{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T05:06:56Z","timestamp":1771564016838,"version":"3.50.1"},"reference-count":81,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T00:00:00Z","timestamp":1771545600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T00:00:00Z","timestamp":1771545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["309386\/2025-0"],"award-info":[{"award-number":["309386\/2025-0"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004586","name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","doi-asserted-by":"publisher","award":["E-26\/210.430\/2024"],"award-info":[{"award-number":["E-26\/210.430\/2024"]}],"id":[{"id":"10.13039\/501100004586","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004909","name":"Universidade Federal Do Rio Grande","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004909","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The use of optimization tools in distillation processes can be computationally intensive, due to the scale of the simulation problems associated with the optimization structure. In many situations, it is desirable to obtain a distillation column configuration that is capable of achieving pre-established degrees of purity for the products of interest while simultaneously minimizing operating costs and annualized investments. In this paper, we present the development of an optimization\u2013simulation tool for distillation problems using a low-parameter metaheuristic (the Symbiotic Organisms Search algorithm, SOS) coupled with a simulation tool with sparse Jacobian matrix calculations (using a coloring graph algorithm) and code vectorization. The applicability of the developed framework was demonstrated in a separation train for a non-ideal ternary mixture. The numerical results obtained indicate that the computational tool proved to be viable from a computational time standpoint\u2014with significant gains over the calculation of the Jacobian matrix using finite differences\u2014approaching the vicinity of the optimum region in a small number of iterations. In addition, the possibility of integrating simulation and optimization tools for distillation processes in a single environment was demonstrated, avoiding complex communication structures between the simulator and the optimizer. The results obtained also indicated substantial improvements\u2014in terms of minimizing a metric that involves investments and energy expenditures\u2014in comparison with non-optimized designs for the same separation train.<\/jats:p>","DOI":"10.1007\/s11227-026-08309-8","type":"journal-article","created":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T03:57:27Z","timestamp":1771559847000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An efficient optimization\u2013simulation tool for distillation processes"],"prefix":"10.1007","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0506-2561","authenticated-orcid":false,"given":"Gustavo Mendes","family":"Platt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9847-7290","authenticated-orcid":false,"given":"Francisco Bruno Souza","family":"Oliveira","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4583-6026","authenticated-orcid":false,"given":"Gustavo Barbosa","family":"Libotte","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7401-4718","authenticated-orcid":false,"given":"Fran S\u00e9rgio","family":"Lobato","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,20]]},"reference":[{"key":"8309_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.seppur.2024.131061","volume":"360","author":"M Adami","year":"2025","unstructured":"Adami M, Farheen K, Skiborowski M (2025) Electrifying distillation: optimization-based evaluation of internally heat-integrated distillation columns. Sep Purif Technol 360:131061. https:\/\/doi.org\/10.1016\/j.seppur.2024.131061","journal-title":"Sep Purif Technol"},{"issue":"13","key":"8309_CR2","doi-asserted-by":"publisher","first-page":"2398","DOI":"10.1016\/j.energy.2005.10.030","volume":"31","author":"M Gadalla","year":"2006","unstructured":"Gadalla M, Olujic Z, Jobson M, Smith R (2006) Estimation and reduction of CO2 emissions from crude oil distillation units. Energy 31(13):2398\u20132408. https:\/\/doi.org\/10.1016\/j.energy.2005.10.030","journal-title":"Energy"},{"issue":"11","key":"8309_CR3","doi-asserted-by":"publisher","first-page":"2413","DOI":"10.3390\/pr12112413","volume":"12","author":"M He","year":"2024","unstructured":"He M, Chen F, Wen P, Jin Y, Zhao J, Zhang L, Gao J, Lu X, Wan L (2024) Vinyl chloride distillation process simulation optimization evaluation: optimization based on NSGA-III algorithm and quantitative risk analysis. Processes 12(11):2413. https:\/\/doi.org\/10.3390\/pr12112413","journal-title":"Processes"},{"key":"8309_CR4","doi-asserted-by":"publisher","unstructured":"Vel\u00e1zquez JJH, Hern\u00e1ndez ELP, Vega LA, Espinoza DEC, Avila JRA, Ruiz JC (2025) Comparative and statistical study on Aspen Plus interfaces used for stochastic optimization. In: Proceedings of the 35th European Symposium on Computer Aided Process Engineering (ESCAPE 35). ESCAPE 35, vol 4, PSE Press, Belgium, pp 1409\u20131414. https:\/\/doi.org\/10.69997\/sct.102858","DOI":"10.69997\/sct.102858"},{"key":"8309_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2022.107785","volume":"162","author":"P Santos Bartolome","year":"2022","unstructured":"Santos Bartolome P, Van Gerven T (2022) A comparative study on Aspen Hysys interconnection methodologies. Comput Chem Eng 162:107785. https:\/\/doi.org\/10.1016\/j.compchemeng.2022.107785","journal-title":"Comput Chem Eng"},{"issue":"5","key":"8309_CR6","doi-asserted-by":"publisher","first-page":"914","DOI":"10.1002\/cjce.22152","volume":"93","author":"AL Guedes","year":"2015","unstructured":"Guedes AL, Moura Neto FD, Platt GM (2015) Prediction of azeotropic behaviour by the inversion of functions from the plane to the plane. Can J Chem Eng 93(5):914\u2013928. https:\/\/doi.org\/10.1002\/cjce.22152","journal-title":"Can J Chem Eng"},{"key":"8309_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.cep.2020.108224","volume":"159","author":"J Lu","year":"2021","unstructured":"Lu J, Wang Q, Zhang Z, Tang J, Cui M, Chen X, Liu Q, Fei Z, Qiao X (2021) Surrogate modeling-based multi-objective optimization for the integrated distillation processes. Chem Eng Process Process Intensif 159:108224. https:\/\/doi.org\/10.1016\/j.cep.2020.108224","journal-title":"Chem Eng Process Process Intensif"},{"key":"8309_CR8","doi-asserted-by":"publisher","unstructured":"Savsani V, Tejani G, Patel V (2024) MATLAB Codes of Metaheuristics Methods, Springer, Cham, pp 385\u2013425. https:\/\/doi.org\/10.1007\/978-3-031-49295-2_8","DOI":"10.1007\/978-3-031-49295-2_8"},{"issue":"1","key":"8309_CR9","doi-asserted-by":"publisher","DOI":"10.1049\/ell2.13192","volume":"61","author":"TAC Barros","year":"2025","unstructured":"Barros TAC, Fontgalland G, Teixeira FL, Silva PHF, Oliveira EEC (2025) Low-profile circular-polarized fractal antenna design with reduced orbital angular momentum beam divergence. Electron Lett 61(1):e13192. https:\/\/doi.org\/10.1049\/ell2.13192","journal-title":"Electron Lett"},{"key":"8309_CR10","doi-asserted-by":"publisher","unstructured":"Bhattacharjee N, Sen N, Sahoo L (2025) In: Sahoo L, Senapati T, Pal M, Yager RR (eds) Root Hair Algorithm: A Swarm Intelligence Algorithm, Springer, Singapore, pp 583\u2013595. https:\/\/doi.org\/10.1007\/978-981-96-0085-4_31","DOI":"10.1007\/978-981-96-0085-4_31"},{"key":"8309_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.padiff.2025.101193","volume":"14","author":"R Nalini","year":"2025","unstructured":"Nalini R, Meena A, Rajendran L, Izadi M (2025) A nonlinear mathematical analysis of nanoparticle\u2019s velocity, temperature and concentration in magnetohydrodynamic convective flow. Partial Differ Equ Appl Math 14:101193. https:\/\/doi.org\/10.1016\/j.padiff.2025.101193","journal-title":"Partial Differ Equ Appl Math"},{"key":"8309_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijbiomac.2025.145438","volume":"319","author":"EV Dubrovin","year":"2025","unstructured":"Dubrovin EV, Barinov NA, Klinov DV (2025) Anomalous long- and short-scale behavior of DNA conformation on a highly charged monomolecular film at different ionic strength. Int J Biol Macromol 319:145438. https:\/\/doi.org\/10.1016\/j.ijbiomac.2025.145438","journal-title":"Int J Biol Macromol"},{"issue":"2","key":"8309_CR13","doi-asserted-by":"publisher","first-page":"39","DOI":"10.3390\/agriengineering7020039","volume":"7","author":"P Bodor-Pesti","year":"2025","unstructured":"Bodor-Pesti P, Nguyen LLP, Nguyen TB, Dam MS, Taranyi D, Baranyai L (2025) LeafLaminaMap: exploring leaf color patterns using RGB color indices. Agric Eng 7(2):39. https:\/\/doi.org\/10.3390\/agriengineering7020039","journal-title":"Agric Eng"},{"issue":"1","key":"8309_CR14","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1177\/0020720920980974","volume":"62","author":"A Fern\u00e1ndez-Guillam\u00f3n","year":"2021","unstructured":"Fern\u00e1ndez-Guillam\u00f3n A, Molina-Garc\u00eda A (2021) Simulation of variable speed wind turbines based on open-source solutions: application to bachelor and master degrees. Int J Electr Eng Educ 62(1):87\u2013109. https:\/\/doi.org\/10.1177\/0020720920980974","journal-title":"Int J Electr Eng Educ"},{"key":"8309_CR15","doi-asserted-by":"publisher","unstructured":"Baudin M, Steer S (2009) Optimization with Scilab, present and future. In: 2009 IEEE International Workshop on Open-Source Software for Scientific Computation (OSSC), pp 99\u2013106. https:\/\/doi.org\/10.1109\/OSSC.2009.5416860","DOI":"10.1109\/OSSC.2009.5416860"},{"key":"8309_CR16","doi-asserted-by":"publisher","unstructured":"Kudryashova AY, Semyonova TI, Frisk VV, Shakin VN (2020) Study of effectiveness of Scilab software means for solving optimization problems. In: 2020 Wave Electronics and Its Application in Information and Telecommunication Systems (WECONF), pp 1\u20135. https:\/\/doi.org\/10.1109\/WECONF48837.2020.9131166","DOI":"10.1109\/WECONF48837.2020.9131166"},{"key":"8309_CR17","doi-asserted-by":"publisher","unstructured":"Braun W, Gallardo\u00a0Yances S, Link K, Bachmann B (2012) Fast simulation of fluid models with colored Jacobians. In: Proceedings of the 9th International MODELICA Conference, September 3\u20135, 2012, Munich, Germany, MODELLICA, vol 76, pp 247\u2013252. https:\/\/doi.org\/10.3384\/ecp12076247","DOI":"10.3384\/ecp12076247"},{"issue":"4","key":"8309_CR18","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1137\/s0036144504444711","volume":"47","author":"AH Gebremedhin","year":"2005","unstructured":"Gebremedhin AH, Manne F, Pothen A (2005) What color is your Jacobian? Graph coloring for computing derivatives. SIAM Rev 47(4):629\u2013705. https:\/\/doi.org\/10.1137\/s0036144504444711","journal-title":"SIAM Rev"},{"key":"8309_CR19","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/j.cherd.2024.06.029","volume":"208","author":"JC Andrade","year":"2024","unstructured":"Andrade JC, Lobato FS, Neiro SMS, Libotte GB, Platt GM (2024) A novel multi-objective optimization strategy based on vibrating particle system algorithm applied to chemical process design. Chem Eng Res Des 208:161\u2013183. https:\/\/doi.org\/10.1016\/j.cherd.2024.06.029","journal-title":"Chem Eng Res Des"},{"key":"8309_CR20","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/j.cherd.2024.12.013","volume":"214","author":"R Murrieta-Due\u00f1as","year":"2025","unstructured":"Murrieta-Due\u00f1as R, Cortez-Gonz\u00e1lez J, Segovia-Hern\u00e1ndez JG, Hern\u00e1ndez-Aguirre A, Guti\u00e9rrez-Guerra R, Hern\u00e1ndez S (2025) A comparative analysis of differential evolution and Boltzmann-based distribution algorithms with constraint handling techniques for distillation process optimization. Chem Eng Res Des 214:39\u201353. https:\/\/doi.org\/10.1016\/j.cherd.2024.12.013","journal-title":"Chem Eng Res Des"},{"key":"8309_CR21","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.cherd.2024.12.021","volume":"214","author":"JM N\u00fa\u00f1ez-L\u00f3pez","year":"2025","unstructured":"N\u00fa\u00f1ez-L\u00f3pez JM, Segovia-Hern\u00e1ndez JG, S\u00e1nchez-Ram\u00edrez E, Ponce-Ortega JM (2025) Integrating metaheuristic methods and deterministic strategies for optimizing supply chain equipment design in process engineering. Chem Eng Res Des 214:93\u2013104. https:\/\/doi.org\/10.1016\/j.cherd.2024.12.021","journal-title":"Chem Eng Res Des"},{"key":"8309_CR22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cjche.2025.09.020","volume":"1","author":"C Xing","year":"2025","unstructured":"Xing C, Wu Y, Zhou X, Wu B, Chen K, Ji L (2025) An optimization strategy for complex distillation configurations to escape local optima and analysis of its occurrence. Chin J Chem Eng 1:1. https:\/\/doi.org\/10.1016\/j.cjche.2025.09.020","journal-title":"Chin J Chem Eng"},{"issue":"8","key":"8309_CR23","doi-asserted-by":"publisher","first-page":"4485","DOI":"10.1007\/s11831-024-10168-6","volume":"31","author":"EH Houssein","year":"2024","unstructured":"Houssein EH, Saeed MK, Hu G, Al-Sayed MM (2024) Metaheuristics for solving global and engineering optimization problems: review, applications, open issues and challenges. Archiv Comput Methods Eng 31(8):4485\u20134519. https:\/\/doi.org\/10.1007\/s11831-024-10168-6","journal-title":"Archiv Comput Methods Eng"},{"issue":"1","key":"8309_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11721-021-00202-9","volume":"16","author":"C Aranha","year":"2021","unstructured":"Aranha C, Camacho Villal\u00f3n CL, Campelo F, Dorigo M, Ruiz R, Sevaux M, S\u00f6rensen K, St\u00fctzle T (2021) Metaphor-based metaheuristics, a call for action: the elephant in the room. Swarm Intell 16(1):1\u20136. https:\/\/doi.org\/10.1007\/s11721-021-00202-9","journal-title":"Swarm Intell"},{"issue":"3","key":"8309_CR25","doi-asserted-by":"publisher","first-page":"1645","DOI":"10.1007\/s41870-023-01694-w","volume":"16","author":"D Kaushik","year":"2024","unstructured":"Kaushik D, Nadeem M (2024) Parameter tuning in metaheuristics: a bibliometric and gap analysis. Int J Inf Technol 16(3):1645\u20131651. https:\/\/doi.org\/10.1007\/s41870-023-01694-w","journal-title":"Int J Inf Technol"},{"key":"8309_CR26","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.compstruc.2014.03.007","volume":"139","author":"M-Y Cheng","year":"2014","unstructured":"Cheng M-Y, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98\u2013112. https:\/\/doi.org\/10.1016\/j.compstruc.2014.03.007","journal-title":"Comput Struct"},{"issue":"9","key":"8309_CR27","doi-asserted-by":"publisher","first-page":"1271","DOI":"10.1016\/S0098-1354(98)00011-8","volume":"22","author":"MH Bauer","year":"1998","unstructured":"Bauer MH, Stichlmair J (1998) Design and economic optimization of azeotropic distillation processes using mixed-integer nonlinear programming. Comput Chem Eng 22(9):1271\u20131286. https:\/\/doi.org\/10.1016\/S0098-1354(98)00011-8","journal-title":"Comput Chem Eng"},{"issue":"2","key":"8309_CR28","doi-asserted-by":"publisher","first-page":"752","DOI":"10.1021\/ie402232w","volume":"53","author":"MA Ramos","year":"2014","unstructured":"Ramos MA, G\u00f3mez JM, Reneaume J-M (2014) Simultaneous optimal design and control of an extractive distillation system for the production of fuel grade ethanol using a mathematical program with complementarity constraints. Ind Eng Chem Res 53(2):752\u2013764. https:\/\/doi.org\/10.1021\/ie402232w","journal-title":"Ind Eng Chem Res"},{"key":"8309_CR29","doi-asserted-by":"publisher","unstructured":"Frey T, Stichlmair J (2000) MINLP optimization of reactive distillation columns. In: Pierucci S (ed) European Symposium on Computer Aided Process Engineering-10. Computer Aided Chemical Engineering, vol 8, Elsevier, Milan, pp 115\u2013120. https:\/\/doi.org\/10.1016\/S1570-7946(00)80021-8 . https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1570794600800218","DOI":"10.1016\/S1570-7946(00)80021-8"},{"issue":"4","key":"8309_CR30","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/bf00934810","volume":"10","author":"AM Geoffrion","year":"1972","unstructured":"Geoffrion AM (1972) Generalized Benders decomposition. J Optim Theory Appl 10(4):237\u2013260. https:\/\/doi.org\/10.1007\/bf00934810","journal-title":"J Optim Theory Appl"},{"issue":"3","key":"8309_CR31","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/bf02592064","volume":"36","author":"MA Duran","year":"1986","unstructured":"Duran MA, Grossmann IE (1986) An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math Program 36(3):307\u2013339. https:\/\/doi.org\/10.1007\/bf02592064","journal-title":"Math Program"},{"issue":"9","key":"8309_CR32","doi-asserted-by":"publisher","first-page":"3088","DOI":"10.1021\/ie0711426","volume":"47","author":"T Farkas","year":"2008","unstructured":"Farkas T, Czuczai B, Rev E, Lelkes Z (2008) New MINLP model and modified Outer Approximation algorithm for distillation column synthesis. Ind Eng Chem Res 47(9):3088\u20133103. https:\/\/doi.org\/10.1021\/ie0711426","journal-title":"Ind Eng Chem Res"},{"issue":"4","key":"8309_CR33","doi-asserted-by":"publisher","first-page":"977","DOI":"10.3390\/pr13040977","volume":"13","author":"C Tian","year":"2025","unstructured":"Tian C, Zhang X, Lan Y, Sun J (2025) An enhanced logic-based Bender\u2019s decomposition algorithm with proximity principle for simulator-based distillation process optimization. Processes 13(4):977. https:\/\/doi.org\/10.3390\/pr13040977","journal-title":"Processes"},{"issue":"2","key":"8309_CR34","doi-asserted-by":"publisher","first-page":"34","DOI":"10.3390\/modelling6020034","volume":"6","author":"GM Platt","year":"2025","unstructured":"Platt GM, Azevedo OK, Oliveira FBS (2025) An optimal distillation process for turpentine separation using a Firefly algorithm. Modelling 6(2):34. https:\/\/doi.org\/10.3390\/modelling6020034","journal-title":"Modelling"},{"issue":"29\u201348","key":"8309_CR35","doi-asserted-by":"publisher","first-page":"x","DOI":"10.1016\/j.seppur.2022.121437","volume":"207","author":"P Furda","year":"2024","unstructured":"Furda P, Variny M, My\u0161iak J (2024) Parallel genetic algorithm interface II: a novel computational tool for accelerated simulation-based optimization. Chem Eng Res Des 207(29\u201348):x. https:\/\/doi.org\/10.1016\/j.seppur.2022.121437","journal-title":"Chem Eng Res Des"},{"key":"8309_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.seppur.2022.121437","volume":"297","author":"SR Pandit","year":"2022","unstructured":"Pandit SR, Jana AK (2022) Transforming conventional distillation sequence to dividing wall column: minimizing cost, energy usage and environmental impact through genetic algorithm. Sep Purif Technol 297:121437. https:\/\/doi.org\/10.1016\/j.seppur.2022.121437","journal-title":"Sep Purif Technol"},{"issue":"3","key":"8309_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/amp2.10095","volume":"3","author":"A Lee","year":"2021","unstructured":"Lee A, Ghouse JH, Eslick JC, Laird CD, Siirola JD, Zamarripa MA, Gunter D, Shinn JH, Dowling AW, Bhattacharyya D, Biegler LT, Burgard AP, Miller DC (2021) The IDAES process modeling framework and model library-flexibility for process simulation and optimization. J Adv Manuf Process 3(3):1. https:\/\/doi.org\/10.1002\/amp2.10095","journal-title":"J Adv Manuf Process"},{"issue":"3","key":"8309_CR38","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1016\/j.cherd.2012.09.005","volume":"91","author":"R Monroy-Loperena","year":"2013","unstructured":"Monroy-Loperena R, Vacahern M (2013) A simple, reliable and fast algorithm for the simulation of multicomponent distillation columns. Chem Eng Res Des 91(3):389\u2013395. https:\/\/doi.org\/10.1016\/j.cherd.2012.09.005","journal-title":"Chem Eng Res Des"},{"issue":"1","key":"8309_CR39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2513109.2513110","volume":"40","author":"AH Gebremedhin","year":"2013","unstructured":"Gebremedhin AH, Nguyen D, Patwary MMA, Pothen A (2013) ColPack: software for graph coloring and related problems in scientific computing. ACM Trans Math Softw 40(1):1\u201331. https:\/\/doi.org\/10.1145\/2513109.2513110","journal-title":"ACM Trans Math Softw"},{"key":"8309_CR40","doi-asserted-by":"crossref","unstructured":"Pal A, Holtorf F, Larsson A, Loman T, Utkarsh Sch\u00e4efer F, Qu Q, Edelman A, Rackauckas C (2025) NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia. https:\/\/arxiv.org\/abs\/2403.16341","DOI":"10.1145\/3779117"},{"issue":"17","key":"8309_CR41","doi-asserted-by":"publisher","first-page":"6010","DOI":"10.1021\/acs.iecr.2c00237","volume":"61","author":"IH Bell","year":"2022","unstructured":"Bell IH, Deiters UK, Leal AMM (2022) Implementing an equation of state without derivatives: teqp. Ind Eng Chem Res 61(17):6010\u20136027. https:\/\/doi.org\/10.1021\/acs.iecr.2c00237","journal-title":"Ind Eng Chem Res"},{"key":"8309_CR42","unstructured":"Laue S (2022) On the Equivalence of Automatic and Symbolic Differentiation . https:\/\/arxiv.org\/abs\/1904.02990"},{"key":"8309_CR43","unstructured":"Xu P, Gottlieb R, Tauqir W, Bollas G, Stube MD (2025) Automated symbolic thermodynamic modeling and global parameter estimation for brine electrolyte systems. In: 2025 AIChE Annual Meeting, AIChE, Boston, USA, p 530"},{"key":"8309_CR44","unstructured":"Yang S, Yang M, Du W (2023) A Novel Perspective Process Simulation Framework Based on Automatic Differentiation. https:\/\/arxiv.org\/abs\/2311.11129"},{"issue":"1","key":"8309_CR45","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1002\/aic.690140124","volume":"14","author":"H Renon","year":"1968","unstructured":"Renon H, Prausnitz JM (1968) Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J 14(1):135\u2013144. https:\/\/doi.org\/10.1002\/aic.690140124","journal-title":"AIChE J"},{"issue":"1","key":"8309_CR46","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1002\/aic.690210115","volume":"21","author":"DS Abrams","year":"1975","unstructured":"Abrams DS, Prausnitz JM (1975) Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J 21(1):116\u2013128. https:\/\/doi.org\/10.1002\/aic.690210115","journal-title":"AIChE J"},{"key":"8309_CR47","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.bdr.2016.10.002","volume":"8","author":"D Schmidt","year":"2017","unstructured":"Schmidt D, Chen W-C, Matheson MA, Ostrouchov G (2017) Programming with BIG data in R: scaling analytics from one to thousands of nodes. Big Data Res 8:1\u201311. https:\/\/doi.org\/10.1016\/j.bdr.2016.10.002","journal-title":"Big Data Res"},{"key":"8309_CR48","doi-asserted-by":"crossref","unstructured":"Langtangen HP, Cai X (2008) On the efficiency of Python for high-performance computing: a case study involving stencil updates for partial differential equations. In: Bock HG, Kostina E, Phu HX, Rannacher R (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, pp 337\u2013357","DOI":"10.1007\/978-3-540-79409-7_23"},{"key":"8309_CR49","doi-asserted-by":"publisher","DOI":"10.1016\/j.fluid.2023.114018","volume":"579","author":"R Privat","year":"2024","unstructured":"Privat R, Jaubert J-N, Kontogeorgis GM (2024) The secret of the Wilson equation. Fluid Phase Equilib 579:114018. https:\/\/doi.org\/10.1016\/j.fluid.2023.114018","journal-title":"Fluid Phase Equilib"},{"issue":"2","key":"8309_CR50","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1109\/tevc.2019.2921598","volume":"24","author":"C Huang","year":"2020","unstructured":"Huang C, Li Y, Yao X (2020) A survey of automatic parameter tuning methods for metaheuristics. IEEE Trans Evol Comput 24(2):201\u2013216. https:\/\/doi.org\/10.1109\/tevc.2019.2921598","journal-title":"IEEE Trans Evol Comput"},{"key":"8309_CR51","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2021.107779","volume":"236","author":"S Chakraborty","year":"2022","unstructured":"Chakraborty S, Nama S, Saha AK (2022) An improved symbiotic organisms search algorithm for higher dimensional optimization problems. Knowl Based Syst 236:107779. https:\/\/doi.org\/10.1016\/j.knosys.2021.107779","journal-title":"Knowl Based Syst"},{"key":"8309_CR52","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1016\/j.eswa.2018.10.045","volume":"119","author":"AE Ezugwu","year":"2019","unstructured":"Ezugwu AE, Prayogo D (2019) Symbiotic organisms search algorithm: theory, recent advances and applications. Expert Syst Appl 119:184\u2013209. https:\/\/doi.org\/10.1016\/j.eswa.2018.10.045","journal-title":"Expert Syst Appl"},{"issue":"3","key":"8309_CR53","doi-asserted-by":"publisher","first-page":"3998","DOI":"10.1007\/s11227-021-04015-9","volume":"78","author":"MJ Goldanloo","year":"2021","unstructured":"Goldanloo MJ, Gharehchopogh FS (2021) A hybrid OBL-based firefly algorithm with symbiotic organisms search algorithm for solving continuous optimization problems. J Supercomput 78(3):3998\u20134031. https:\/\/doi.org\/10.1007\/s11227-021-04015-9","journal-title":"J Supercomput"},{"issue":"8","key":"8309_CR54","doi-asserted-by":"publisher","first-page":"9102","DOI":"10.1007\/s11227-021-03626-6","volume":"77","author":"H Mohmmadzadeh","year":"2021","unstructured":"Mohmmadzadeh H, Gharehchopogh FS (2021) An efficient binary chaotic symbiotic organisms search algorithm approaches for feature selection problems. J Supercomput 77(8):9102\u20139144. https:\/\/doi.org\/10.1007\/s11227-021-03626-6","journal-title":"J Supercomput"},{"issue":"10","key":"8309_CR55","doi-asserted-by":"publisher","first-page":"11170","DOI":"10.1007\/s11227-023-05083-9","volume":"79","author":"P Zhao","year":"2023","unstructured":"Zhao P, Liu S (2023) An improved symbiotic organisms search algorithm with good point set and memory mechanism. J Supercomput 79(10):11170\u201311197. https:\/\/doi.org\/10.1007\/s11227-023-05083-9","journal-title":"J Supercomput"},{"issue":"1","key":"8309_CR56","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1504\/ijmheur.2018.091878","volume":"7","author":"GM Platt","year":"2018","unstructured":"Platt GM, Lima LVPC (2018) Azeotropy in a refrigerant system: a useful scenario to test and compare metaheuristics. Int J Metaheur 7(1):43. https:\/\/doi.org\/10.1504\/ijmheur.2018.091878","journal-title":"Int J Metaheur"},{"issue":"7","key":"8309_CR57","doi-asserted-by":"publisher","first-page":"0200030","DOI":"10.1371\/journal.pone.0200030","volume":"13","author":"AE Ezugwu","year":"2018","unstructured":"Ezugwu AE, Adeleke OJ, Viriri S (2018) Symbiotic organisms search algorithm for the unrelated parallel machines scheduling with sequence-dependent setup times. PLoS ONE 13(7):0200030. https:\/\/doi.org\/10.1371\/journal.pone.0200030","journal-title":"PLoS ONE"},{"key":"8309_CR58","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2020.113230","volume":"148","author":"D Liu","year":"2020","unstructured":"Liu D, Li H, Wang H, Qi C, Rose T (2020) Discrete symbiotic organisms search method for solving large-scale time-cost trade-off problem in construction scheduling. Expert Syst Appl 148:113230. https:\/\/doi.org\/10.1016\/j.eswa.2020.113230","journal-title":"Expert Syst Appl"},{"key":"8309_CR59","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2017\/8404231","volume":"2017","author":"B Crawford","year":"2017","unstructured":"Crawford B, Soto R, Astorga G, Garc\u00eda J, Castro C, Paredes F (2017) Putting continuous metaheuristics to work in binary search spaces. Complexity 2017:1\u201319. https:\/\/doi.org\/10.1155\/2017\/8404231","journal-title":"Complexity"},{"issue":"1\u20132","key":"8309_CR60","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s00158-003-0318-3","volume":"26","author":"G Venter","year":"2004","unstructured":"Venter G, Sobieszczanski-Sobieski J (2004) Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization. Struct Multidiscip Optim 26(1\u20132):121\u2013131. https:\/\/doi.org\/10.1007\/s00158-003-0318-3","journal-title":"Struct Multidiscip Optim"},{"issue":"8","key":"8309_CR61","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/S0141-9331(02)00053-4","volume":"26","author":"A Salman","year":"2002","unstructured":"Salman A, Ahmad I, Al-Madani S (2002) Particle swarm optimization for task assignment problem. Microprocess Microsyst 26(8):363\u2013371. https:\/\/doi.org\/10.1016\/S0141-9331(02)00053-4","journal-title":"Microprocess Microsyst"},{"key":"8309_CR62","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1016\/j.cherd.2023.04.041","volume":"194","author":"DN Chia","year":"2023","unstructured":"Chia DN, Duanmu F, Sorensen E (2023) Single- and multi-objective optimisation of hybrid distillation-pervaporation and dividing wall column structures. Chem Eng Res Des 194:280\u2013305. https:\/\/doi.org\/10.1016\/j.cherd.2023.04.041","journal-title":"Chem Eng Res Des"},{"key":"8309_CR63","doi-asserted-by":"publisher","unstructured":"Ezugwu AE, Els R, Fonou-Dombeu JV, Naidoo D, Pillay K (2019) Parallel Symbiotic Organisms Search Algorithm, Springer, Cham, pp 658\u2013672. https:\/\/doi.org\/10.1007\/978-3-030-24308-1_52","DOI":"10.1007\/978-3-030-24308-1_52"},{"key":"8309_CR64","unstructured":"Bradbury J, Frostig R, Hawkins P, Johnson MJ, Leary C, Maclaurin D, Necula G, Paszke A, VanderPlas J, Wanderman-Milne S, Zhang Q. JAX: Composable Transformations of Python+NumPy programs. http:\/\/github.com\/jax-ml\/jax"},{"key":"8309_CR65","doi-asserted-by":"publisher","unstructured":"Ismail M, Suh GE (2018) Quantitative overhead analysis for Python. In: 2018 IEEE International Symposium on Workload Characterization (IISWC), IEEE, Raleigh, NC, pp 36\u201347. https:\/\/doi.org\/10.1109\/IISWC.2018.8573512. https:\/\/ieeexplore.ieee.org\/document\/8573512\/","DOI":"10.1109\/IISWC.2018.8573512"},{"issue":"2","key":"8309_CR66","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1002\/spe.3267","volume":"54","author":"Q Zhang","year":"2024","unstructured":"Zhang Q, Xu L, Xu B (2024) Python meets JIT compilers: a simple implementation and a comparative evaluation. Softw Pract Exp 54(2):225\u2013256. https:\/\/doi.org\/10.1002\/spe.3267","journal-title":"Softw Pract Exp"},{"key":"8309_CR67","unstructured":"Lanaro G (2017) Python High Performance: Build High-Performing, Concurrent, and Distributed Applications, 2nd edn. Packt Publishing, Birmingham"},{"key":"8309_CR68","unstructured":"Kooijman H (2019) The ChemSep Book. Books on Demand, Hamburg"},{"issue":"1","key":"8309_CR69","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s00013-023-01858-x","volume":"121","author":"P Heid","year":"2023","unstructured":"Heid P (2023) A short note on an adaptive damped Newton method for strongly monotone and Lipschitz continuous operator equations. Arch Math 121(1):55\u201365. https:\/\/doi.org\/10.1007\/s00013-023-01858-x","journal-title":"Arch Math"},{"issue":"11","key":"8309_CR70","doi-asserted-by":"publisher","first-page":"775","DOI":"10.3390\/pr7110775","volume":"7","author":"C Tangsathitkulchai","year":"2019","unstructured":"Tangsathitkulchai C, Punsuwan N, Weerachanchai P (2019) Simulation of batch slow pyrolysis of biomass materials using the process-flow-diagram COCO simulator. Processes 7(11):775. https:\/\/doi.org\/10.3390\/pr7110775","journal-title":"Processes"},{"key":"8309_CR71","doi-asserted-by":"publisher","DOI":"10.1016\/j.rineng.2024.102239","volume":"22","author":"Y Alqaheem","year":"2024","unstructured":"Alqaheem Y, Alobaid M (2024) Development of a membrane process in CAPE-OPEN to CAPE-OPEN (COCO) simulator for carbon dioxide separation. Results Eng 22:102239. https:\/\/doi.org\/10.1016\/j.rineng.2024.102239","journal-title":"Results Eng"},{"key":"8309_CR72","doi-asserted-by":"publisher","first-page":"955","DOI":"10.3303\/CET25117160","volume":"117","author":"GAC Sousa","year":"2025","unstructured":"Sousa GAC, Miranda NT, Rezende AB, Nascimento UM, Maciel Filho R, Wolf Maciel MR (2025) Simulation of sugarcane bagasse pyrolysis using COCO simulator. Chem Eng Trans 117:955\u2013960. https:\/\/doi.org\/10.3303\/CET25117160","journal-title":"Chem Eng Trans"},{"key":"8309_CR73","doi-asserted-by":"publisher","unstructured":"Testard L, Belaud JP (2005) A CAPE-PEN based framework for process simulation solutions integration. In: Puigjaner L, Espu\u00f1a A (eds) European Symposium on Computer-Aided Process Engineering-15, 38th European Symposium of the Working Party on Computer Aided Process Engineering. Computer Aided Chemical Engineering, vol 20, Elsevier, Barcelona, pp 607\u2013612. https:\/\/doi.org\/10.1016\/S1570-7946(05)80223-8. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1570794605802238","DOI":"10.1016\/S1570-7946(05)80223-8"},{"issue":"3","key":"8309_CR74","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1590\/s0104-66321999000300004","volume":"16","author":"GM Platt","year":"1999","unstructured":"Platt GM, Medeiros JL (1999) Phase rule calculations and the thermodynamics of reactive systems under chemical equilibrium. Braz J Chem Eng 16(3):247\u2013265. https:\/\/doi.org\/10.1590\/s0104-66321999000300004","journal-title":"Braz J Chem Eng"},{"key":"8309_CR75","doi-asserted-by":"publisher","unstructured":"Joy G, Huyck C, Yang XS (2023) In: Yang XS (ed) Review of Parameter Tuning Methods for Nature-Inspired Algorithms, Springer, Singapore, pp 33\u201347. https:\/\/doi.org\/10.1007\/978-981-99-3970-1_3","DOI":"10.1007\/978-981-99-3970-1_3"},{"issue":"3\u20134","key":"8309_CR76","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1093\/biomet\/52.3-4.591","volume":"52","author":"SS Shapiro","year":"1965","unstructured":"Shapiro SS, Wilk MB (1965) An analysis of variance test for normality (complete samples). Biometrika 52(3\u20134):591\u2013611. https:\/\/doi.org\/10.1093\/biomet\/52.3-4.591","journal-title":"Biometrika"},{"issue":"1","key":"8309_CR77","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s13194-016-0146-0","volume":"7","author":"C Lisciandra","year":"2016","unstructured":"Lisciandra C (2016) Robustness analysis and tractability in modeling. Eur J Philos Sci 7(1):79\u201395. https:\/\/doi.org\/10.1007\/s13194-016-0146-0","journal-title":"Eur J Philos Sci"},{"issue":"1","key":"8309_CR78","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1093\/biomet\/72.1.45","volume":"72","author":"B Efron","year":"1985","unstructured":"Efron B (1985) Bootstrap confidence intervals for a class of parametric problems. Biometrika 72(1):45\u201358. https:\/\/doi.org\/10.1093\/biomet\/72.1.45","journal-title":"Biometrika"},{"issue":"3","key":"8309_CR79","doi-asserted-by":"publisher","first-page":"484","DOI":"10.3390\/pr12030484","volume":"12","author":"L Cong","year":"2024","unstructured":"Cong L, Liu D, Ling H (2024) Global modeling of heat-integrated distillation column based on limited local measurements. Processes 12(3):484. https:\/\/doi.org\/10.3390\/pr12030484","journal-title":"Processes"},{"key":"8309_CR80","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2020.113907","volume":"165","author":"YA Baysal","year":"2021","unstructured":"Baysal YA, Ketenci S, Altas IH, Kayikcioglu T (2021) Multi-objective symbiotic organism search algorithm for optimal feature selection in brain computer interfaces. Expert Syst Appl 165:113907. https:\/\/doi.org\/10.1016\/j.eswa.2020.113907","journal-title":"Expert Syst Appl"},{"issue":"9","key":"8309_CR81","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1007\/s10586-025-05223-1","volume":"28","author":"AO Abdulsalami","year":"2025","unstructured":"Abdulsalami AO, Gharehchopogh FS, Elaziz MA, Xiong S (2025) Multi-objective heterogeneous comprehensive learning symbiotic organism search with application to convolutional neural network pruning. Clust Comput 28(9):578. https:\/\/doi.org\/10.1007\/s10586-025-05223-1","journal-title":"Clust Comput"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-026-08309-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-026-08309-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-026-08309-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T03:57:32Z","timestamp":1771559852000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-026-08309-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,20]]},"references-count":81,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["8309"],"URL":"https:\/\/doi.org\/10.1007\/s11227-026-08309-8","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,20]]},"assertion":[{"value":"5 October 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 February 2026","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 no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"184"}}