Improving kinetic model fitting for total titratable acidity in bananas using genetic algorithms
DOI:
https://doi.org/10.54167/tch.v19iEspecial.1847Keywords:
ripening kinetics, genetic algorithms, parameter estimation, post-harvest modeling, TTA decreasing, food qualityAbstract
This research aimed to automate the fitting of kinetic models using genetic algorithms (GAs) to optimize the estimation of kinetic parameters—the reaction rate constant (k) and the initial value of total titratable acidity (TTA, C₀)—and enhance predictive accuracy. Experimental data were collected from bananas (Musa paradisiaca L.) at ripening stage 2 on Von Loesecke scale, measuring TTA at specific intervals, and three kinetic models—zero-order, first-order, and second-order—were fitted. For optimization, Python-based GA was used to minimize the mean squared error (MSE) and evaluate performance based on R2, AIC, and BIC. Results indicated that while the zero-order model provided the best statistical fit (R2 = 0.918, lowest AIC and BIC), validation on unseen data favored the second-order model, which exhibited superior predictive accuracy (test R2 = 0.9349, lowest test MSE). The integration of GAs enhanced the robustness of kinetic fitting by effectively navigating parameter space and avoiding local minima, outperforming traditional optimization methods, demonstrating their ability to refine parameter estimation and improve model generalization. Future research should explore hybrid models that combine mechanistic kinetic equations with machine learning techniques (e.g., neural networks, or support vector regression), to better capture the biochemical processes underlying acidity changes in bananas.
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Alonso-Salinas, R., López-Miranda, S., Pérez-López, A. J., & Acosta-Motos, J. R. (2024). Strategies to Delay Ethylene-Mediated Ripening in Climacteric Fruits: Implications for Shelf Life Extension and Postharvest Quality. Horticulturae, 10(8): 840. https://doi.org/10.3390/horticulturae10080840
Aquino, C. F., Salomão, L. C. C., Cecon, P. R., Siqueira2, D. L. D., & Ribeiro, S. M. R. (2017). Physical, Chemical and Morphological Characteristics of Banana Cultivars Depending on Maturation Stages. Revista Caatinga, 30(1): 87–96. https://doi.org/10.1590/1983-21252017v30n110rc
Bao, Y., Zhou, Z., Lu, H., Luo, Y., & Shen, H. (2013). Modelling quality changes in S ongpu mirror carp (Cyprinus carpio) fillets stored at chilled temperatures: Comparison between A rrhenius model and log‐logistic model. International Journal of Food Science & Technology, 48(2): 387–393. https://doi.org/10.1111/j.1365-2621.2012.03200.x
Batista-Silva, W., Nascimento, V. L., Medeiros, D. B., Nunes-Nesi, A., Ribeiro, D. M., Zsögön, A., & Araújo, W. L. (2018). Modifications in Organic Acid Profiles During Fruit Development and Ripening: Correlation or Causation? Frontiers in Plant Science, 9: 1689. https://doi.org/10.3389/fpls.2018.01689
Brewer, M. J., Butler, A., & Cooksley, S. L. (2016). The relative performance of AIC, AICC and BIC in the presence of unobserved heterogeneity. Methods in Ecology and Evolution, 7(6): 679–692. https://doi.org/10.1111/2041-210X.12541
Buehler, E. A., & Mesbah, A. (2016). Kinetic Study of Acetone-Butanol-Ethanol Fermentation in Continuous Culture. PLOS ONE, 11(8): e0158243. https://doi.org/10.1371/journal.pone.0158243
Casorzo, G., Ferrão, L. F., Adunola, P., Tavares Flores, E., Azevedo, C., Amadeu, R., & Munoz, P. R. (2024). Understanding the genetic basis of blueberry postharvest traits to define better breeding strategies. G3: Genes, Genomes, Genetics, 14(9): jkae163. https://doi.org/10.1093/g3journal/jkae163
Chai, K., Xia, W., Shen, R., Luo, G., Cheng, Y., Su, W., & Su, A. (2024). Optimization of heterogeneous continuous flow hydrogenation using FTIR inline analysis: A comparative study of multi-objective Bayesian optimization and kinetic modeling. Chemistry. https://doi.org/10.26434/chemrxiv-2024-m0kf5
Chakrabarti, A., Miskovic, L., Soh, K. C., & Hatzimanikatis, V. (2013). Towards kinetic modeling of genome‐scale metabolic networks without sacrificing stoichiometric, thermodynamic and physiological constraints. Biotechnology Journal, 8(9): 1043–1057. https://doi.org/10.1002/biot.201300091
Coelho De Queiroz, L. G., Oliveira De Jesus, M., Aguiar, F. S., Paraizo, E. A., Soares, M. D. C., Da Silva Pinheiro, J. M., Mizobutsi, G. P., Mendes Rodrigues, M. L., & Santos, T. C. (2019). Influence of Different ‘Prata-Anã’ Banana Bunch Ages on Post-Harvest Quality. Journal of Experimental Agriculture International, 1–14. https://doi.org/10.9734/jeai/2019/v36i130227
Collenteur, R. A. (2021). How Good Is Your Model Fit? Weighted Goodness‐of‐Fit Metrics for Irregular Time Series. Groundwater, 59(4): 474–478. https://doi.org/10.1111/gwat.13111
Contreras-López, E., Jaimez-Ordaz, J., Ugarte-Bautista, I., Ramírez-Godínez, J., González-Olivares, L. G., García-Curiel, L., & Pérez-Flores, J. G. (2022). Use of image analysis to determine the shelf-life of an apple compote with wine. Food Science and Technology, 42, e04122. https://doi.org/10.1590/fst.04122
Cordenunsi-Lysenko, B. R., Nascimento, J. R. O., Castro-Alves, V. C., Purgatto, E., Fabi, J. P., & Peroni-Okyta, F. H. G. (2019). The Starch Is (Not) Just Another Brick in the Wall: The Primary Metabolism of Sugars During Banana Ripening. Frontiers in Plant Science, 10: 391. https://doi.org/10.3389/fpls.2019.00391
Corrales, J. D., Munilla, S., & Cantet, R. J. C. (2015). Polynomial order selection in random regression models via penalizing adaptively the likelihood. Journal of Animal Breeding and Genetics, 132(4): 281–288. https://doi.org/10.1111/jbg.12130
De Souza, F. G., De Araújo, F. F., Orlando, E. A., Rodrigues, F. M., Chávez, D. W. H., Pallone, J. A. L., Neri-Numa, I. A., Sawaya, A. C. H. F., & Pastore, G. M. (2022). Characterization of Buritirana (Mauritiella armata) Fruits from the Brazilian Cerrado: Biometric and Physicochemical Attributes, Chemical Composition and Antioxidant and Antibacterial Potential. Foods, 11(6): 786. https://doi.org/10.3390/foods11060786
De-Graft H., A. (2017). The Effect of Outliers on the Performance of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) in Selection of an Asymmetric Price Relationship. Russian Journal of Agricultural and Socio-Economic Sciences, 65(5): 32–37. https://doi.org/10.18551/rjoas.2017-05.05
Dong, F., Zhang, Y., & Yang, J. (2017). Attention-based Recurrent Convolutional Neural Network for Automatic Essay Scoring. Proceedings of the 21st Conference on Computational Natural Language Learning (CoNLL 2017), 153–162. https://doi.org/10.18653/v1/K17-1017
Dos Santos, E. X., Santana, P. J. A., Diniz, A. C. C., Sanches, A. G., & Cordeiro, C. A. M. (2019). Postharvest technologies in the ripening of ‘Maçã’ bananas stored in ambient condition. Amazonian Journal of Plant Research, 3(1): 290–297. https://doi.org/10.26545/ajpr.2019.b00036x
Fischer, S. H., De Oliveira, J. A. A., Mumford, J. D., & Kell, L. T. (2021). Using a genetic algorithm to optimize a data-limited catch rule. ICES Journal of Marine Science, 78(8): 3013–3014. https://doi.org/10.1093/icesjms/fsab070
Gao, L., Zhao, S., Lu, X., He, N., Zhu, H., Dou, J., & Liu, W. (2018). Comparative transcriptome analysis reveals key genes potentially related to soluble sugar and organic acid accumulation in watermelon. PLOS ONE, 13(1): e0190096. https://doi.org/10.1371/journal.pone.0190096
García-Curiel, L., Pérez-Flores, J. G., Contreras-López, E., Pérez-Escalante, E., & Hernández-Hernández, A. A. (2023). Anthocyanin content prediction in frozen strawberry puree. Italian Journal of Food Science, 35(2): 88–97. https://doi.org/10.15586/ijfs.v35i2.2315
García-Gómez, B. E., Salazar, J. A., Nicolás-Almansa, M., Razi, M., Rubio, M., Ruiz, D., & Martínez-Gómez, P. (2020). Molecular Bases of Fruit Quality in Prunus Species: An Integrated Genomic, Transcriptomic, and Metabolic Review with a Breeding Perspective. International Journal of Molecular Sciences, 22(1): 333. https://doi.org/10.3390/ijms22010333
González-Agüero, M., Tejerina Pardo, L., Zamudio, M., Contreras, C., Undurraga, P., & Defilippi, B. (2016). The Unusual Acid-Accumulating Behavior during Ripening of Cherimoya (Annona cherimola Mill.) is Linked to Changes in Transcription and Enzyme Activity Related to Citric and Malic Acid Metabolism. Molecules, 21(5): 398. https://doi.org/10.3390/molecules21050398
Guo, Z., Ge, X., Yu, Q. L., Han, L., Zhao, H., & Cao, H. (2018). Quality predictive models for bovine liver during storage and changes in volatile flavors. International Journal of Food Properties, 21(1): 2452–2468. https://doi.org/10.1080/10942912.2018.1522330
Gutierrez-Aguirre, B. R., Llave-Davila, R. E., Olivera-Montenegro, L. A., Herrera-Nuñez, E., & Marzano-Barreda, L. A. (2023). Effect of Potassium Permanganate as an Ethylene Scavenger and Physicochemical Characterization during the Shelf Life of Fresh Banana (Musa paradisiaca). International Journal of Food Science, 2023: 1–7. https://doi.org/10.1155/2023/4650023
Hazrat, M. A., Rasul, M. G., Khan, M. M. K., Ashwath, N., Silitonga, A. S., Fattah, I. M. R., & Mahlia, T. M. I. (2022). Kinetic Modelling of Esterification and Transesterification Processes for Biodiesel Production Utilising Waste-Based Resource. Catalysts, 12(11): 1472. https://doi.org/10.3390/catal12111472
Hoekstra, R. H. A., Epskamp, S., Nierenberg, A., Borsboom, D., & McNally, R. J. (2023). Testing similarity in longitudinal networks: The Individual Network Invariance Test (INIT). PsyArXiv. https://doi.org/10.31234/osf.io/ugs2r
Jaimez-Ordaz, J., Pérez-Flores, J. G., Castañeda-Ovando, A., González-Olivares, L. G., Añorve-Morga, J., & Contreras-López, E. (2019). Kinetic parameters of lipid oxidation in third generation (3G) snacks and its influence on shelf-life. Food Science and Technology, 39(1): 136–140. https://doi.org/10.1590/fst.38917
Jiang, W., Zhang, M., He, J., & Zhou, L. (2004). Regulation of 1-MCP-Treated Banana Fruit Quality by Exogenous Ethylene and Temperature. Food Science and Technology International, 10(1): 15–20. https://doi.org/10.1177/1082013204042189
Jiang, X., Liu, K., Peng, H., Fang, J., Zhang, A., Han, Y., & Zhang, X. (2023). Comparative network analysis reveals the dynamics of organic acid diversity during fruit ripening in peach (Prunus persica L. Batsch). BMC Plant Biology, 23(1): 16.
Jorayev, P., Russo, D., Tibbetts, J. D., Schweidtmann, A. M., Deutsch, P., Bull, S. D., & Lapkin, A. A. (2022). Multi-objective Bayesian optimisation of a two-step synthesis of p-cymene from crude sulphate turpentine. Chemical Engineering Science, 247: 116938. https://doi.org/10.1016/j.ces.2021.116938
Kaczmarek, A., & Muzolf-Panek, M. (2021). Prediction of Thiol Group Changes in Minced Raw and Cooked Chicken Meat with Plant Extracts—Kinetic and Neural Network Approaches. Animals, 11(6): 1647. https://doi.org/10.3390/ani11061647
Kaka, A. K., Kumar, E. A., Ibupoto, K. A., Chattha, A. H., Soomro, S. A., Mangio, H. U. R., Junejo, S. A., Soomro, A. H., Khaskheli, S. G., & Kaka, S. K. (2019). Effect of hot water treatments and storage period on the quality attributes of banana (Musa sp.) fruit. Pure and Applied Biology, 7(4). https://doi.org/10.19045/bspab.2018.700195
Khodabakhshian, R., & Baghbani, R. (2021). Classification of bananas during ripening using peel roughness analysis—An application of atomic force microscopy to food process. Journal of Food Process Engineering, 44(11): e13857. https://doi.org/10.1111/jfpe.13857
Koop, L., Ramos, N. M. D. V., Bonilla-Petriciolet, A., Corazza, M. L., & Voll, F. A. P. (2024). A Review of Stochastic Optimization Algorithms Applied in Food Engineering. International Journal of Chemical Engineering, 2024: 1–31. https://doi.org/10.1155/2024/3636305
Kousaalya, A. B., Beyene, S. D., Ayalew, B., & Pilla, S. (2019). Epoxidation Kinetics of High-Linolenic Triglyceride Catalyzed by Solid Acidic-Ion Exchange Resin. Scientific Reports, 9(1): 8987. https://doi.org/10.1038/s41598-019-45458-8
Lei, Z., Zhang, Y., & Cui, P. (2018). Investigate the kinetics of coke solution loss reaction with an alkali metal as a catalyst based on the improved genetic algorithm. International Journal of Coal Science & Technology, 5(4): 430–438. https://doi.org/10.1007/s40789-017-0176-z
López-Pérez, P. A., Cuervo-Parra, J. A., Robles-Olvera, V. J., Del C Rodriguez Jimenes, G., Pérez España, V. H., & Romero-Cortes, T. (2018). Development of a Novel Kinetic Model for Cocoa Fermentation Applying the Evolutionary Optimization Approach. International Journal of Food Engineering, 14(5–6): 20170206. https://doi.org/10.1515/ijfe-2017-0206
Luciano, G., & Svoboda, R. (2024). Simulation and non-linear optimization of kinetic models for solid-state processes. Modelling and Simulation in Materials Science and Engineering, 32(3): 035014. https://doi.org/10.1088/1361-651X/ad2788
Manzhula, V., Dyvak, M., & Zabchuk, V. (2024). The Improved Method for Identifying Parameters of Interval Nonlinear Models of Static Systems. International Journal of Computing, 23(1): 19-25. https://doi.org/10.47839/ijc.23.1.3431
Mírian L. F. Freitas & T. H. B. F. (2019). Production, physical, chemical and sensory evaluation of dried banana (Musa cavendish). Emirates Journal of Food and Agriculture, 31(2):102–108. https://doi.org/10.9755/ejfa.2019.v31.i2.1912
Nguyen, V. P., Tran, H. X. N., & Phan, T. L. K. (2023). Effect of pre-treatments on qualities and storage life of banana dried by using solar dryer dome. IOP Conference Series: Earth and Environmental Science, 1155(1): 012020. https://doi.org/10.1088/1755-1315/1155/1/012020
Nirere, A., Sun, J., Kama, R., Atindana, V. A., Nikubwimana, F. D., Dusabe, K. D., & Zhong, Y. (2023). Nondestructive detection of adulterated wolfberry (Lycium Chinens) fruits based on hyperspectral imaging technology. Journal of Food Process Engineering, 46(4): e14293. https://doi.org/10.1111/jfpe.14293
Novita, M., Husna, N. E., & Alfiana, D. (2024). The Use of Chitosan and Beeswax Coatings on Berangan Banana (Musa paradisiaca) in Different Maturity Stages. IOP Conference Series: Earth and Environmental Science, 1290(1): 012049. https://doi.org/10.1088/1755-1315/1290/1/012049
Odediran, A., Yu, J., & Gu, S. (2023). The effect of layers of high tunnel covering and soil mulching on tomato fruit quality. Journal of the Science of Food and Agriculture, 103(14): 7176–7186. https://doi.org/10.1002/jsfa.12805
Olivera, D. F., Bambicha, R., Laporte, G., Cárdenas, F. C., & Mestorino, N. (2013). Kinetics of colour and texture changes of beef during storage. Journal of Food Science and Technology, 50(4): 821–825. https://doi.org/10.1007/s13197-012-0885-7
Onik, J. C., Xie, Y., Duan, Y., Hu, X., Wang, Z., & Lin, Q. (2019). UV-C treatment promotes quality of early ripening apple fruit by regulating malate metabolizing genes during postharvest storage. PLOS ONE, 14(4): e0215472. https://doi.org/10.1371/journal.pone.0215472
Ozbuyukkaya, G., Parker, R. S., & Veser, G. (2022). Determining robust reaction kinetics from limited data. AIChE Journal, 68(3): e17538. https://doi.org/10.1002/aic.17538
Pandey, S. K., Rathee, D., & Tripathi, A. K. (2020). Software defect prediction using K-PCA and various kernel-based extreme learning machine: An empirical study. IET Software, 14(7): 768–782. https://doi.org/10.1049/iet-sen.2020.0119
Poonnakasem, N., Laohasongkram, K., Chaiwanichsiri, S., & Prinyawiwatkul, W. (2018). Changes in physicochemical properties and starch crystallinity of sponge cake containing HPMC and extra virgin coconut oil during room temperature storage. Journal of Food Processing and Preservation, 42(5): e13600. https://doi.org/10.1111/jfpp.13600
Razdan, N. K., Lin, T. C., & Bhan, A. (2023). Concepts Relevant for the Kinetic Analysis of Reversible Reaction Systems. Chemical Reviews, 123(6): 2950–3006. https://doi.org/10.1021/acs.chemrev.2c00510
Rivera, E. C., Summerscales, R. L., Tadi Uppala, P. P., & Kwon, H. J. (2020). Electrochemiluminescence Mechanisms Investigated with Smartphone‐Based Sensor Data Modeling, Parameter Estimation and Sensitivity Analysis. ChemistryOpen, 9(8): 854–863. https://doi.org/10.1002/open.202000165
Rooban, R., Shanmugam, M., Venkatesan, T., & Tamilmani, C. (2016). Physiochemical changes during different stages of fruit ripening of climacteric fruit of mango (Mangifera indica L.) and non-climacteric of fruit cashew apple (Anacardium occidentale L.). Journal of Applied and Advanced Research, 1(2): 53–58. https://doi.org/10.21839/jaar.2016.v1i2.27
Salehi, F. (2019). Recent Advances in the Modeling and Predicting Quality Parameters of Fruits and Vegetables during Postharvest Storage: A Review. International Journal of Fruit Science, 20(3): 506–520. https://doi.org/10.1080/15538362.2019.1653810
Sivakumar, M., Parthasarathy, S., & Padmapriya, T. (2024). Trade-off between training and testing ratio in machine learning for medical image processing. PeerJ Computer Science, 10: e2245. https://doi.org/10.7717/peerj-cs.2245
Souza, D. G., Resende, O., Moura, L. C. D., Ferreira Junior, W. N., & Andrade, J. W. D. S. (2019). Drying Kinetics of the Sliced Pulp of Biofortified Sweet Potato (Ipomoea batatas L.). Engenharia Agrícola, 39(2): 176–181. https://doi.org/10.1590/1809-4430-eng.agric.v39n2p176-181/2019
Stangierski, J., Weiss, D., & Kaczmarek, A. (2019). Multiple regression models and Artificial Neural Network (ANN) as prediction tools of changes in overall quality during the storage of spreadable processed Gouda cheese. European Food Research and Technology, 245(11): 2539–2547. https://doi.org/10.1007/s00217-019-03369-y
Taylor, C. J., Felton, K. C., Wigh, D., Jeraal, M. I., Grainger, R., Chessari, G., Johnson, C. N., & Lapkin, A. A. (2023). Accelerated Chemical Reaction Optimization Using Multi-Task Learning. ACS Central Science, 9(5): 957–968. https://doi.org/10.1021/acscentsci.3c00050
Thakur, R., Pristijono, P., Bowyer, M., Singh, S. P., Scarlett, C. J., Stathopoulos, C. E., & Vuong, Q. V. (2019). A starch edible surface coating delays banana fruit ripening. LWT, 100: 341–347. https://doi.org/10.1016/j.lwt.2018.10.055
Tijskens, L. M. M., Dos Santos, N., Obando-Ulloa, J. M., Moreno, E., Schouten, R. E., García-Mas, J., Monforte, A. J., & Fernández-Trujillo, J. P. (2008). First Attempts of Linking Modelling, Postharvest Behaviour and Melon Genetics. Acta Horticulturae, 802: 401–408. https://doi.org/10.17660/ActaHortic.2008.802.53
Ton Nu, P. T., & Kobayashi, T. (2020). Nylon-6–Mordenite Composite Membranes for Adsorption of Ethylene Gas Released from Chiquita Bananas. Industrial & Engineering Chemistry Research, 59(17): 8212–8222. https://doi.org/10.1021/acs.iecr.9b06149
Turgut, H. (2018). Artificial Intelligence Algorithms Inspired By Life Sciences. Journal of the Turkish Chemical Society Section A: Chemistry, 5(3): 1233–1238. https://doi.org/10.18596/jotcsa.471300
Umbarkar, A. J., Joshi, M. S., & Sheth, P. D. (2015). Dual Population Genetic Algorithm for Solving Constrained Optimization Problems. International Journal of Intelligent Systems and Applications, 7(2): 34–40. https://doi.org/10.5815/ijisa.2015.02.05
Vaga, S., Bernardo‐Faura, M., Cokelaer, T., Maiolica, A., Barnes, C. A., Gillet, L. C., Hegemann, B., Van Drogen, F., Sharifian, H., Klipp, E., Peter, M., Saez‐Rodriguez, J., & Aebersold, R. (2014). Phosphoproteomic analyses reveal novel cross‐modulation mechanisms between two signaling pathways in yeast. Molecular Systems Biology, 10(12): 767. https://doi.org/10.15252/msb.20145112
Vrieze, S. I. (2012). Model selection and psychological theory: A discussion of the differences between the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Psychological Methods, 17(2): 228–243. https://doi.org/10.1037/a0027127
Wawrzyniak, J. (2023). Predictive Assessment of Mycological State of Bulk-Stored Barley Using B-Splines in Conjunction with Genetic Algorithms. Applied Sciences, 13(9): 5264. https://doi.org/10.3390/app13095264
Wei, W., Yang, Y., Wu, C., Kuang, J., Chen, J., Lu, W., & Shan, W. (2023). MaMADS1–MaNAC083 transcriptional regulatory cascade regulates ethylene biosynthesis during banana fruit ripening. Horticulture Research, 10(10): uhad177. https://doi.org/10.1093/hr/uhad177
Wrzecionek, M., Matyszczak, G., Bandzerewicz, A., Ruśkowski, P., & Gadomska-Gajadhur, A. (2021). Kinetics of Polycondensation of Citric Acid with Glycerol Based on a Genetic Algorithm. Organic Process Research & Development, 25(2): 271–281. https://doi.org/10.1021/acs.oprd.0c00492
Xu, T. (2022). Reflection on Randomness from an Interdisciplinary Perspective. SHS Web of Conferences, 148: 02001. https://doi.org/10.1051/shsconf/202214802001
Xue, H., Qi, T., Su, W., Wu, K.-J., & Su, A. (2023). Heterogeneous Continuous Flow Hydrogenation of Hexafluoroacetone Trihydrate and Its Kinetic Modeling. Industrial & Engineering Chemistry Research, acs.iecr.3c00291. https://doi.org/10.1021/acs.iecr.3c00291
Yang, J., & Xu, Y. (2021). Prediction of fruit quality based on the RGB values of time–temperature indicator. Journal of Food Science, 86(3): 932–941. https://doi.org/10.1111/1750-3841.15518
Zarejousheghani, F., Kariminia, H., & Khorasheh, F. (2016). Kinetic modelling of enzymatic biodiesel production from castor oil: Temperature dependence of the Ping Pong parameters. The Canadian Journal of Chemical Engineering, 94(3): 512–517. https://doi.org/10.1002/cjce.22408
Zhang, Y., & Meng, G. (2023). Simulation of an Adaptive Model Based on AIC and BIC ARIMA Predictions. Journal of Physics: Conference Series, 2449(1): 012027. https://doi.org/10.1088/1742-6596/2449/1/012027
Zhao, X., Yuan, X., Chen, S., Fu, D.-Q., & Jiang, C.-Z. (2019). Metabolomic and Transcriptomic Analyses Reveal That a MADS-Box Transcription Factor TDR4 Regulates Tomato Fruit Quality. Frontiers in Plant Science, 10: 792. https://doi.org/10.3389/fpls.2019.00792
Zhong, W., & Tian, Z. (2011). Application of Genetic Algorithm in Chemical Reaction Kinetics. Applied Mechanics and Materials, 79: 71–76. https://doi.org/10.4028/www.scientific.net/AMM.79.71
Zhou, X., Cheng, J., Sun, J., Guo, S., Guo, X., Chen, Q., Wang, X., Zhu, X., & Liu, B. (2023). Effect of Red Visible Lighting on Postharvest Ripening of Bananas via the Regulation of Energy Metabolism. Horticulturae, 9(7): 840. https://doi.org/10.3390/horticulturae9070840
Zomo, S. A., Ismail, S. M., Jahan, M. S., Kabir, K., & Kabir, M. H. (2015). Chemical Properties and Shelf Life of Banana (Musa sapientum L.) as Influenced by Different Postharvest Treatments. The Agriculturists, 12(2): 06–17. https://doi.org/10.3329/agric.v12i2.21725
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