{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T18:52:55Z","timestamp":1775760775459,"version":"3.50.1"},"reference-count":64,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,15]],"date-time":"2018-02-15T00:00:00Z","timestamp":1518652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key Research and Development Program of China","award":["2017YFB0701700"],"award-info":[{"award-number":["2017YFB0701700"]}]},{"name":"Educational Commission of Hunan Province of China","award":["16c1307"],"award-info":[{"award-number":["16c1307"]}]},{"name":"Innovation Foundation for Postgraduate of Hunan Province of China","award":["CX2016B045"],"award-info":[{"award-number":["CX2016B045"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Particle swarm optimization (PSO) algorithm is generally improved by adaptively adjusting the inertia weight or combining with other evolution algorithms. However, in most modified PSO algorithms, the random values are always generated by uniform distribution in the range of [0, 1]. In this study, the random values, which are generated by uniform distribution in the ranges of [0, 1] and [\u22121, 1], and Gauss distribution with mean 0 and variance 1 (\r\n          \r\n            \r\n              \r\n                U\r\n                \r\n                  [\r\n                  \r\n                    0\r\n                    ,\r\n                    1\r\n                  \r\n                  ]\r\n                \r\n              \r\n            \r\n          \r\n        , \r\n      \r\n        \r\n          \r\n            U\r\n            \r\n              [\r\n              \r\n                \u2212\r\n                1\r\n                ,\r\n                1\r\n              \r\n              ]\r\n            \r\n          \r\n        \r\n      \r\n     and \r\n      \r\n        \r\n          \r\n            G\r\n            (\r\n            0\r\n            ,\r\n            1\r\n            )\r\n          \r\n        \r\n      \r\n    ), are respectively used in the standard PSO and linear decreasing inertia weight (LDIW) PSO algorithms. For comparison, the deterministic PSO algorithm, in which the random values are set as 0.5, is also investigated in this study. Some benchmark functions and the pressure vessel design problem are selected to test these algorithms with different types of random values in three space dimensions (10, 30, and 100). The experimental results show that the standard PSO and LDIW-PSO algorithms with random values generated by \r\n      \r\n        \r\n          \r\n            U\r\n            \r\n              [\r\n              \r\n                \u2212\r\n                1\r\n                ,\r\n                1\r\n              \r\n              ]\r\n            \r\n          \r\n        \r\n      \r\n     or \r\n      \r\n        \r\n          \r\n            G\r\n            (\r\n            0\r\n            ,\r\n            1\r\n            )\r\n          \r\n        \r\n      \r\n     are more likely to avoid falling into local optima and quickly obtain the global optima. This is because the large-scale random values can expand the range of particle velocity to make the particle more likely to escape from local optima and obtain the global optima. Although the random values generated by \r\n      \r\n        \r\n          \r\n            U\r\n            \r\n              [\r\n              \r\n                \u2212\r\n                1\r\n                ,\r\n                1\r\n              \r\n              ]\r\n            \r\n          \r\n        \r\n      \r\n     or \r\n      \r\n        \r\n          \r\n            G\r\n            (\r\n            0\r\n            ,\r\n            1\r\n            )\r\n          \r\n        \r\n      \r\n     are beneficial to improve the global searching ability, the local searching ability for a low dimensional practical optimization problem may be decreased due to the finite particles.<\/jats:p>","DOI":"10.3390\/a11020023","type":"journal-article","created":{"date-parts":[[2018,2,20]],"date-time":"2018-02-20T03:54:22Z","timestamp":1519098862000},"page":"23","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":67,"title":["Effects of Random Values for Particle Swarm Optimization Algorithm"],"prefix":"10.3390","volume":"11","author":[{"given":"Hou-Ping","family":"Dai","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410083, China"},{"name":"School of Mathematics and Statistics, Jishou University, Jishou 416000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5892-6891","authenticated-orcid":false,"given":"Dong-Dong","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410083, China"},{"name":"State Key Laboratory of High Performance Complex Manufacturing, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8792-6310","authenticated-orcid":false,"given":"Zhou-Shun","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,15]]},"reference":[{"key":"ref_1","unstructured":"Kennedy, J., and Eberhart, R.C. (December, January 27). Particle swarm optimization. Proceedings of the IEEE International Conference on Neuron Networks, Perth, WA, Australia."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4515","DOI":"10.1016\/j.ins.2010.07.013","article-title":"Self-adaptive learning based particle swarm optimization","volume":"180","author":"Wang","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1109\/TEVC.2005.857610","article-title":"Comprehensive learning particleswarm optimizer for global optimization of multimodal functions","volume":"10","author":"Liang","year":"2006","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.asoc.2008.03.001","article-title":"Particle swarm optimization with adaptive population size and its application","volume":"9","author":"Chen","year":"2009","journal-title":"Appl. Soft Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4560","DOI":"10.1016\/j.amc.2012.10.067","article-title":"An adaptive parameter tuning of particle swarm optimization algorithm","volume":"219","author":"Xu","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"11125","DOI":"10.1016\/j.amc.2012.04.069","article-title":"Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm","volume":"218","author":"Mirjalili","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.knosys.2013.11.015","article-title":"Optimal parameters selection for BP neural network based on particle swarm optimization: A case study of wind speed forecasting","volume":"56","author":"Ren","year":"2014","journal-title":"Knowl. Based Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1016\/j.amc.2006.07.025","article-title":"A hybrid particle swarmoptimization\u2013back-propagation algorithm for feedforward neural network training","volume":"185","author":"Zhang","year":"2007","journal-title":"Appl. Math. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3491","DOI":"10.1016\/j.eswa.2013.10.053","article-title":"Artificial Neural Network trained by Particle Swarm Optimization for non-linear channel equalization","volume":"41","author":"Das","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TSMCC.2008.2002333","article-title":"A hybrid of cooperative particle swarm optimization and cultural algorithm for neural fuzzy networks and its prediction applications","volume":"39","author":"Lin","year":"2009","journal-title":"IEEE Trans. Syst. Man Cybern. Part C Appl. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/TFUZZ.2009.2034529","article-title":"Hierarchical cluster-based multispecies particle-swarm optimization for fuzzy-system optimization","volume":"18","author":"Juang","year":"2010","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3976","DOI":"10.1016\/j.apm.2010.03.033","article-title":"Integration of particle swarm optimization-based fuzzy neural network and artificial neural network for supplier selection","volume":"34","author":"Kuo","year":"2010","journal-title":"Appl. Math. Model."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1109\/TSG.2013.2237795","article-title":"Optimized control of DFIG-based wind generation using sensitivity analysis and particle swarm optimization","volume":"4","author":"Tang","year":"2013","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2539","DOI":"10.1109\/TPWRS.2014.2305977","article-title":"Energy-storage-based low-frequency oscillation damping control using particle swarm optimization and heuristic dynamic programming","volume":"29","author":"Sui","year":"2014","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.eswa.2011.07.007","article-title":"Chaos particle swarm optimization and T\u2013S fuzzy modeling approaches to constrained predictive control","volume":"39","author":"Jiang","year":"2012","journal-title":"Expert Syst. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1016\/j.asoc.2015.10.041","article-title":"Design of optimal PID controller using hybrid differential evolution and particle swarm optimization with an aging leader and challengers","volume":"38","author":"Moharam","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/j.asoc.2007.01.010","article-title":"On the improved performances of the particle swarm optimization algorithms with adaptive parameters, cross-over operators and root mean square (RMS) variants for computing optimal control of a class of hybrid systems","volume":"8","author":"Arumugam","year":"2008","journal-title":"Appl. Soft Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1109\/TEVC.2012.2196047","article-title":"A new particle swarm optimization method enhanced with a periodic mutation strategy and neural networks","volume":"17","author":"Pehlivanoglu","year":"2013","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/TEVC.2004.826071","article-title":"Self-organizing hierarchical particle optimizer with time-varying acceleration coefficients","volume":"8","author":"Ratnaweera","year":"2004","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_20","unstructured":"Shi, Y.H., and Eberhart, R.C. (1998, January 4\u20139). A modified particle swarm optimizer. Proceedings of the IEEE International Conference on Computational Intelligence, Anchorage, AK, USA."},{"key":"ref_21","unstructured":"Xing, J., and Xiao, D. (2008, January 2\u20134). New Metropolis coefficients of particle swarm optimization. Proceedings of the IEEE Chinese Control and Decision Conference, Yantai, China."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.asoc.2015.10.004","article-title":"A novel stability-based adaptive inertia weight for particle swarm optimization","volume":"38","author":"Taherkhani","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3658","DOI":"10.1016\/j.asoc.2011.01.037","article-title":"A novel particle swarm optimization algorithm with adaptive inertia weight","volume":"11","author":"Nickabadi","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.asoc.2014.11.018","article-title":"A new particle swarm optimization algorithm with adaptive inertia weight based on Bayesian techniques","volume":"28","author":"Zhang","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1109\/TEVC.2012.2232931","article-title":"An adaptive particle swarm optimization with multiple adaptive methods","volume":"17","author":"Hu","year":"2013","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.ipl.2004.11.003","article-title":"An improved GA and a novel PSOGA-based hybrid algorithm","volume":"93","author":"Shi","year":"2005","journal-title":"Inf. Process. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1109\/TEVC.2009.2014613","article-title":"JADE: Adaptive differential evolution with optional external archive","volume":"13","author":"Zhang","year":"2009","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2011.11.005","article-title":"Local search based hybrid particle swarm optimization algorithm for multiobjective optimization","volume":"3","author":"Mousa","year":"2012","journal-title":"Swarm Evol. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1016\/j.neucom.2014.03.081","article-title":"Hybrid learning particle swarm optimizer with genetic disturbance","volume":"151","author":"Liu","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/MCI.2013.2264577","article-title":"Hybrid Particle Swarm Optimization and Genetic Algorithm for Multi-UAV Formation Reconfiguration","volume":"8","author":"Duan","year":"2013","journal-title":"IEEE Computat. Intell. Mag."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.ins.2012.05.017","article-title":"Evolving cognitive and social experience in particle swarm optimization through differential evolution: A hybrid approach","volume":"216","author":"Epitropakis","year":"2012","journal-title":"Inf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1109\/TEVC.2005.857074","article-title":"Multiswarms, exclusion, and anti-convergence in dynamic environments","volume":"10","author":"Blackwell","year":"2006","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1109\/TEVC.2005.859468","article-title":"Locating and tracking multiple dynamic optima by a particle swarm model using speciation","volume":"10","author":"Parrott","year":"2006","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Li, C., and Yang, S. (2009, January 18\u201321). A clustering particle swarm optimizer for dynamic optimization. Proceedings of the 2009 Congress on Evolutionary Computation, Trondheim, Norway.","DOI":"10.1109\/CEC.2009.4982979"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Kamosi, M., Hashemi, A.B., and Meybodi, M.R. (2010, January 16\u201318). A new particle swarm optimization algorithm for dynamic environments. Proceedings of the 2010 Congress on Swarm, Evolutionary, and Memetic Computing, Chennai, India.","DOI":"10.1109\/NABIC.2010.5716372"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3096","DOI":"10.1016\/j.ins.2008.01.020","article-title":"Multi-strategy ensemble particle swarm optimization for dynamic optimization","volume":"178","author":"Du","year":"2008","journal-title":"Inf. Sci."},{"key":"ref_37","unstructured":"Dong, D.M., Jie, J., Zeng, J.C., and Wang, M. (2008, January 17\u201319). Chaos-mutation-based particle swarm optimizer for dynamic environment. Proceedings of the 2008 Conference on Intelligent System and Knowledge Engineering, Xiamen, China."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Cui, X., and Potok, T.E. (2007, January 26\u201330). Distributed adaptive particle swarm optimizer in dynamic environment. Proceedings of the 2007 Conference on Parallel and Distributed Processing Symposium, Rome, Italy.","DOI":"10.1109\/IPDPS.2007.370434"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"De, M.K., Slawomir, N.J., and Mark, B. (2006). Stochastic diffusion search: Partial function evaluation in swarm intelligence dynamic optimization. Stigmergic Optimization, Springer.","DOI":"10.1007\/978-3-540-34690-6_8"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s10710-006-9014-6","article-title":"A hierarchical particle swarm optimizer for noisy and dynamic environments","volume":"7","author":"Janson","year":"2006","journal-title":"Genet. Program. Evol. Mach."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Zheng, X., and Liu, H. (2009, January 14\u201316). A different topology multi-swarm PSO in dynamic environment. Proceedings of the 2009 Conference on Medicine & Education, Jinan, China.","DOI":"10.1109\/ITIME.2009.5236313"},{"key":"ref_42","unstructured":"Shi, Y.H., and Eberhart, R.C. (1998, January 25\u201327). Parameter selection in particle swarm optimization. Proceedings of the 7th Annual International Conference on Evolutionary Programming, San Diego, CA, USA."},{"key":"ref_43","unstructured":"Eberhart, R.C., and Shi, Y.H. (2001, January 27\u201330). Tracking and optimizing dynamic systems with particle swarms. Proceedings of the 2001 Congress on Evolutionary Computation, Seoul, Korea."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1016\/j.asoc.2015.01.004","article-title":"Low-discrepancy sequence initialized particle swarm optimization algorithm with high-order nonlinear time-varying inertia weight","volume":"29","author":"Yang","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_45","unstructured":"Shi, Y.H., and Eberhart, R.C. (1999, January 6\u20139). Empirical study of particle swarm optimization. Proceedings of the 1999 Congress on Evolutionary Computation, Washington, DC, USA."},{"key":"ref_46","unstructured":"Eberhart, R.C., and Shi, Y.H. (2000, January 16\u201319). Comparing inertia weights and constriction factors in particle swarm optimization. Proceedings of the IEEE Congress on Evolutionary Computation, La Jolla, CA, USA."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1016\/j.cor.2004.08.012","article-title":"Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization","volume":"33","author":"Chatterjee","year":"2006","journal-title":"Comput. Oper. Res."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Feng, Y., Teng, G.F., Wang, A.X., and Yao, Y.M. (2007, January 5\u20137). Chaotic inertia weight in particle swarm optimization. Proceedings of the 2nd International Conference on Innovative Computing, Information and Control, Kumamoto, Japan.","DOI":"10.1109\/ICICIC.2007.209"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1080\/03052150601047362","article-title":"A decreasing inertia weight particle swarm optimizer","volume":"39","author":"Fan","year":"2007","journal-title":"Eng. Optimiz."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1016\/j.chaos.2006.09.063","article-title":"A dynamic inertia weight particle swarm optimization algorithm","volume":"37","author":"Jiao","year":"2008","journal-title":"Chaos Solitons Fract."},{"key":"ref_51","unstructured":"Lei, K., Qiu, Y., and He, Y. (2006, January 19\u201321). A new adaptive well-chosen inertia weight strategy to automatically harmonize global and local search ability in particle swarm optimization. Proceedings of the 1st International Symposium on Systems and Control in Aerospace and Astronautics, Harbin, China."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1016\/j.amc.2006.12.045","article-title":"A modified particle swarm optimizer with dynamic adaptation","volume":"189","author":"Yang","year":"2007","journal-title":"Appl. Math. Comput."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1407","DOI":"10.1016\/j.enconman.2007.12.023","article-title":"Adaptive particle swarm optimization approach for static and dynamic economic load dispatch","volume":"49","author":"Panigrahi","year":"2008","journal-title":"Energ. Convers. Manag."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Suresh, K., Ghosh, S., Kundu, D., Sen, A., Das, S., and Abraham, A. (2008, January 26\u201328). Inertia-adaptiveparticle swarm optimizer for improved global search. Proceedings of the Eighth International Conference on Intelligent Systems Design and Applications, Kaohsiung, Taiwan.","DOI":"10.1109\/ISDA.2008.199"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.ins.2014.09.053","article-title":"Self-regulating particle swarm optimization algorithm","volume":"294","author":"Tanweer","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_56","first-page":"1331","article-title":"Particle swarm optimization using velocity control","volume":"129","author":"Nakagawa","year":"2009","journal-title":"IEEJ Trans. Electr. Inf. Syst."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/4235.985692","article-title":"The particle swarm: Explosion stability and convergence in a multi-dimensional complex space","volume":"6","author":"Clerc","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1002\/tee.20078","article-title":"Dynamic parameter tuning of particle swarm optimization","volume":"1","author":"Iwasaki","year":"2006","journal-title":"IEEJ Trans. Electr. Electr."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1109\/TSMCB.2008.925757","article-title":"PSO-based multiobjective optimization with dynamic population size and adaptive local archives","volume":"38","author":"Leong","year":"2008","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_60","first-page":"1","article-title":"Population statistics for particle swarm optimization: Single-evaluation methods in noisy optimization problems","volume":"19","author":"Johnston","year":"2014","journal-title":"Soft Comput."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1109\/TSMCB.2008.2006628","article-title":"Efficient population utilization strategy for particle swarm optimizer","volume":"39","author":"Hsieh","year":"2009","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.asoc.2016.07.034","article-title":"A new multi-function global particle swarm optimization","volume":"49","author":"Ruan","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.asoc.2016.08.028","article-title":"Parameter selection in synchronous and asynchronous deterministic particle swarm optimization for ship hydrodynamics problems","volume":"49","author":"Serani","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1115\/1.2912596","article-title":"Nonlinear integer and discrete programming in mechanical design optimization","volume":"112","author":"Sandgren","year":"1990","journal-title":"J. Mech. Des. 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