{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T16:33:15Z","timestamp":1774888395211,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2015,3,12]],"date-time":"2015-03-12T00:00:00Z","timestamp":1426118400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2016,6]]},"DOI":"10.1007\/s00500-015-1641-5","type":"journal-article","created":{"date-parts":[[2015,3,11]],"date-time":"2015-03-11T09:29:21Z","timestamp":1426066161000},"page":"2281-2307","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["An improved fruit fly optimization algorithm to solve the homogeneous fuzzy series\u2013parallel redundancy allocation problem under discount strategies"],"prefix":"10.1007","volume":"20","author":[{"given":"Seyed Mohsen","family":"Mousavi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Najmeh","family":"Alikar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seyed Taghi Akhavan","family":"Niaki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,3,12]]},"reference":[{"key":"1641_CR1","doi-asserted-by":"crossref","unstructured":"Abouei Ardakan M, Zeinal Hamadani A (2014) Reliability\u2013redundancy allocation problem with cold-standby redundancy strategy. Simul Model Pract Theory 42:107\u2013118","DOI":"10.1016\/j.simpat.2013.12.013"},{"key":"1641_CR2","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1016\/j.apm.2009.07.016","volume":"34","author":"M Agarwal","year":"2010","unstructured":"Agarwal M, Sharma VK (2010) Ant colony approach to constrained redundancy optimization in binary systems. Appl Math Model 34:992\u20131003","journal-title":"Appl Math Model"},{"key":"1641_CR3","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.jocs.2010.06.001","volume":"1","author":"N Beji","year":"2010","unstructured":"Beji N, Jarboui B, Eddaly M, Chabchoub H (2010) A hybrid particle swarm optimization algorithm for the redundancy allocation problem. J Comput Sci 1:159\u2013167","journal-title":"J Comput Sci"},{"key":"1641_CR4","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0167-6377(92)90008-Q","volume":"11","author":"M-S Chern","year":"1992","unstructured":"Chern M-S (1992) On the computational complexity of reliability redundancy allocation in a series system. Oper Res Lett 11:309\u2013315","journal-title":"Oper Res Lett"},{"key":"1641_CR5","doi-asserted-by":"crossref","unstructured":"Chiou J-S, Tsai S-H, Liu M-T (2012) A PSO-based adaptive fuzzy PID-controllers. Simul Model Pract Theory 26:49\u201359","DOI":"10.1016\/j.simpat.2012.04.001"},{"key":"1641_CR6","doi-asserted-by":"crossref","unstructured":"Coit DW, Smith AE (1996a) Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Trans Reliab 45:254\u2013260, 266","DOI":"10.1109\/24.510811"},{"key":"1641_CR7","doi-asserted-by":"crossref","unstructured":"Coit DW, Smith AE (1996b) Penalty guided genetic search for reliability design optimization. Comput Ind Eng 30:895\u2013904","DOI":"10.1016\/0360-8352(96)00040-X"},{"key":"1641_CR8","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.knosys.2011.07.001","volume":"26","author":"H Dai","year":"2012","unstructured":"Dai H, Zhao G, Lu J, Dai S (2012) Comment and improvement on \u201cA new fruit fly optimization algorithm: taking the financial distress model as an example\u201d. Knowl Based Syst 26:69\u201374","journal-title":"Knowl Based Syst"},{"key":"1641_CR9","doi-asserted-by":"crossref","unstructured":"Dai H, Liu A, Lu J, Dai S, Wu X, Sun Y (2014) Optimization about the layout of IMUs in large ship based on fruit fly optimization algorithm. Opt Int J Light Electron Opt. doi: 10.1016\/j.ijleo.2014.08.037","DOI":"10.1016\/j.ijleo.2014.08.037"},{"key":"1641_CR10","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.cie.2012.09.015","volume":"64","author":"H Garg","year":"2013","unstructured":"Garg H, Sharma S (2013) Multi-objective reliability\u2013redundancy allocation problem using particle swarm optimization. Comput Ind Eng 64:247\u2013255","journal-title":"Comput Ind Eng"},{"key":"1641_CR11","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.jmsy.2014.02.008","volume":"33","author":"H Garg","year":"2014","unstructured":"Garg H, Rani M, Sharma S, Vishwakarma Y (2014) Bi-objective optimization of the reliability\u2013redundancy allocation problem for series\u2013parallel system. J Manuf Syst 33:335\u2013347","journal-title":"J Manuf Syst"},{"key":"1641_CR12","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.ejor.2004.06.006","volume":"171","author":"C Ha","year":"2006","unstructured":"Ha C, Kuo W (2006) Reliability redundancy allocation: an improved realization for nonconvex nonlinear programming problems. Eur J Oper Res 171:24\u201338","journal-title":"Eur J Oper Res"},{"key":"1641_CR13","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1016\/j.simpat.2010.01.001","volume":"18","author":"P Hu","year":"2010","unstructured":"Hu P, Cao G-Y, Zhu X-J, Li J (2010) Modeling of a proton exchange membrane fuel cell based on the hybrid particle swarm optimization with Levenberg\u2013Marquardt neural network. Simul Model Pract Theory 18:574\u2013588","journal-title":"Simul Model Pract Theory"},{"key":"1641_CR14","doi-asserted-by":"crossref","unstructured":"Jarboui B, Ibrahim S, Siarry P, Rebai A (2008a) A combinatorial particle swarm optimisation for solving permutation flowshop problems. Comput Ind Eng 54:526\u2013538","DOI":"10.1016\/j.cie.2007.09.006"},{"key":"1641_CR15","doi-asserted-by":"crossref","unstructured":"Jarboui B, Damak N, Siarry P, Rebai A (2008b) A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems. Appl Math Comput 195:299\u2013308","DOI":"10.1016\/j.amc.2007.04.096"},{"key":"1641_CR16","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1016\/j.cie.2013.08.003","volume":"66","author":"G Kanagaraj","year":"2013","unstructured":"Kanagaraj G, Ponnambalam S, Jawahar N (2013) A hybrid cuckoo search and genetic algorithm for reliability\u2013redundancy allocation problems. Comput Ind Eng 66:1115\u20131124","journal-title":"Comput Ind Eng"},{"key":"1641_CR17","doi-asserted-by":"crossref","unstructured":"Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, Perth, Australia, pp 1942\u20131948","DOI":"10.1109\/ICNN.1995.488968"},{"key":"1641_CR18","doi-asserted-by":"crossref","unstructured":"Khalili-Damghani K, Amiri M (2012) Solving binary-state multi-objective reliability redundancy allocation series\u2013parallel problem using efficient epsilon-constraint, multi-start partial bound enumeration algorithm, and DEA. Reliab Eng Syst Saf 103:35\u201344","DOI":"10.1016\/j.ress.2012.03.006"},{"key":"1641_CR19","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1080\/07408170304422","volume":"35","author":"S Kulturel-Konak","year":"2003","unstructured":"Kulturel-Konak S, Smith AE, Coit DW (2003) Efficiently solving the redundancy allocation problem using Tabu search. IIE Trans 35:515\u2013526","journal-title":"IIE Trans"},{"key":"1641_CR20","unstructured":"Kuo W (2001) Optimal reliability design: fundamentals and applications. Cambridge University Press, Cambridge"},{"key":"1641_CR21","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1109\/24.877336","volume":"49","author":"W Kuo","year":"2000","unstructured":"Kuo W, Prasad VR (2000) An annotated overview of system-reliability optimization. IEEE Trans Reliab 49:176\u2013187","journal-title":"IEEE Trans Reliab"},{"key":"1641_CR22","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1109\/24.722283","volume":"47","author":"G Levitin","year":"1998","unstructured":"Levitin G, Lisnianski A, Ben-Haim H, Elmakis D (1998) Redundancy optimization for series\u2013parallel multi-state systems. IEEE Trans Reliab 47:165\u2013172","journal-title":"IEEE Trans Reliab"},{"key":"1641_CR23","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.knosys.2012.08.015","volume":"37","author":"H-Z Li","year":"2013","unstructured":"Li H-Z, Guo S, Li C-J, Sun J-Q (2013) A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm. Knowl Based Syst 37:378\u2013387","journal-title":"Knowl Based Syst"},{"key":"1641_CR24","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.knosys.2014.08.022","volume":"72","author":"J-Q Li","year":"2014","unstructured":"Li J-Q, Pan Q-K, Mao K, Suganthan P (2014) Solving the steelmaking casting problem using an effective fruit fly optimisation algorithm. Knowl Based Syst 72:28\u201336","journal-title":"Knowl Based Syst"},{"key":"1641_CR25","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1109\/TR.2004.832816","volume":"53","author":"Y-C Liang","year":"2004","unstructured":"Liang Y-C, Smith AE (2004) An ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Trans Reliab 53:417\u2013423","journal-title":"IEEE Trans Reliab"},{"key":"1641_CR26","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.ress.2006.04.013","volume":"92","author":"Y-C Liang","year":"2007","unstructured":"Liang Y-C, Chen Y-C (2007) Redundancy allocation of series\u2013parallel systems using a variable neighborhood search algorithm. Reliab Eng Syst Saf 92:323\u2013331","journal-title":"Reliab Eng Syst Saf"},{"key":"1641_CR27","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/j.simpat.2010.07.010","volume":"19","author":"ID Lins","year":"2011","unstructured":"Lins ID, Droguett EL (2011) Redundancy allocation problems considering systems with imperfect repairs using multi-objective genetic algorithms and discrete event simulation. Simul Model Pract Theory 19:362\u2013381","journal-title":"Simul Model Pract Theory"},{"key":"1641_CR28","first-page":"1","volume":"27","author":"G Mahapatra","year":"2011","unstructured":"Mahapatra G, Roy T (2011) Optimal redundancy allocation in series\u2013parallel system using generalized fuzzy number. Tamsui Oxf J Inf Math Sci 27:1\u201320","journal-title":"Tamsui Oxf J Inf Math Sci"},{"key":"1641_CR29","doi-asserted-by":"crossref","unstructured":"Mousavi SM, Hajipour V, Niaki STA, Aalikar N (2013a) A multi-product multi-period inventory control problem under inflation and discount: a parameter-tuned particle swarm optimization algorithm. Int J Adv Manuf Technol 70:1739\u20131756","DOI":"10.1007\/s00170-013-5378-y"},{"key":"1641_CR30","doi-asserted-by":"crossref","unstructured":"Mousavi SM, Hajipour V, Niaki STA, Alikar N (2013b) Optimizing multi-item multi-period inventory control system with discounted cash flow and inflation: two calibrated meta-heuristic algorithms. Appl Math Model 37:2241\u20132256","DOI":"10.1016\/j.apm.2012.05.019"},{"key":"1641_CR31","doi-asserted-by":"crossref","unstructured":"Mousavi SM, Bahreininejad A, Musa SN, Yusof F (2014a) A modified particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network. J Intell Manuf. doi: 10.1007\/s10845-014-0970-z","DOI":"10.1007\/s10845-014-0970-z"},{"key":"1641_CR32","doi-asserted-by":"crossref","unstructured":"Mousavi SM, Sadeghi J, Niaki STA, Alikar N, Bahreininejad A, Metselaar HSC (2014b) Two parameter-tuned meta-heuristics for a discounted inventory control problem in a fuzzy environment. Inf Sci 276:42\u201362","DOI":"10.1016\/j.ins.2014.02.046"},{"key":"1641_CR33","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.ress.2005.12.002","volume":"92","author":"N Nahas","year":"2007","unstructured":"Nahas N, Nourelfath M, Ait-Kadi D (2007) Coupling ant colony and the degraded ceiling algorithm for the redundancy allocation problem of series\u2013parallel systems. Reliab Eng Syst Saf 92:211\u2013222","journal-title":"Reliab Eng Syst Saf"},{"key":"1641_CR34","doi-asserted-by":"crossref","unstructured":"Naka S, Genji T, Yura T, Fukuyama Y (2001) Practical distribution state estimation using hybrid particle swarm optimization. In: Power engineering society winter meeting, 2001. IEEE, pp 815\u2013820","DOI":"10.1109\/PESW.2001.916969"},{"key":"1641_CR35","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1016\/j.ress.2007.06.004","volume":"93","author":"M Ouzineb","year":"2008","unstructured":"Ouzineb M, Nourelfath M, Gendreau M (2008) Tabu search for the redundancy allocation problem of homogenous series-parallel multi-state systems. Reliab Eng Syst Saf 93:1257\u20131272","journal-title":"Reliab Eng Syst Saf"},{"key":"1641_CR36","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.knosys.2011.07.001","volume":"26","author":"W-T Pan","year":"2012","unstructured":"Pan W-T (2012) A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowl Based Syst 26:69\u201374","journal-title":"Knowl Based Syst"},{"key":"1641_CR37","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.knosys.2014.02.021","volume":"62","author":"Q-K Pan","year":"2014","unstructured":"Pan Q-K, Sang H-Y, Duan J-H, Gao L (2014) An improved fruit fly optimization algorithm for continuous function optimization problems. Knowl Based Syst 62:69\u201383","journal-title":"Knowl Based Syst"},{"key":"1641_CR38","doi-asserted-by":"crossref","unstructured":"Sadeghi J, Mousavi SM, Niaki STA, Sadeghi S (2013) Optimizing a multi-vendor multi-retailer vendor managed inventory problem: two tuned meta-heuristic algorithms. Knowl Based Syst 50:159\u2013170","DOI":"10.1016\/j.knosys.2013.06.006"},{"key":"1641_CR39","doi-asserted-by":"crossref","first-page":"3243","DOI":"10.1016\/j.cor.2007.02.019","volume":"35","author":"D Sha","year":"2008","unstructured":"Sha D, Hsu C-Y (2008) A new particle swarm optimization for the open shop scheduling problem. Comput Oper Res 35:3243\u20133261","journal-title":"Comput Oper Res"},{"key":"1641_CR40","doi-asserted-by":"crossref","unstructured":"Shi Y, Eberhart RC (1999) Empirical study of particle swarm optimization. In: Proceedings of the 1999 Congress on evolutionary computation, 1999. CEC 99. IEEE","DOI":"10.1109\/CEC.1999.785511"},{"key":"1641_CR41","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1016\/j.ress.2007.02.009","volume":"93","author":"R Tavakkoli-Moghaddam","year":"2008","unstructured":"Tavakkoli-Moghaddam R, Safari J, Sassani F (2008) Reliability optimization of series\u2013parallel systems with a choice of redundancy strategies using a genetic algorithm. Reliab Eng Syst Saf 93:550\u2013556","journal-title":"Reliab Eng Syst Saf"},{"key":"1641_CR42","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1109\/TR.1977.5220100","volume":"26","author":"FA Tillman","year":"1977","unstructured":"Tillman FA, Hwang C-L, Kuo W (1977) Optimization techniques for system reliability with redundancy? A review. IEEE Trans. Reliab 26:148\u2013155","journal-title":"IEEE Trans. Reliab"},{"key":"1641_CR43","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/j.cam.2009.06.034","volume":"232","author":"S Wang","year":"2009","unstructured":"Wang S, Watada J (2009) Modelling redundancy allocation for a fuzzy random parallel\u2013series system. J Comput Appl Math 232:539\u2013557","journal-title":"J Comput Appl Math"},{"key":"1641_CR44","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.knosys.2013.04.003","volume":"48","author":"L Wang","year":"2013","unstructured":"Wang L, Zheng X-L, Wang S-Y (2013) A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem. Knowl Based Syst 48:17\u201323","journal-title":"Knowl Based Syst"},{"key":"1641_CR45","first-page":"1072","volume":"494","author":"LS Wei","year":"2014","unstructured":"Wei LS, Wu X, Niu MQ, Chen ZY (2014) FOA based PID controller for human balance keeping. Appl Mech Mater 494:1072\u20131075","journal-title":"Appl Mech Mater"},{"key":"1641_CR46","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.amc.2014.02.005","volume":"233","author":"X Yuan","year":"2014","unstructured":"Yuan X, Dai X, Zhao J, He Q (2014) On a novel multi-swarm fruit fly optimization algorithm and its application. Appl Math Comput 233:260\u2013271","journal-title":"Appl Math Comput"},{"key":"1641_CR47","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1111\/j.1467-8667.2005.00420.x","volume":"21","author":"H Zhang","year":"2006","unstructured":"Zhang H, Tam C, Li H (2006) Multimode project scheduling based on particle swarm optimization. Comput Aided Civil Infrastruct Eng 21:93\u2013103","journal-title":"Comput Aided Civil Infrastruct Eng"},{"key":"1641_CR48","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.knosys.2013.12.011","volume":"57","author":"X-L Zheng","year":"2014","unstructured":"Zheng X-L, Wang L, Wang S-Y (2014) A novel fruit fly optimization algorithm for the semiconductor final testing scheduling problem. Knowl Based Syst 57:95\u2013103","journal-title":"Knowl Based Syst"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1641-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-015-1641-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1641-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,21]],"date-time":"2019-08-21T17:42:56Z","timestamp":1566409376000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-015-1641-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,12]]},"references-count":48,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2016,6]]}},"alternative-id":["1641"],"URL":"https:\/\/doi.org\/10.1007\/s00500-015-1641-5","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,12]]}}}