{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T12:00:46Z","timestamp":1784808046791,"version":"3.55.0"},"reference-count":83,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T00:00:00Z","timestamp":1740441600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T00:00:00Z","timestamp":1740441600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research, India","doi-asserted-by":"publisher","award":["09\/1152(0024)\/2020-EMR-1"],"award-info":[{"award-number":["09\/1152(0024)\/2020-EMR-1"]}],"id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cluster Comput"],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1007\/s10586-024-04931-4","type":"journal-article","created":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T14:02:31Z","timestamp":1740492151000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Enhanced zebra optimization algorithm for reliability redundancy allocation and engineering optimization problems"],"prefix":"10.1007","volume":"28","author":[{"given":"Parul","family":"Punia","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amit","family":"Raj","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pawan","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,2,25]]},"reference":[{"issue":"1","key":"4931_CR1","first-page":"537","volume":"71","author":"H Marouani","year":"2022","unstructured":"Marouani, H., Al-Mutiri, O.: Optimization of reliability-redundancy allocation problems: a review of the evolutionary algorithms. Comput. Mater. Contin. 71(1), 537\u2013571 (2022)","journal-title":"Comput. Mater. Contin."},{"issue":"04","key":"4931_CR2","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1080\/03052150500465541","volume":"38","author":"GS Liu","year":"2006","unstructured":"Liu, G.S.: A combination method for reliability-redundancy optimization. Eng. Optim. 38(04), 485\u2013499 (2006)","journal-title":"Eng. Optim."},{"issue":"2","key":"4931_CR3","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1109\/24.877336","volume":"49","author":"W Kuo","year":"2000","unstructured":"Kuo, W., Prasad, V.R.: An annotated overview of system-reliability optimization. IEEE Trans. Reliab. 49(2), 176\u2013187 (2000)","journal-title":"IEEE Trans. Reliab."},{"issue":"3","key":"4931_CR4","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1109\/TR.1977.5220100","volume":"26","author":"FA Tillman","year":"1977","unstructured":"Tillman, F.A., Hwang, C.L., Kuo, W.: Optimization techniques for system reliability with redundancy\u2014a review. IEEE Trans. Reliab. 26(3), 148\u2013155 (1977)","journal-title":"IEEE Trans. Reliab."},{"key":"4931_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/s11518-024-5608-x","author":"P Punia","year":"2024","unstructured":"Punia, P., Raj, A., Kumar, P.: An enhanced beluga whale optimization algorithm for engineering optimization problems. J. Syst. Sci. Syst. Eng. (2024). https:\/\/doi.org\/10.1007\/s11518-024-5608-x","journal-title":"J. Syst. Sci. Syst. Eng."},{"issue":"6","key":"4931_CR6","doi-asserted-by":"publisher","first-page":"556","DOI":"10.1080\/02533839.2022.2078418","volume":"45","author":"J Gong","year":"2022","unstructured":"Gong, J., Karimzadeh Parizi, M.: GWMA: the parallel implementation of woodpecker mating algorithm on the GPU. J. Chinese Inst. Eng. 45(6), 556\u2013568 (2022)","journal-title":"J. Chinese Inst. Eng."},{"key":"4931_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/s13198-024-02386-9","author":"A Raj","year":"2024","unstructured":"Raj, A., Punia, P., Kumar, P.: A novel hybrid pelican-particle swarm optimization algorithm (HPPSO) for global optimization problem. Int. J. Syst. Assur. Eng. Manage. (2024). https:\/\/doi.org\/10.1007\/s13198-024-02386-9","journal-title":"Int. J. Syst. Assur. Eng. Manage."},{"key":"4931_CR8","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/3927.001.0001","volume-title":"An Introduction to Genetic Algorithms","author":"M Mitchell","year":"1998","unstructured":"Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press, Cambridge (1998). https:\/\/doi.org\/10.7551\/mitpress\/3927.001.0001"},{"issue":"2","key":"4931_CR9","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1109\/4235.771163","volume":"3","author":"X Yao","year":"1999","unstructured":"Yao, X., Liu, Y., Lin, G.: Evolutionary programming made faster. IEEE Trans. Evol. Comput. 3(2), 82\u2013102 (1999)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"6","key":"4931_CR10","doi-asserted-by":"publisher","first-page":"702","DOI":"10.1109\/TEVC.2008.919004","volume":"12","author":"D Simon","year":"2008","unstructured":"Simon, D.: Biogeography-based optimization. IEEE Trans. Evol. Comput. 12(6), 702\u2013713 (2008)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"4931_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.swevo.2016.01.004","volume":"27","author":"S Das","year":"2016","unstructured":"Das, S., Mullick, S.S., Suganthan, P.N.: Recent advances in differential evolution-an updated survey. Swarm Evol. Comput. 27, 1\u201330 (2016)","journal-title":"Swarm Evol. Comput."},{"key":"4931_CR12","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s00366-011-0241-y","volume":"29","author":"AH Gandomi","year":"2016","unstructured":"Gandomi, A.H., Yang, X.S., Alavi, A.H.: Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng. Comput. 29, 17\u201335 (2016)","journal-title":"Eng. Comput."},{"issue":"1","key":"4931_CR13","first-page":"931256","volume":"2015","author":"Y Zhang","year":"2015","unstructured":"Zhang, Y., Wang, S., Ji, G.: A comprehensive survey on particle swarm optimization algorithm and its applications. Math. Probl. Eng. 2015(1), 931256 (2015)","journal-title":"Math. Probl. Eng."},{"issue":"5","key":"4931_CR14","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1108\/02644401211235834","volume":"29","author":"XS Yang","year":"2012","unstructured":"Yang, X.S., Hossein Gandomi, A.: Bat algorithm: a novel approach for global engineering optimization. Eng. Comput. 29(5), 464\u2013483 (2012)","journal-title":"Eng. Comput."},{"issue":"4","key":"4931_CR15","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1109\/MCI.2006.329691","volume":"1","author":"M Dorigo","year":"2006","unstructured":"Dorigo, M., Birattari, M., Stutzle, T.: Ant colony optimization. IEEE Comput. Intell. Mag. 1(4), 28\u201339 (2006)","journal-title":"IEEE Comput. Intell. Mag."},{"key":"4931_CR16","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","volume":"95","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili, S., Lewis, A.: The whale optimization algorithm. Adv. Eng. Software 95, 51\u201367 (2016)","journal-title":"Adv. Eng. Software"},{"issue":"04","key":"4931_CR17","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1142\/S0219622022500675","volume":"22","author":"J Zhang","year":"2023","unstructured":"Zhang, J., Li, H., Parizi, M.K.: HWMWOA: a hybrid WMA-WOA algorithm with adaptive cauchy mutation for global optimization and data classification. Int. J. Inf. Technol. Decis. Mak. 22(04), 1195\u20131252 (2023)","journal-title":"Int. J. Inf. Technol. Decis. Mak."},{"issue":"4","key":"4931_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10586-023-04221-5","volume":"27","author":"B Abdollahzadeh","year":"2024","unstructured":"Abdollahzadeh, B., Khodadadi, N., Barshandeh, S., Trojovsk\u00fd, P., Gharehchopogh, F.S., El-kenawy, E.S.M., Mirjalili, S.: Puma optimizer (PO): a novel metaheuristic optimization algorithm and its application in machine learning. Cluster Comput. 27(4), 1\u201349 (2024)","journal-title":"Cluster Comput."},{"key":"4931_CR19","doi-asserted-by":"publisher","first-page":"736","DOI":"10.1016\/j.asoc.2017.10.040","volume":"62","author":"S Ghambari","year":"2018","unstructured":"Ghambari, S., Rahati, A.: An improved artificial bee colony algorithm and its application to reliability optimization problems. Appl. Soft Comput. 62, 736\u2013767 (2018)","journal-title":"Appl. Soft Comput."},{"key":"4931_CR20","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1016\/j.future.2019.02.028","volume":"97","author":"AA Heidari","year":"2019","unstructured":"Heidari, A.A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., Chen, H.: Harris hawks optimization: algorithm and applications. Future Gener. Comput. Syst. 97, 849\u2013872 (2019)","journal-title":"Future Gener. Comput. Syst."},{"issue":"1","key":"4931_CR21","doi-asserted-by":"publisher","first-page":"31","DOI":"10.18280\/rces.090103","volume":"9","author":"A Khare","year":"2022","unstructured":"Khare, A., Kakandikar, G.M., Kulkarni, O.K.: An insight review on jellyfish optimization algorithm and its application in engineering. Rev. Comput. Stud. 9(1), 31\u201340 (2022)","journal-title":"Rev. Comput. Stud."},{"issue":"5","key":"4931_CR22","doi-asserted-by":"publisher","first-page":"5269","DOI":"10.3934\/mbe.2022247","volume":"19","author":"D Chen","year":"2022","unstructured":"Chen, D., Liu, J., Yao, C., Zhang, Z., Du, X.: Multi-strategy improved salp swarm algorithm and its application in reliability optimization. Math. Biosci. Eng. 19(5), 5269\u20135292 (2022)","journal-title":"Math. Biosci. Eng."},{"key":"4931_CR23","doi-asserted-by":"publisher","first-page":"103282","DOI":"10.1016\/j.advengsoft.2022.103282","volume":"174","author":"B Abdollahzadeh","year":"2022","unstructured":"Abdollahzadeh, B., Gharehchopogh, F.S., Khodadadi, N., Mirjalili, S.: Mountain gazelle optimizer: a new nature-inspired metaheuristic algorithm for global optimization problems. Adv. Eng. Software. 174, 103282 (2022)","journal-title":"Adv. Eng. Software."},{"issue":"3","key":"4931_CR24","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.cad.2010.12.015","volume":"43","author":"RV Rao","year":"2011","unstructured":"Rao, R.V., Savsani, V.J., Vakharia, D.P.: Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43(3), 303\u2013315 (2011)","journal-title":"Comput. Aided Des."},{"issue":"5","key":"4931_CR25","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.3390\/math11051273","volume":"11","author":"I Faridmehr","year":"2023","unstructured":"Faridmehr, I., Nehdi, M.L., Davoudkhani, I.F., Poolad, A.: Mountaineering team-based optimization: a novel human-based metaheuristic algorithm. Mathematics 11(5), 1273 (2023)","journal-title":"Mathematics"},{"issue":"10","key":"4931_CR26","doi-asserted-by":"publisher","first-page":"107212","DOI":"10.1016\/j.compbiomed.2023.107212","volume":"164","author":"M Zhong","year":"2023","unstructured":"Zhong, M., Wen, J., Ma, J., Cui, H., Zhang, Q., Parizi, M.K.: A hierarchical multi-leadership sine cosine algorithm to dissolving global optimization and data classification: the COVID-19 case study. Comput. Biol. Med. 164(10), 107212 (2023)","journal-title":"Comput. Biol. Med."},{"key":"4931_CR27","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.knosys.2015.12.022","volume":"96","author":"S Mirjalili","year":"2016","unstructured":"Mirjalili, S.: SCA: a sine cosine algorithm for solving optimization problems. Knowl.-Based Syst. 96, 120\u2013133 (2016)","journal-title":"Knowl.-Based Syst."},{"issue":"02","key":"4931_CR28","doi-asserted-by":"publisher","first-page":"775","DOI":"10.1142\/S0219622021500176","volume":"20","author":"MK Parizi","year":"2021","unstructured":"Parizi, M.K., Keynia, F., Bardsiri, A.K.: HSCWMA: a new hybrid SCA-WMA algorithm for solving optimization problems. Int. J. Inf. Technol. Decis. Making. 20(02), 775\u2013808 (2021)","journal-title":"Int. J. Inf. Technol. Decis. Making."},{"key":"4931_CR29","doi-asserted-by":"crossref","unstructured":"Tan, Y., Zhu, Y.: Fireworks algorithm for optimization. In: Advances in Swarm Intelligence: First International Conference. ICSI, pp. 355\u2013364. Springer, Berlin Heidelberg (2010)","DOI":"10.1007\/978-3-642-13495-1_44"},{"key":"4931_CR30","doi-asserted-by":"publisher","first-page":"5011","DOI":"10.1007\/s00521-020-05296-6","volume":"33","author":"MA Al-Betar","year":"2021","unstructured":"Al-Betar, M.A., Alyasseri, Z.A.A., Awadallah, M.A., Abu Doush, I.: Coronavirus herd immunity optimizer (CHIO). Neural Comput. Appl. 33, 5011\u20135042 (2021)","journal-title":"Neural Comput. Appl."},{"key":"4931_CR31","doi-asserted-by":"publisher","first-page":"107408","DOI":"10.1016\/j.cie.2021.107408","volume":"158","author":"B Abdollahzadeh","year":"2021","unstructured":"Abdollahzadeh, B., Gharehchopogh, F.S., Mirjalili, S.: African vultures optimization algorithm: a new nature-inspired metaheuristic algorithm for global optimization problems. Comput. Ind. Eng. 158, 107408 (2021)","journal-title":"Comput. Ind. Eng."},{"issue":"1","key":"4931_CR32","first-page":"137","volume":"11","author":"M Karimzadeh Parizi","year":"2020","unstructured":"Karimzadeh Parizi, M., Keynia, F., Khatibi Bardsiri, A.: Woodpecker mating algorithm (WMA): a nature-inspired algorithm for solving optimization problems. Int. J. Nonlinear Anal. Appl. 11(1), 137\u2013157 (2020)","journal-title":"Int. J. Nonlinear Anal. Appl."},{"issue":"10","key":"4931_CR33","doi-asserted-by":"publisher","first-page":"5887","DOI":"10.1002\/int.22535","volume":"36","author":"B Abdollahzadeh","year":"2021","unstructured":"Abdollahzadeh, B., Soleimanian Gharehchopogh, F., Mirjalili, S.: Artificial gorilla troops optimizer: a new nature-inspired metaheuristic algorithm for global optimization problems. Int. J. Intell. Syst. 36(10), 5887\u20135958 (2021)","journal-title":"Int. J. Intell. Syst."},{"issue":"1","key":"4931_CR34","doi-asserted-by":"publisher","first-page":"20099","DOI":"10.1038\/s41598-024-70497-1","volume":"14","author":"Z Benmamoun","year":"2024","unstructured":"Benmamoun, Z., Khlie, K., Bektemyssova, G., Dehghani, M., Gherabi, Y.: Bobcat optimization algorithm: an effective bio-inspired metaheuristic algorithm for solving supply chain optimization problems. Sci. Rep. 14(1), 20099 (2024)","journal-title":"Sci. Rep."},{"issue":"2","key":"4931_CR35","first-page":"221","volume":"4","author":"M Karimzadeh Parizi","year":"2021","unstructured":"Karimzadeh Parizi, M., Keynia, F., Khatibi Bardsiri, A.: Woodpecker mating algorithm for optimal economic load dispatch in a power system with conventional generators. Int. J. Indus. Electron. Control Opt. 4(2), 221\u2013234 (2021)","journal-title":"Int. J. Indus. Electron. Control Opt."},{"issue":"1","key":"4931_CR36","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1109\/4235.585893","volume":"1","author":"DH Wolpert","year":"1997","unstructured":"Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67\u201382 (1997)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"4931_CR37","doi-asserted-by":"publisher","first-page":"13075","DOI":"10.1007\/s13369-024-08952-4","volume":"49","author":"P Punia","year":"2024","unstructured":"Punia, P., Raj, A., Kumar, P.: ILO: an improved Lemur optimizer for global optimization. Arab. J. Sci. Eng. 49, 13075\u201313098 (2024)","journal-title":"Arab. J. Sci. Eng."},{"issue":"7","key":"4931_CR38","doi-asserted-by":"publisher","first-page":"7595","DOI":"10.1007\/s12652-020-02481-2","volume":"12","author":"TK Sharma","year":"2021","unstructured":"Sharma, T.K.: Enhanced butterfly optimization algorithm for reliability optimization problems. J. Ambient Intell. Hum. Comput. 12(7), 7595\u20137619 (2021)","journal-title":"J. Ambient Intell. Hum. Comput."},{"key":"4931_CR39","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1007\/s10845-014-0918-3","volume":"27","author":"K Yu","year":"2016","unstructured":"Yu, K., Wang, X., Wang, Z.: An improved teaching-learning-based optimization algorithm for numerical and engineering optimization problems. J. Intell. Manuf. 27, 831\u2013843 (2016)","journal-title":"J. Intell. Manuf."},{"issue":"4","key":"4931_CR40","doi-asserted-by":"publisher","first-page":"2811","DOI":"10.1007\/s10462-022-10218-0","volume":"56","author":"SK Sahoo","year":"2023","unstructured":"Sahoo, S.K., Saha, A.K., Nama, S., Masdari, M.: An improved moth flame optimization algorithm based on modified dynamic opposite learning strategy. Artif. Intell. Rev. 56(4), 2811\u20132869 (2023)","journal-title":"Artif. Intell. Rev."},{"issue":"1","key":"4931_CR41","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1016\/j.cie.2012.07.011","volume":"64","author":"E Valian","year":"2013","unstructured":"Valian, E., Tavakoli, S., Mohanna, S., Haghi, A.: Improved cuckoo search for reliability optimization problems. Comput. Ind. Eng. 64(1), 459\u2013468 (2013)","journal-title":"Comput. Ind. Eng."},{"key":"4931_CR42","doi-asserted-by":"publisher","first-page":"113122","DOI":"10.1016\/j.eswa.2019.113122","volume":"145","author":"M Tubishat","year":"2020","unstructured":"Tubishat, M., Idris, N., Shuib, L., Abushariah, M.A., Mirjalili, S.: Improved salp swarm algorithm based on opposition based learning and novel local search algorithm for feature selection. Expert Syst. Appl. 145, 113122 (2020)","journal-title":"Expert Syst. Appl."},{"issue":"2","key":"4931_CR43","doi-asserted-by":"publisher","first-page":"1653","DOI":"10.1007\/s00366-022-01746-y","volume":"39","author":"G Hu","year":"2023","unstructured":"Hu, G., Wang, J., Li, Y., Yang, M., Zheng, J.: An enhanced hybrid seagull optimization algorithm with its application in engineering optimization. Eng. Comput. 39(2), 1653\u20131696 (2023)","journal-title":"Eng. Comput."},{"issue":"1","key":"4931_CR44","first-page":"919","volume":"40","author":"M Karimzadeh Parizi","year":"2021","unstructured":"Karimzadeh Parizi, M., Keynia, F.: OWMA: An improved self-regulatory woodpecker mating algorithm using opposition-based learning and allocation of local memory for solving optimization problems. J. Intell. Fuzzy Syst. 40(1), 919\u2013946 (2021)","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"6","key":"4931_CR45","doi-asserted-by":"publisher","first-page":"5251","DOI":"10.1007\/s00366-021-01572-8","volume":"38","author":"T Kundu","year":"2022","unstructured":"Kundu, T., Garg, H.: A hybrid TLNNABC algorithm for reliability optimization and engineering design problems. Eng. Comput. 38(6), 5251\u20135295 (2022)","journal-title":"Eng. Comput."},{"issue":"5","key":"4931_CR46","first-page":"9277","volume":"40","author":"H Jia","year":"2021","unstructured":"Jia, H., Lang, C.: Salp swarm algorithm with crossover scheme and L\u00e9vy flight for global optimization. J. Intell. Fuzzy Syst. 40(5), 9277\u20139288 (2021)","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"1","key":"4931_CR47","first-page":"6385713","volume":"2021","author":"H Marouani","year":"2021","unstructured":"Marouani, H.: Optimization for the redundancy allocation problem of reliability using an improved particle swarm optimization algorithm. J. Optim. 2021(1), 6385713 (2021)","journal-title":"J. Optim."},{"key":"4931_CR48","doi-asserted-by":"publisher","first-page":"49445","DOI":"10.1109\/ACCESS.2022.3172789","volume":"10","author":"E Trojovsk\u00e1","year":"2022","unstructured":"Trojovsk\u00e1, E., Dehghani, M., Trojovsk\u00fd, P.: Zebra optimization algorithm: a new bio-inspired optimization algorithm for solving optimization algorithm. IEEE Access 10, 49445\u201349473 (2022)","journal-title":"IEEE Access"},{"key":"4931_CR49","doi-asserted-by":"publisher","first-page":"103731","DOI":"10.1016\/j.engappai.2020.103731","volume":"94","author":"EH Houssein","year":"2020","unstructured":"Houssein, E.H., Saad, M.R., Hashim, F.A., Shaban, H., Hassaballah, M.: L\u00e9vy flight distribution: a new metaheuristic algorithm for solving engineering optimization problems. Eng. Appl. Artif. Intell. 94, 103731 (2020)","journal-title":"Eng. Appl. Artif. Intell."},{"key":"4931_CR50","doi-asserted-by":"crossref","unstructured":"Tizhoosh, H. R.: Opposition-based learning: a new scheme for machine intelligence. In International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC\u201906), vol. 1, pp. 695-701 IEEE (2005)","DOI":"10.1109\/CIMCA.2005.1631345"},{"key":"4931_CR51","doi-asserted-by":"crossref","unstructured":"Wong, W. K., Ming, C. I.: A review on metaheuristic algorithms: recent trends, benchmarking and applications. In 2019 7th International Conference on Smart Computing & Communications (ICSCC), pp. 1-5. IEEE (2019)","DOI":"10.1109\/ICSCC.2019.8843624"},{"key":"4931_CR52","doi-asserted-by":"publisher","first-page":"100693","DOI":"10.1016\/j.swevo.2020.100693","volume":"56","author":"A Kumar","year":"2020","unstructured":"Kumar, A., Wu, G., Ali, M.Z., Mallipeddi, R., Suganthan, P.N., Das, S.: A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm Evol. Comput. 56, 100693 (2020)","journal-title":"Swarm Evol. Comput."},{"key":"4931_CR53","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.simpat.2013.12.013","volume":"42","author":"MA Ardakan","year":"2014","unstructured":"Ardakan, M.A., Hamadani, A.Z.: Reliability-redundancy allocation problem with cold-standby redundancy strategy. Simul. Pract. Theory 42, 107\u2013118 (2014)","journal-title":"Simul. Pract. Theory"},{"issue":"9","key":"4931_CR54","doi-asserted-by":"publisher","first-page":"3794","DOI":"10.1016\/j.eswa.2012.12.093","volume":"40","author":"LD Ardakan","year":"2013","unstructured":"Ardakan, L.D., Mariani, V.C., dos Santos Coelho, L.: Modified imperialist competitive algorithm based on attraction and repulsion concepts for reliability-redundancy optimization. Expert Syst. Appl. 40(9), 3794\u20133802 (2013)","journal-title":"Expert Syst. Appl."},{"issue":"4","key":"4931_CR55","doi-asserted-by":"publisher","first-page":"905","DOI":"10.1016\/0360-8352(96)00041-1","volume":"30","author":"T Yokota","year":"1996","unstructured":"Yokota, T., Gen, M., Li, Y.X.: Genetic algorithm for non-linear mixed integer programming problems and its applications. Comput. Ind. Eng. 30(4), 905\u2013917 (1996)","journal-title":"Comput. Ind. Eng."},{"issue":"1","key":"4931_CR56","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.isatra.2010.08.005","volume":"50","author":"P Wu","year":"2011","unstructured":"Wu, P., Gao, L., Zou, D., Li, S.: An improved particle swarm optimization algorithm for reliability problems. ISA Trans. 50(1), 71\u201381 (2011)","journal-title":"ISA Trans."},{"key":"4931_CR57","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.ins.2015.01.020","volume":"305","author":"HB Ouyang","year":"2015","unstructured":"Ouyang, H.B., Gao, L.Q., Li, S., Kong, X.Y.: Improved novel global harmony search with a new relaxation method for reliability optimization problems. Inf. Sci. 305, 14\u201355 (2015)","journal-title":"Inf. Sci."},{"issue":"9","key":"4931_CR58","doi-asserted-by":"publisher","first-page":"1008","DOI":"10.1016\/j.ress.2005.11.053","volume":"91","author":"M Gen","year":"2006","unstructured":"Gen, M., Yun, Y.: Soft computing approach for reliability optimization: state-of-the-art survey. Reliab. Eng. Syst. Saf. 91(9), 1008\u20131026 (2006)","journal-title":"Reliab. Eng. Syst. Saf."},{"issue":"2","key":"4931_CR59","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/j.cie.2009.11.003","volume":"58","author":"D Zou","year":"2010","unstructured":"Zou, D., Gao, L., Wu, J., Li, S., Li, Y.: A novel global harmony search algorithm for reliability problems. Comput. Ind. Eng. 58(2), 307\u2013316 (2010)","journal-title":"Comput. Ind. Eng."},{"issue":"11","key":"4931_CR60","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1080\/0305215X.2012.729055","volume":"45","author":"E Valian","year":"2013","unstructured":"Valian, E., Valian, E.: A cuckoo search algorithm by L\u00e9vy flights for solving reliability redundancy allocation problems. Eng. Optim. 45(11), 1273\u20131286 (2013)","journal-title":"Eng. Optim."},{"issue":"4","key":"4931_CR61","first-page":"1297","volume":"218","author":"YC Hsieh","year":"2011","unstructured":"Hsieh, Y.C., You, P.S.: An effective immune based two-phase approach for the optimal reliability-redundancy allocation problem. Appl. Math. Comput. 218(4), 1297\u20131307 (2011)","journal-title":"Appl. Math. Comput."},{"key":"4931_CR62","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.swevo.2015.05.001","volume":"24","author":"H Garg","year":"2015","unstructured":"Garg, H.: An efficient biogeography based optimization algorithm for solving reliability optimization problems. Swarm Evol. Comput. 24, 1\u201310 (2015)","journal-title":"Swarm Evol. Comput."},{"key":"4931_CR63","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1007\/s00500-018-3102-4","volume":"23","author":"S Arora","year":"2019","unstructured":"Arora, S., Singh, S.: Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput. 23, 715\u2013734 (2019)","journal-title":"Soft Comput."},{"key":"4931_CR64","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2020.103541","volume":"90","author":"S Kaur","year":"2020","unstructured":"Kaur, S., Awasthi, L.K., Sangal, A.L., Dhiman, G.: Tunicate swarm algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Eng. Appl. Artif. Intell. 90, 103541 (2020)","journal-title":"Eng. Appl. Artif. Intell."},{"key":"4931_CR65","doi-asserted-by":"publisher","first-page":"8457","DOI":"10.1007\/s12652-020-02580-0","volume":"12","author":"G Dhiman","year":"2021","unstructured":"Dhiman, G., Garg, M., Nagar, A., Kumar, V., Dehghani, M.: A novel algorithm for global optimization: rat swarm optimizer. J. Ambient Intell. Hum. Comput. 12, 8457\u20138482 (2021)","journal-title":"J. Ambient Intell. Hum. Comput."},{"issue":"3","key":"4931_CR66","doi-asserted-by":"publisher","first-page":"855","DOI":"10.3390\/s22030855","volume":"22","author":"P Trojovsk\u00fd","year":"2022","unstructured":"Trojovsk\u00fd, P., Dehghani, M.: Pelican optimization algorithm: a novel nature-inspired algorithm for engineering applications. Sensors 22(3), 855 (2022)","journal-title":"Sensors"},{"issue":"1","key":"4931_CR67","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1007\/s10489-022-03533-0","volume":"53","author":"H Mohammed","year":"2023","unstructured":"Mohammed, H., Rashid, T.: FOX: A FOX-inspired optimization algorithm. Appl. Intell. 53(1), 1030\u20131050 (2023)","journal-title":"Appl. Intell."},{"key":"4931_CR68","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.advengsoft.2015.01.010","volume":"83","author":"S Mirjalili","year":"2015","unstructured":"Mirjalili, S.: The ant lion optimizer. Adv. Eng. Software 83, 80\u201398 (2015)","journal-title":"Adv. Eng. Software"},{"key":"4931_CR69","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.knosys.2018.11.024","volume":"165","author":"G Dhiman","year":"2019","unstructured":"Dhiman, G., Kumar, V.: Seagull optimization algorithm: theory and its applications for large-scale industrial engineering problems. Knowl.-Based Syst. 165, 169\u2013196 (2019)","journal-title":"Knowl.-Based Syst."},{"key":"4931_CR70","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1016\/j.engappai.2019.03.021","volume":"82","author":"G Dhiman","year":"2019","unstructured":"Dhiman, G., Kaur, A.: STOA: a bio-inspired based optimization algorithm for industrial engineering problems. Eng. Appl. Artif. Intell. 82, 148\u2013174 (2019)","journal-title":"Eng. Appl. Artif. Intell."},{"key":"4931_CR71","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.ress.2015.06.002","volume":"142","author":"CL Huang","year":"2015","unstructured":"Huang, C.L.: A particle-based simplified swarm optimization algorithm for reliability redundancy allocation problems. Reliab. Eng. Syst. Saf. 142, 221\u2013230 (2015)","journal-title":"Reliab. Eng. Syst. Saf."},{"issue":"1","key":"4931_CR72","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.engappai.2006.03.003","volume":"20","author":"Q He","year":"2007","unstructured":"He, Q., Wang, L.: An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng. Appl. Artif. Intell. 20(1), 89\u201399 (2007)","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"9","key":"4931_CR73","first-page":"2124","volume":"9","author":"Y Liu","year":"2014","unstructured":"Liu, Y., Qin, G.: A modified particle swarm optimization algorithm for reliability redundancy optimization problem. J. Comput. 9(9), 2124\u20132131 (2014)","journal-title":"J. Comput."},{"issue":"4","key":"4931_CR74","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1108\/13552510610705928","volume":"12","author":"HG Kim","year":"2006","unstructured":"Kim, H.G., Bae, C.O., Park, D.J.: Reliability-redundancy optimization using simulated annealing algorithms. J. Qual. Maint. Eng. 12(4), 354\u2013363 (2006)","journal-title":"J. Qual. Maint. Eng."},{"issue":"11","key":"4931_CR75","doi-asserted-by":"publisher","first-page":"1465","DOI":"10.1016\/j.cor.2010.10.028","volume":"38","author":"WC Yeh","year":"2011","unstructured":"Yeh, W.C., Hsieh, T.J.: Solving reliability redundancy allocation problems using an artificial bee colony algorithm. Comput. Oper. Res. 38(11), 1465\u20131473 (2011)","journal-title":"Comput. Oper. Res."},{"issue":"12","key":"4931_CR76","doi-asserted-by":"publisher","first-page":"2961","DOI":"10.1016\/j.cor.2013.07.014","volume":"40","author":"H Garg","year":"2013","unstructured":"Garg, H., Rani, M., Sharma, S.P.: An efficient two phase approach for solving reliability-redundancy allocation problem using artificial bee colony technique. Comput. Oper. Res. 40(12), 2961\u20132969 (2013)","journal-title":"Comput. Oper. Res."},{"issue":"1","key":"4931_CR77","first-page":"14","volume":"4","author":"H Garg","year":"2015","unstructured":"Garg, H.: An approach for solving constrained reliability-redundancy allocation problems using cuckoo search algorithm. Beni-Suef Univ. J. Basic Appl. Sci. 4(1), 14\u201325 (2015)","journal-title":"Beni-Suef Univ. J. Basic Appl. Sci."},{"issue":"4","key":"4931_CR78","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1016\/j.cie.2013.08.003","volume":"66","author":"G Kanagaraj","year":"2013","unstructured":"Kanagaraj, G., Ponnambalam, S.G., Jawahar, N.: A hybrid cuckoo search and genetic algorithm for reliability-redundancy allocation problems. Comput. Ind. Eng. 66(4), 1115\u20131124 (2013)","journal-title":"Comput. Ind. Eng."},{"key":"4931_CR79","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.isatra.2015.09.015","volume":"59","author":"Q He","year":"2015","unstructured":"He, Q., Hu, X., Ren, H., Zhang, H.: A novel artificial fish swarm algorithm for solving large-scale reliability-redundancy application problem. ISA Trans. 59, 105\u2013113 (2015)","journal-title":"ISA Trans."},{"issue":"5","key":"4931_CR80","first-page":"113","volume":"8","author":"Y Liu","year":"2015","unstructured":"Liu, Y., Qin, G.: A DE algorithm combined with levy flight for reliability redundancy allocation problems. Int. J. Hybrid Inf. Technol. 8(5), 113\u2013118 (2015)","journal-title":"Int. J. Hybrid Inf. Technol."},{"issue":"6","key":"4931_CR81","doi-asserted-by":"publisher","first-page":"1608","DOI":"10.1016\/j.camwa.2011.01.029","volume":"61","author":"D Zou","year":"2011","unstructured":"Zou, D., Liu, H., Gao, L., Li, S.: A novel modified differential evolution algorithm for constrained optimization problems. Comput. Math. Appl. 61(6), 1608\u20131623 (2011)","journal-title":"Comput. Math. Appl."},{"issue":"9","key":"4931_CR82","first-page":"2050","volume":"9","author":"Y Liu","year":"2014","unstructured":"Liu, Y., Qin, G.: A hybrid TS-DE algorithm for reliability redundancy optimization problem. J. Comput. 9(9), 2050\u20132057 (2014)","journal-title":"J. Comput."},{"issue":"23","key":"4931_CR83","doi-asserted-by":"publisher","first-page":"20865","DOI":"10.1007\/s00521-022-07565-y","volume":"34","author":"T Kundu","year":"2022","unstructured":"Kundu, T., Garg, H.: INNA: an improved neural network algorithm for solving reliability optimization problems. Neural Comput. Appl. 34(23), 20865\u201320898 (2022)","journal-title":"Neural Comput. Appl."}],"container-title":["Cluster Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10586-024-04931-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10586-024-04931-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10586-024-04931-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T07:26:08Z","timestamp":1757143568000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10586-024-04931-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,25]]},"references-count":83,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["4931"],"URL":"https:\/\/doi.org\/10.1007\/s10586-024-04931-4","relation":{},"ISSN":["1386-7857","1573-7543"],"issn-type":[{"value":"1386-7857","type":"print"},{"value":"1573-7543","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,25]]},"assertion":[{"value":"30 July 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 October 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 November 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 February 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no competing interests to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not Applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Not Applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"267"}}