{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T19:58:30Z","timestamp":1766087910496,"version":"3.37.3"},"reference-count":73,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T00:00:00Z","timestamp":1658880000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T00:00:00Z","timestamp":1658880000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of  China","doi-asserted-by":"crossref","award":["62002289"],"award-info":[{"award-number":["62002289"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Genome-wide association studies have succeeded in identifying genetic variants associated with complex diseases, but the findings have not been well interpreted biologically. Although it is widely accepted that epistatic interactions of high-<jats:italic>order<\/jats:italic> single nucleotide polymorphisms (SNPs) [(1) <jats:bold><jats:italic>Single nucleotide polymorphisms (SNP)<\/jats:italic><\/jats:bold> are mainly deoxyribonucleic acid (DNA) sequence polymorphisms caused by variants at a single nucleotide at the genome level. They are the most common type of heritable variation in humans.] are important causes of complex diseases, the combinatorial explosion of millions of SNPs and multiple tests impose a large computational burden. Moreover, it is extremely challenging to correctly distinguish high-<jats:italic>order<\/jats:italic> SNP epistatic interactions from other high-<jats:italic>order<\/jats:italic> SNP combinations due to small sample sizes. In this study, a multitasking harmony search algorithm (MTHSA-DHEI) is proposed for detecting high-<jats:italic>order<\/jats:italic> epistatic interactions [(2) In classical genetics, if genes X1 and X2 are mutated and each mutation by itself produces a unique disease status (phenotype) but the mutations together cause the same disease status as the gene X1 mutation, gene X1 is <jats:bold><jats:italic>epistatic<\/jats:italic><\/jats:bold> and gene X2 is hypostatic, and gene X1 has an epistatic effect (main effect) on disease status. In this work, a high-order <jats:bold><jats:italic>epistatic interaction<\/jats:italic><\/jats:bold> occurs when two or more SNP loci have a joint influence on disease status.], with the goal of simultaneously detecting multiple types of high-<jats:italic>order<\/jats:italic> (<jats:italic>k<\/jats:italic><jats:sub>1<\/jats:sub>-<jats:italic>order<\/jats:italic>, <jats:italic>k<\/jats:italic><jats:sub>2<\/jats:sub>-<jats:italic>order<\/jats:italic>, \u2026, <jats:italic>k<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>-<jats:italic>order<\/jats:italic>) SNP epistatic interactions. Unified coding is adopted for multiple tasks, and four complementary association evaluation functions are employed to improve the capability of discriminating the high-<jats:italic>order<\/jats:italic> SNP epistatic interactions. We compare the proposed MTHSA-DHEI method with four excellent methods for detecting high-<jats:italic>order<\/jats:italic> SNP interactions for 8 high-<jats:italic>order<\/jats:italic><jats:underline>e<\/jats:underline>pistatic <jats:underline>i<\/jats:underline>nteraction models with <jats:underline>n<\/jats:underline>o <jats:underline>m<\/jats:underline>arginal <jats:underline>e<\/jats:underline>ffect (EINMEs) and 12 <jats:underline>e<\/jats:underline>pistatic <jats:underline>i<\/jats:underline>nteraction models with <jats:underline>m<\/jats:underline>arginal <jats:underline>e<\/jats:underline>ffects (EIMEs) <jats:sup>(*)<\/jats:sup> and implement the MTHSA-DHEI algorithm with a real dataset: age-related macular degeneration (AMD). The experimental results indicate that MTHSA-DHEI has power and an F1-score exceeding 90% for all EIMEs and five EINMEs and reduces the computational time by more than 90%. It can efficiently perform multiple high-<jats:italic>order<\/jats:italic> detection tasks for high-<jats:italic>order<\/jats:italic> epistatic interactions and improve the discrimination ability for diverse epistasis models.\n<\/jats:p>","DOI":"10.1007\/s40747-022-00813-7","type":"journal-article","created":{"date-parts":[[2022,7,28]],"date-time":"2022-07-28T01:37:23Z","timestamp":1658972243000},"page":"637-658","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["MTHSA-DHEI: multitasking harmony search algorithm for detecting high-order SNP epistatic interactions"],"prefix":"10.1007","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6696-0085","authenticated-orcid":false,"given":"Shouheng","family":"Tuo","sequence":"first","affiliation":[]},{"given":"Chao","family":"Li","sequence":"additional","affiliation":[]},{"given":"Fan","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Aimin","family":"Li","sequence":"additional","affiliation":[]},{"given":"Lang","family":"He","sequence":"additional","affiliation":[]},{"given":"Zong Woo","family":"Geem","sequence":"additional","affiliation":[]},{"given":"JunLiang","family":"Shang","sequence":"additional","affiliation":[]},{"given":"Haiyan","family":"Liu","sequence":"additional","affiliation":[]},{"given":"YanLing","family":"Zhu","sequence":"additional","affiliation":[]},{"given":"ZengYu","family":"Feng","sequence":"additional","affiliation":[]},{"given":"TianRui","family":"Chen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,7,27]]},"reference":[{"key":"813_CR1","unstructured":"Guo X (2015) Searching genome-wide disease association through SNP Data. Dissertation, Georgia State University. https:\/\/scholarworks.gsu.edu\/cs_diss\/101."},{"key":"813_CR2","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1038\/nature08494","volume":"461","author":"TA Manolio","year":"2009","unstructured":"Manolio TA et al (2009) Finding the missing heritability of complex diseases. Nature 461:747\u2013753","journal-title":"Nature"},{"key":"813_CR3","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1038\/nature05887","volume":"447","author":"DF Easton","year":"2007","unstructured":"Easton DF et al (2007) Genome-wide association study identifies novel breast cancer susceptibility loci. Nature 447:1087\u20131093","journal-title":"Nature"},{"key":"813_CR4","doi-asserted-by":"publisher","first-page":"944","DOI":"10.1126\/science.1143767","volume":"317","author":"J Fellay","year":"2007","unstructured":"Fellay J et al (2007) A whole-genome association study of major determinants for host control of HIV-1. Science 317:944\u2013947","journal-title":"Science"},{"key":"813_CR5","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.semcancer.2018.04.008","volume":"55","author":"MH Wang","year":"2019","unstructured":"Wang MH, Cordell HJ, Van Steen K (2019) Statistical methods for genome-wide association studies. Semin Cancer Biol 55:53\u201360","journal-title":"Semin Cancer Biol"},{"key":"813_CR6","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/j.ajhg.2017.06.005","volume":"101","author":"PM Visscher","year":"2017","unstructured":"Visscher PM, Wray NR, Zhang Q et al (2017) 10 years of GWAS discovery: biology, function, and translation. Am J Hum Genet 101:5\u201322","journal-title":"Am J Hum Genet"},{"issue":"3","key":"813_CR7","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1093\/bib\/bbv058","volume":"17","author":"A Upton","year":"2016","unstructured":"Upton A, Trelles O, Cornejo-Garcia JA, Perkins JR (2016) Review: high-performance computing to detect epistasis in genome scale datasets. Brief Bioinform 17(3):368\u2013379. https:\/\/doi.org\/10.1093\/bib\/bbv058","journal-title":"Brief Bioinform"},{"issue":"3","key":"813_CR8","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1093\/bib\/bbw039","volume":"18","author":"C Loucoubar","year":"2017","unstructured":"Loucoubar C, Grant AV, Bureau J-F et al (2017) Detecting multiway epistasis in family-based association studies. Brief Bioinform 18(3):394\u2013402. https:\/\/doi.org\/10.1093\/bib\/bbw039","journal-title":"Brief Bioinform"},{"key":"813_CR9","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1093\/bfgp\/elu036","volume":"14","author":"P Li","year":"2015","unstructured":"Li P, Guo MZ, Wang CY et al (2015) An overview of SNP interactions in genome-wide association studies. Brief Funct Genomics 14:143\u2013155","journal-title":"Brief Funct Genomics"},{"key":"813_CR10","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1371\/journal.pgen.1007856","volume":"14","author":"S Banerjee","year":"2018","unstructured":"Banerjee S, Zeng LY, Schunkert H et al (2018) Bayesian multiple logistic regression for case\u2013control GWAS. PLoS Genet 14:27","journal-title":"PLoS Genet"},{"issue":"4","key":"813_CR11","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1093\/bib\/bbaa263","volume":"22","author":"S Sun","year":"2021","unstructured":"Sun S, Dong B, Zou Q (2021) Revisiting genome-wide association studies from statistical modelling to machine learning. Brief Bioinform 22(4):263. https:\/\/doi.org\/10.1093\/bib\/bbaa263","journal-title":"Brief Bioinform"},{"issue":"1","key":"813_CR12","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1534\/genetics.108.099127","volume":"182","author":"PA Gros","year":"2009","unstructured":"Gros PA, Le Nagard H, Tenaillon O (2009) The evolution of epistasis and its links with genetic robustness, complexity and drift in a phenotypic model of adaptation. Genetics 182(1):277\u2013293. https:\/\/doi.org\/10.1534\/genetics.108.099127","journal-title":"Genetics"},{"key":"813_CR13","doi-asserted-by":"publisher","first-page":"1167","DOI":"10.1038\/ng2110","volume":"39","author":"Y Zhang","year":"2007","unstructured":"Zhang Y, Liu J (2007) Bayesian inference of epistatic interactions in case\u2013control studies. Nat Genet 39:1167\u20131173. https:\/\/doi.org\/10.1038\/ng2110","journal-title":"Nat Genet"},{"issue":"1","key":"813_CR14","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1186\/1471-2105-15-102","volume":"5","author":"X Guo","year":"2014","unstructured":"Guo X, Meng Y, Yu N, Pan Y (2014) Cloud computing for detecting high order genome-wide epistatic interaction via dynamic clustering. BMC Bioinformatic 5(1):102","journal-title":"BMC Bioinformatic"},{"issue":"9","key":"813_CR15","doi-asserted-by":"publisher","first-page":"1460","DOI":"10.1093\/bioinformatics\/btu840","volume":"2014","author":"GYJW Yang","year":"2014","unstructured":"Yang GYJW, Yang Q et al (2014) PBOOST: a GPU-based tool for parallel permutation tests in genome-wide association studies. Bioinformatics 2014(9):1460\u20131462","journal-title":"Bioinformatics"},{"issue":"1","key":"813_CR16","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1177\/1094342019852128","volume":"34","author":"JM Cecilia","year":"2020","unstructured":"Cecilia JM, Ponte-Fern\u00e1ndez C, Gonz\u00e1lez-Dom\u00ednguez J, Mart\u00edn MJ (2020) Fast search of third-order epistatic interactions on CPU and GPU clusters. Int J High Perform Comput Appl 34(1):20\u201329. https:\/\/doi.org\/10.1177\/1094342019852128","journal-title":"Int J High Perform Comput Appl"},{"key":"813_CR17","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1186\/s12864-015-2217-6","volume":"16","author":"J Wang","year":"2015","unstructured":"Wang J, Joshi T, Valliyodan B, Shi H, Liang Y et al (2015) A Bayesian model for detection of high-order interactions among genetic variants in genome-wide association studies. BMC Genomics 16:1011. https:\/\/doi.org\/10.1186\/s12864-015-2217-6","journal-title":"BMC Genomics"},{"issue":"Suppl 3","key":"813_CR18","doi-asserted-by":"publisher","first-page":"S14","DOI":"10.1186\/1752-0509-6-S3-S14","volume":"6","author":"B Han","year":"2012","unstructured":"Han B, Chen XW, Talebizadeh Z, Xu H (2012) Genetic studies of complex human diseases: characterizing SNP-disease associations using Bayesian networks. BMC Syst Biol 6(Suppl 3):S14. https:\/\/doi.org\/10.1186\/1752-0509-6-S3-S14","journal-title":"BMC Syst Biol"},{"issue":"12","key":"813_CR19","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btq186","volume":"26","author":"W Wang","year":"2010","unstructured":"Wang W (2010) TEAM: efficient two-locus epistasis tests in human genome-wide association study. Bioinformatics 26(12):i217","journal-title":"Bioinformatics"},{"key":"813_CR20","unstructured":"Moore JH, Hahn LW, Ritchie MD, Thornton TA, White BC (2002) Application of genetic algorithms to the discovery of complex genetic models for simulation studies in human genetics. In: Langdon WB, et al., editors. Proceedings of the Genetic and Evolutionary Computation Conference. Morgan Kaufmann Publishers; San Francisco"},{"issue":"1","key":"813_CR21","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.asoc.2003.08.003","volume":"4","author":"JH Moore","year":"2004","unstructured":"Moore JH, Hahn LW, Ritchie MD et al (2004) Routine discovery of complex genetic models using genetic algorithms. Appl Soft Comput 4(1):79\u201386","journal-title":"Appl Soft Comput"},{"key":"813_CR22","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1186\/s13040-017-0139-3","volume":"10","author":"JH Moore","year":"2017","unstructured":"Moore JH, Andrews PC, Olson RS, Carlson SE, Larock CR, Bulhoes MJ, Armentrout SL (2017) Grid-based stochastic search for hierarchical gene\u2013gene interactions in population-based genetic studies of common human diseases. BioData Mining 10:19. https:\/\/doi.org\/10.1186\/s13040-017-0139-3","journal-title":"BioData Mining"},{"issue":"1","key":"813_CR23","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1186\/1756-0500-3-117","volume":"3","author":"Y Wang","year":"2010","unstructured":"Wang Y, Liu X, Robbins K et al (2010) AntEpiSeeker: detecting epistatic interactions for case\u2013control studies using a two-stage ant colony optimization algorithm. BMC Res Notes 3(1):117","journal-title":"BMC Res Notes"},{"issue":"3","key":"813_CR24","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s13258-012-0003-2","volume":"34","author":"J Shang","year":"2012","unstructured":"Shang J, Zhang J, Lei X, Zhang Y, Chen B (2012) Incorporating heuristic information into ant colony optimization for epistasis detection. Genes Genom 34(3):321\u2013327","journal-title":"Genes Genom"},{"key":"813_CR25","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1186\/s13040-017-0143-7","volume":"10","author":"Y Sun","year":"2017","unstructured":"Sun Y, Shang J, Liu JX, Li S, Zheng CH (2017) epiACO\u2014a method for identifying epistasis based on ant Colony optimization algorithm. BioData Mining 10:23. https:\/\/doi.org\/10.1186\/s13040-017-0143-7","journal-title":"BioData Mining"},{"key":"813_CR26","doi-asserted-by":"publisher","DOI":"10.1109\/TCBB.2018.2879673","author":"Y Sun","year":"2019","unstructured":"Sun Y, Wang X, Shang J, Liu J, Zheng C, Lei X (2019) Introducing heuristic information into ant colony optimization algorithm for identifying epistasis. IEEE\/ACM Trans Comput Biol Bioinform. https:\/\/doi.org\/10.1109\/TCBB.2018.2879673","journal-title":"IEEE\/ACM Trans Comput Biol Bioinform"},{"issue":"1","key":"813_CR27","doi-asserted-by":"publisher","first-page":"12869","DOI":"10.1038\/s41598-017-12773-x","volume":"7","author":"CH Yang","year":"2017","unstructured":"Yang CH, Chuang LY, Lin YD (2017) Multi-objective differential evolution-based multifactor dimensionality reduction for detecting gene\u2013gene interactions. Sci Rep 7(1):12869. https:\/\/doi.org\/10.1038\/s41598-017-12773-x","journal-title":"Sci Rep"},{"issue":"3","key":"813_CR28","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1109\/TNB.2018.2844342","volume":"17","author":"CH Yang","year":"2018","unstructured":"Yang CH, Kao YK, Chuang LY, Lin YD (2018) Catfish taguchi-based binary differential evolution algorithm for analysing single nucleotide polymorphism interactions in chronic dialysis. IEEE Trans Nanobiosci 17(3):291\u2013299","journal-title":"IEEE Trans Nanobiosci"},{"key":"813_CR29","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1038\/hdy.2014.4","volume":"112","author":"M Aflakparast","year":"2014","unstructured":"Aflakparast M et al (2014) Cuckoo search epitasis: a new method for exploring significant genetic interactions. Heredity 112:666\u2013674","journal-title":"Heredity"},{"issue":"3","key":"813_CR30","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0150669","volume":"11","author":"S Tuo","year":"2016","unstructured":"Tuo S, Zhang J, Yuan X et al (2016) FHSA-SED: two-locus model detection for genome-wide association study with harmony search algorithm. PLoS\u00a0One 11(3):e0150669","journal-title":"PLoS\u00a0One"},{"key":"813_CR31","doi-asserted-by":"publisher","first-page":"11529","DOI":"10.1038\/s41598-017-11064-9","volume":"7","author":"S Tuo","year":"2017","unstructured":"Tuo S, Zhang J, Yuan X, He Z, Liu Y, Liu Z (2017) Niche harmony search algorithm for detecting complex disease associated high-order SNP combinations. Sci Rep 7:11529","journal-title":"Sci Rep"},{"key":"813_CR32","doi-asserted-by":"publisher","first-page":"4389","DOI":"10.1093\/bioinformatics\/btaa215","volume":"36","author":"T Shouheng","year":"2020","unstructured":"Shouheng T, Haiyan L, Hao C (2020) Multipopulation harmony search algorithm for the detection of high-order SNP interactions. Bioinformatics 36:4389\u20134398. https:\/\/doi.org\/10.1093\/bioinformatics\/btaa215","journal-title":"Bioinformatics"},{"key":"813_CR33","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1186\/s12864-015-2217-6","volume":"16","author":"J Wang","year":"2015","unstructured":"Wang J, Joshi T, Valliyodan B, Shi H, Liang Y, Nguyen HT et al (2015) A Bayesian model for detection of high-order interactions among genetic variants in genome-wide association studies. BMC Genomics 16:1011. https:\/\/doi.org\/10.1186\/s12864-015-2217-6","journal-title":"BMC Genomics"},{"issue":"1","key":"813_CR34","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1186\/s12859-019-3022-z","volume":"20","author":"Y Guo","year":"2019","unstructured":"Guo Y, Zhong Z, Yang C, Hu J, Jiang Y, Liang Z et al (2019) Epi-GTBN: an approach of epistasis mining based on genetic Tabu algorithm and Bayesian network. BMC Bioinform 20(1):444. https:\/\/doi.org\/10.1186\/s12859-019-3022-z","journal-title":"BMC Bioinform"},{"key":"813_CR35","unstructured":"Visweswaran S, Wong AKI, Barmada MM (2009) A Bayesian method for identifying genetic interactions[C]. AMIA Ann Sympos Proc Am Med Inform Assoc: 673"},{"issue":"8","key":"813_CR36","doi-asserted-by":"publisher","first-page":"2267","DOI":"10.3390\/ijms19082267","volume":"19","author":"X Cao","year":"2018","unstructured":"Cao X, Yu G, Liu J, Jia L, Wang J (2018) ClusterMI: detecting high-Order SNP interactions based on clustering and mutual information. Int J Mol Sci 19(8):2267","journal-title":"Int J Mol Sci"},{"key":"813_CR37","doi-asserted-by":"publisher","first-page":"634","DOI":"10.1093\/bioinformatics\/btu702","volume":"31","author":"PJ Jing","year":"2015","unstructured":"Jing PJ, Shen HB (2015) MACOED: a multi-objective ant colony optimization algorithm for SNP epistasis detection in genome-wide association studies. Bioinformatics 31:634\u2013641. https:\/\/doi.org\/10.1093\/bioinformatics\/btu702","journal-title":"Bioinformatics"},{"issue":"7","key":"813_CR38","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pgen.1006869","volume":"13","author":"L Crawford","year":"2017","unstructured":"Crawford L, Zeng P, Mukherjee S, Zhou X (2017) Detecting epistasis with the marginal epistasis test in genetic mapping studies of quantitative traits. PLoS Genet 13(7):e1006869. https:\/\/doi.org\/10.1371\/journal.pgen.1006869","journal-title":"PLoS Genet"},{"issue":"2","key":"813_CR39","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1093\/bib\/bbv038","volume":"17","author":"D Gola","year":"2016","unstructured":"Gola D, Mahachie John JM, van Steen K, K\u00f6nig IR (2016) A roadmap to multifactor dimensionality reduction methods. Brief Bioinform 17(2):293\u2013308. https:\/\/doi.org\/10.1093\/bib\/bbv038","journal-title":"Brief Bioinform"},{"key":"813_CR40","doi-asserted-by":"publisher","first-page":"4578983","DOI":"10.1155\/2019\/4578983","volume":"2019","author":"H Kim","year":"2019","unstructured":"Kim H, Jeong HB, Jung HY, Park T, Park M (2019) Multivariate cluster-based multifactor dimensionality reduction to identify genetic interactions for multiple quantitative phenotypes. Biomed Res Int 2019:4578983. https:\/\/doi.org\/10.1155\/2019\/4578983","journal-title":"Biomed Res Int"},{"issue":"3","key":"813_CR41","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1109\/TEVC.2015.2458037","volume":"20","author":"A Gupta","year":"2016","unstructured":"Gupta A, Ong YS, Feng L (2016) Multifactorial evolution: towardstoward evolutionary multitasking. IEEE Trans Evol Comput 20(3):343\u2013357","journal-title":"IEEE Trans Evol Comput"},{"key":"813_CR42","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2020.3043509","author":"ZD Tang","year":"2021","unstructured":"Tang ZD, Gong MG et al (2021) A multifactorial optimization framework based on adaptive intertask coordinate system. IEEE Trans Cybernet. https:\/\/doi.org\/10.1109\/TCYB.2020.3043509","journal-title":"IEEE Trans Cybernet"},{"key":"813_CR43","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2021.107713","volume":"111","author":"JZ Li","year":"2021","unstructured":"Li JZ, Li H et al (2021) Multi-fidelity evolutionary multitasking optimization for hyperspectral endmember extraction. Appl Soft Comput 111:107713","journal-title":"Appl Soft Comput"},{"issue":"6","key":"813_CR44","doi-asserted-by":"publisher","first-page":"3143","DOI":"10.1109\/TCYB.2019.2962865","volume":"51","author":"L Feng","year":"2019","unstructured":"Feng L et al (2019) Explicit evolutionary multitasking for combinatorial optimization: a case study on capacitated vehicle routing problem. IEEE Trans Cybernet 51(6):3143\u20133156. https:\/\/doi.org\/10.1109\/TCYB.2019.2962865","journal-title":"IEEE Trans Cybernet"},{"key":"813_CR45","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1016\/j.ins.2021.05.005","volume":"570","author":"E Osaba","year":"2021","unstructured":"Osaba E, Del Ser J, Martinez AD, Lobo JL, Herrera F (2021) AT-MFCGA: an adaptive transfer-guided multifactorial cellular genetic algorithm for evolutionary multitasking. Inf Sci 570:577\u2013598","journal-title":"Inf Sci"},{"key":"813_CR46","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/j.ins.2021.06.056","volume":"576","author":"NT Tam","year":"2021","unstructured":"Tam NT, Dat VT, Lan PN, Binh HTT, Vinh LT, Swami A (2021) Multifactorial evolutionary optimization to maximize lifetime of wireless sensor network. Inf Sci 576:355\u2013373","journal-title":"Inf Sci"},{"key":"813_CR47","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/s40747-020-00184-x","volume":"7","author":"X Xu","year":"2021","unstructured":"Xu X, Yin G, Wang C (2021) Multitasking scheduling with batch distribution and due date assignment. Complex Intell Syst 7:191\u2013202. https:\/\/doi.org\/10.1007\/s40747-020-00184-x","journal-title":"Complex Intell Syst"},{"key":"813_CR48","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-021-00624-2","author":"Q Dang","year":"2022","unstructured":"Dang Q, Gao W, Gong M (2022) Multi-objective multitasking optimization assisted by multidirectional prediction method. Complex Intell Syst. https:\/\/doi.org\/10.1007\/s40747-021-00624-2","journal-title":"Complex Intell Syst"},{"key":"813_CR49","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-021-00568-7","author":"Y Zhao","year":"2021","unstructured":"Zhao Y, Ye S, Chen X et al (2021) Polynomial Response Surface based on basis function selection by multitask optimization and ensemble modeling. Complex Intell Syst. https:\/\/doi.org\/10.1007\/s40747-021-00568-7","journal-title":"Complex Intell Syst"},{"key":"813_CR50","volume-title":"Learning bayesian networks","author":"RE Neapolitan","year":"2004","unstructured":"Neapolitan RE (2004) Learning bayesian networks. Prentice Hall, Upper Saddle River"},{"key":"813_CR51","doi-asserted-by":"publisher","first-page":"2829","DOI":"10.1093\/bioinformatics\/btx339","volume":"18","author":"X Li","year":"2017","unstructured":"Li X (2017) A fast and exhaustive method for heterogeneity and epistasis analysis based on multi-objective optimization. Bioinformatics 18:2829\u20132836. https:\/\/doi.org\/10.1093\/bioinformatics\/btx339","journal-title":"Bioinformatics"},{"key":"813_CR52","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1186\/1471-2105-9-238","volume":"9","author":"WS Bush","year":"2008","unstructured":"Bush WS, Edwards TL, Dudek SM, McKinney BA, Ritchie MD (2008) Alternative contingency table measures improve the power and detection of multifactor dimensionality reduction. BMC Bioinform 9:238. https:\/\/doi.org\/10.1186\/1471-2105-9-238","journal-title":"BMC Bioinform"},{"key":"813_CR53","first-page":"175","volume":"20A","author":"J Neyman","year":"1928","unstructured":"Neyman J, Pearson ES (1928) On the use and interpretation of certain test criteria for purposes of statistical inference: part 1. Biometrika 20A:175\u2013240","journal-title":"Biometrika"},{"issue":"2","key":"813_CR54","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1177\/003754970107600201","volume":"76","author":"ZW Geem","year":"2001","unstructured":"Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. SIMULATION 76(2):60\u201368","journal-title":"SIMULATION"},{"issue":"1","key":"813_CR55","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1109\/TSMCB.2010.2046035","volume":"41","author":"S Das","year":"2011","unstructured":"Das S, Mukhopadhyay A, Roy A, Abraham A, Panigrahi BK (2011) Exploratory power of the harmony search algorithm: analysis and improvements for global numerical optimization. Syst Man Cybernet Part B 41(1):89\u2013106","journal-title":"Syst Man Cybernet Part B"},{"issue":"9","key":"813_CR56","doi-asserted-by":"publisher","first-page":"1421","DOI":"10.3390\/math8091421","volume":"8","author":"S Tuo","year":"2020","unstructured":"Tuo S, Geem ZW, Yoon JH (2020) A new method for analyzing the performance of the harmony search algorithm. Mathematics 8(9):1421. https:\/\/doi.org\/10.3390\/math8091421","journal-title":"Mathematics"},{"key":"813_CR57","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.swevo.2019.03.012","volume":"48","author":"TH Zhang","year":"2019","unstructured":"Zhang TH, Geem ZW (2019) Review of harmony search with respect to algorithm structure. Swarm Evol Comput 48:31\u201343","journal-title":"Swarm Evol Comput"},{"key":"813_CR58","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1093\/genetics\/152.3.821","volume":"152","author":"Jf Crow","year":"1999","unstructured":"Crow Jf (1999) Hardy. Weinberg and language impediments. Genetics 152:821\u2013825","journal-title":"Genetics"},{"key":"813_CR59","unstructured":"Hoey J (2012) The two-way likelihood ratio (G) test and comparison to two-way chi squared test. arXiv preprint\narXiv:1206.4881"},{"key":"813_CR60","doi-asserted-by":"publisher","DOI":"10.1186\/1756-0381-4-21","author":"Himmelstein","year":"2011","unstructured":"Himmelstein et al (2011) Evolving hard problems: generating human genetics datasets with a complex etiology. BioData Min. https:\/\/doi.org\/10.1186\/1756-0381-4-21","journal-title":"BioData Min"},{"key":"813_CR61","doi-asserted-by":"publisher","DOI":"10.1186\/s12859-020-3456-3","author":"C Ponte-Fern\u00e1ndez","year":"2020","unstructured":"Ponte-Fern\u00e1ndez C, Gonz\u00e1lez-Dom\u00ednguez J, Carvajal-Rodr\u00edguez A et al (2020) Toxo: a library for calculating penetrance tables of high-order epistasis models. BMC Bioinform. https:\/\/doi.org\/10.1186\/s12859-020-3456-3","journal-title":"BMC Bioinform"},{"key":"813_CR62","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1756-0381-5-16","volume":"5","author":"RJ Urbanowicz","year":"2012","unstructured":"Urbanowicz RJ, Kiralis J, Sinnott-Armstrong NA, Heberling T, Fisher JM, Moore JH (2012) GAMETES: a fast, direct algorithm for generating pure, strict, epistatic models with random architectures. BioData mining 5:1\u201314","journal-title":"BioData mining"},{"key":"813_CR63","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1126\/science.1109557","volume":"308","author":"RJ Klein","year":"2005","unstructured":"Klein RJ et al (2005) Complement factor H polymorphism in age-related macular degeneration. Science 308:385\u2013389","journal-title":"Science"},{"issue":"1","key":"813_CR64","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1093\/bioinformatics\/btr603","volume":"28","author":"M Xie","year":"2012","unstructured":"Xie M, Li J, Jiang T (2012) Detecting genome-wide epistasis based on the clustering of relatively frequent items. Bioinformatics 28(1):5\u201312. https:\/\/doi.org\/10.1093\/bioinformatics\/btr603","journal-title":"Bioinformatics"},{"key":"813_CR65","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/j.bone.2018.04.013","volume":"112","author":"M Barba","year":"2018","unstructured":"Barba M, Pietro LD, Massimi L et al (2018) BBS9 gene in nonsyndromic craniosynostosis: Role of the primary cilium in the aberrant ossification of the suture osteogenic niche. Bone 112:58\u201370","journal-title":"Bone"},{"issue":"1","key":"813_CR66","first-page":"19","volume":"2","author":"L Mirabello","year":"2011","unstructured":"Mirabello L, Richards EG, Duong LM et al (2011) Telomere length and variation in telomere biology genes in individuals with osteosarcoma. Int J Mol Epidemiol Genet 2(1):19\u201329","journal-title":"Int J Mol Epidemiol Genet"},{"key":"813_CR67","doi-asserted-by":"crossref","unstructured":"(2003) Cytoscape: a software environment for integrated models of biomolecular interaction networks. Genome Res 13(11):2498\u2013504. https:\/\/cytoscape.org\/","DOI":"10.1101\/gr.1239303"},{"issue":"Suppl 1","key":"813_CR68","doi-asserted-by":"publisher","first-page":"S65","DOI":"10.1186\/1471-2105-10-S1-S65","volume":"10","author":"R Jiang","year":"2009","unstructured":"Jiang R, Tang W, Wu X, Fu W (2009) A random forest approach to the detection of epistatic interactions in case\u2013control studies. BMC Bioinform 10(Suppl 1):S65. https:\/\/doi.org\/10.1186\/1471-2105-10-S1-S65","journal-title":"BMC Bioinform"},{"key":"813_CR69","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1038\/s41576-019-0127-1","volume":"20","author":"V Tam","year":"2019","unstructured":"Tam V, Patel N, Turcotte M et al (2019) Benefits and limitations of genome-wide association studies. Nat Rev Genet 20:467\u2013484. https:\/\/doi.org\/10.1038\/s41576-019-0127-1","journal-title":"Nat Rev Genet"},{"issue":"1","key":"813_CR70","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s13198-019-00941-3","volume":"11","author":"PS Kumar","year":"2020","unstructured":"Kumar PS (2020) Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set. Int J Syst Assur Eng Manag 11(1):189\u2013222. https:\/\/doi.org\/10.1007\/s13198-019-00941-3","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"4","key":"813_CR71","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1007\/s13198-019-00794-w","volume":"10","author":"PS Kumar","year":"2019","unstructured":"Kumar PS (2019) Intuitionistic fuzzy solid assignment problems: a software-based approach. \nInt J Syst Assur Eng Manag 10(4):661\u2013675. https:\/\/doi.org\/10.1007\/s13198-019-00794-w","journal-title":"Int J Syst Assur Eng Manag"},{"key":"813_CR72","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-5225-8458-2.ch009","author":"PS Kumar","year":"2020","unstructured":"Kumar PS (2020) The PSK method for solving fully intuitionistic fuzzy assignment problems with some software tools. Adv Bus Strategy Compet Adv. https:\/\/doi.org\/10.4018\/978-1-5225-8458-2.ch009","journal-title":"Adv Bus Strategy Compet Adv"},{"key":"813_CR73","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-7998-5077-9.ch015","author":"PS Kumar","year":"2021","unstructured":"Kumar PS (2021) Finding the solution of balanced and unbalanced intuitionistic fuzzy transportation problems by using different methods with some software packages. Handbook Res Appl AI Int Bus Market Appl. https:\/\/doi.org\/10.4018\/978-1-7998-5077-9.ch015","journal-title":"Handbook Res Appl AI Int Bus Market Appl"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-022-00813-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-022-00813-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-022-00813-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T18:57:12Z","timestamp":1677092232000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-022-00813-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,27]]},"references-count":73,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["813"],"URL":"https:\/\/doi.org\/10.1007\/s40747-022-00813-7","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"type":"print","value":"2199-4536"},{"type":"electronic","value":"2198-6053"}],"subject":[],"published":{"date-parts":[[2022,7,27]]},"assertion":[{"value":"12 January 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 June 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 July 2022","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 they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}