author":"FA Hashim","year":"2022","unstructured":"Hashim FA, Houssein EH, Hussain K, Mabrouk MS, Al-Atabany W (2022) Honey badger algorithm: new metaheuristic algorithm for solving optimization problems. Math Comput Simul 192:84\u20131104","journal-title":"Math Comput Simul"},{"key":"1082_CR63","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.advengsoft.2017.07.002","volume":"114","author":"S Mirjalili","year":"2017","unstructured":"Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163\u2013191","journal-title":"Adv Eng Softw"},{"key":"1082_CR64","doi-asserted-by":"crossref","first-page":"1531","DOI":"10.1007\/s10489-020-01893-z","volume":"51","author":"FA Hashim","year":"2021","unstructured":"Hashim FA, Hussain K, Houssein EH, Mabrouk MS, Al-Atabany W (2021) Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl Intell 51:1531\u20131551","journal-title":"Appl Intell"},{"key":"1082_CR65","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2022.114570","volume":"391","author":"JO Agushaka","year":"2022","unstructured":"Agushaka JO, Ezugwu AE, Abualigah L (2022) Dwarf mongoose optimization algorithm. Comput Methods Appl Mech Eng 391:114570","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1082_CR66","unstructured":"Awad NH, Ali MZ, Liang JJ, Qu BY, Suganthan PN (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained real-parameter numerical optimization. http:\/\/www.ntu.edu.sg\/home\/epnsugan\/"},{"key":"1082_CR67","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.swevo.2011.02.002","volume":"1","author":"J Derrac","year":"2011","unstructured":"Derrac J, Garc\u00eda S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1:3\u201318","journal-title":"Swarm Evol Comput"},{"key":"1082_CR68","doi-asserted-by":"crossref","DOI":"10.1016\/j.swevo.2020.100693","volume":"56","author":"A Kumar","year":"2020","unstructured":"Kumar A, Wu G, Ali MZ, Mallipeddi R, Suganthan PN, Das S (2020) A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm Evol Comput 56:100693","journal-title":"Swarm Evol Comput"},{"key":"1082_CR69","doi-asserted-by":"crossref","unstructured":"Takahama T, Sakai S (2006) Constrained optimization by the \u03b5 constrained differential evolution with gradient-based mutation and feasible elites. In: 2006 IEEE international conference on evolutionary computation, pp 1\u20138","DOI":"10.1109\/CEC.2006.1688283"},{"key":"1082_CR70","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1109\/TEVC.2021.3110130","volume":"26","author":"G Wu","year":"2021","unstructured":"Wu G, Wen X, Wang L, Pedrycz W, Suganthan PN (2021) A voting-mechanism based ensemble framework for constraint handling techniques. IEEE Trans Evol Comput 26:646\u2013660","journal-title":"IEEE Trans Evol Comput"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-023-01082-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-023-01082-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-023-01082-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T19:23:55Z","timestamp":1698434635000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-023-01082-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,11]]},"references-count":70,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["1082"],"URL":"https:\/\/doi.org\/10.1007\/s40747-023-01082-8","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,11]]},"assertion":[{"value":"6 July 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that there is no competing financial interests or personal relationships influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}