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TECNOCIENCIA CHIHUAHUA, Vol. XIX (Special Issue): e1847 (2025)
https://vocero.uach.mx/index.php/tecnociencia
ISSN-e: 2683-3360
Artículo Científico
Improving kinetic model fitting for total titratable
acidity in bananas using genetic algorithms
Mejora del ajuste del modelo cinético de la acidez titulable total en
bananos mediante algoritmos genéticos
*Corresponding author email: jesus_perez@uaeh.edu.mx (Jesús Guadalupe Pérez-Flores)
DOI: https://doi.org/10.54167/tch.v19iEspecial.1847
Recibido: 21 de febrero de 2025; Aceptado: 22 de mayo de 2025
Publicado por la Universidad Autónoma de Chihuahua, a través de la Dirección de Investigación y Posgrado.
Editor de Sección: Dr. César Ozuna-López
Abstract
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
Alejandro Kevin Méndez-Castillo 1, Elizabeth Contreras-López1, Jesús Guadalupe Pérez-
Flores 2,3*, Laura García-Curiel 2, Emmanuel Pérez-Escalante1, Karla Soto-Vega1, Carlos Ángel-
Jijón1 y Alicia Cervantes-Elizarrarás3
1 Área Académica de Química, Instituto de Ciencias Básicas e Ingeniería, Universidad Autónoma del
Estado de Hidalgo, Carretera Pachuca-Tulancingo km 4.5, 42184 Mineral de la Reforma, Hidalgo, México.
2Área Académica de Enfermería, Instituto de Ciencias de la Salud, Universidad Autónoma del Estado de
Hidalgo, Circuito Ex Hacienda La Concepción S/N, Carretera Pachuca-Actopan, 42060 San Agustín
Tlaxiaca, Hidalgo, México.
3Área Académica de Nutrición, Instituto de Ciencias de la Salud, Universidad Autónoma del Estado de
Hidalgo, Circuito Ex Hacienda La Concepción S/N, Carretera Pachuca-Actopan, 42060 San Agustín
Tlaxiaca, Hidalgo, México.
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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.
Keywords: ripening kinetics, genetic algorithms, parameter estimation, post-harvest modeling,
TTA decreasing, food quality.
Resumen
Esta investigación tuvo como objetivo automatizar el ajuste de modelos cinéticos mediante
algoritmos genéticos (AG) para optimizar la estimación de los parámetros cinéticos — constante de
velocidad de reacción (k) y valor inicial de la acidez total titulable (ATT, C₀)—, y mejorar la precisión
predictiva. Se obtuvieron datos de ATT de plátanos (Musa paradisiaca L.) en etapa 2 de maduración,
según la escala de Von Loesecke, y se ajustaron los modelos cinéticos de orden cero, de primer y
segundo orden. Se implementó AG en Python para minimizar el error cuadrático medio (MSE) y
evaluar el desempeño en función de R2, AIC y BIC. Los resultados muestran mejor ajuste (R2 = 0.918,
menor AIC y BIC) en el modelo de orden cero, mientras que la validación con datos no vistos
favoreció al de segundo orden (R2 = 0.9349, menor MSE). La integración de AG mejoró la robustez
del ajuste cinético, demostrando mejor estimación de parámetros y la generalización del modelo.
Investigaciones futuras deberían explorar modelos que combinan ecuaciones cinéticas mecanicistas
con técnicas de aprendizaje automático (por ejemplo, redes neuronales o regresión de vectores de
soporte), para capturar mejor los procesos bioquímicos subyacentes a los cambios de acidez en
plátanos.
Palabras clave: cinética de maduración, algoritmos genéticos, estimación de parámetros,
modelado poscosecha, disminución de TTA, calidad de los alimentos.
1. Introduction
The kinetic analysis allows for monitoring and predicting food quality changes during storage,
making it highly valuable in food research and industry. By using kinetic models to study
parameters like total titratable acidity (TTA), scientists can quantify quality loss and establish shelf-
life based on the degradation of food products (Contreras-López et al., 2022; Poonnakasem et al.,
2018; Olivera et al., 2013). These models effectively describe changes in texture and color in various
foods, providing insights into degradation rates and the effects of environmental factors (Yang and
Xu, 2021; Jaimez-Ordaz et al., 2019). Additionally, integrating kinetic models with sensory
evaluations and quality assessments enables the development of comprehensive tools for quality
management, helping the industry meet regulatory standards and consumer expectations
(Kaczmarek and Muzolf-Panek, 2021; Stangierski et al., 2019; Guo et al., 2018). This predictive
capability ensures product quality, enhances consumer satisfaction, and supports the industry’s
commitment to safety, innovation, and sustainability by reducing postharvest losses and improving
resource efficiency through informed decision-making. TTA, in particular, is a relevant quality
indicator because it reflects changes in organic acid content. These changes influence flavor,
freshness perception, and microbial stability and are directly associated with ripeness and
senescence (Odediran et al., 2023; De Souza et al., 2022). However, despite the growing interest in
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modeling quality changes in fruits, limited studies have focused on automating the parameter
optimization process using genetic algorithms (GAs) specifically for titratable acidity kinetics in
climacteric fruits. This study addresses this gap by presenting a replicable and structured
computational framework for fitting kinetic models, applied to bananas as a representative system.
Bananas (Musa sapientum L.) are an excellent model for studying food systems due to their high
perishability and the extensive biochemical changes they undergo during storage. As climacteric
fruits, bananas continue ripening after harvest, with processes such as starch breakdown into simple
soluble sugars and increased soluble pectin contributing to fruit softening and flavor enhancement
(Dos Santos et al., 2019; Kaka et al., 2019; Zomo et al., 2015). Organic acids, such as malic acid, fluctuate
throughout the ripening process, initially increasing and subsequently declining as senescence
approaches, which is closely linked to TTA (Gutierrez-Aguirre et al., 2023; Coelho De Queiroz et al.,
2019), as malic acid—the predominant acid in bananas—is progressively metabolized through
enzymatic decarboxylation and transamination reactions. During ripening, increased activity of
enzymes such as NADP-malic enzyme and malate dehydrogenase contributes to malic acid
degradation, reducing the total acid content and decreasing TTA (Zhou et al., 2023; Onik et al., 2019).
These chemical transformations also involve changes in pH and Total Soluble Solids (TSS), both
critical quality attributes during ripening. The gradual reduction in acidity, alongside an increase in
TSS and sugar content, imparts the characteristic sweetness and flavor of ripe bananas, making them
more appealing to consumers (Nguyen et al., 2023; Aquino et al., 2017; Zomo et al., 2015).
Additionally, the interplay between pH and the catalytic activity of cell wall enzymes can influence
the fruit’s texture, color, and stability during storage. Monitoring these biochemical changes—such
as variations in pH, TSS, color, firmness, and TTA—allows for understanding ripening dynamics,
optimizing postharvest treatments, and extending the shelf-life of bananas (Novita et al., 2024; Dos
Santos et al., 2019).
Several studies have demonstrated that TTA is closely related to other physicochemical parameters
during fruit ripening and storage. In bananas, TTA has shown a direct correlation with TSS during
early ripening stages, and an inverse correlation with firmness and skin color development,
reflecting progressive senescence (Coelho De Queiroz et al., 2019; Aquino et al., 2017). TTA also tends
to decline after an initial increase, indicating metabolic transformations such as the conversion of
organic acids and sugar accumulation. Similar relationships have been reported in other climacteric
fruits, where TTA is inversely associated with pH and firmness, and directly with respiration rate
and ethylene production (Odediran et al., 2023). These correlations highlight the role of TTA as an
integrative indicator of postharvest quality. Therefore, improving the prediction of TTA through
kinetic modeling contributes to a better understanding of ripening dynamics in banana and similar
fruit systems.
Performance metrics such as coefficient of determination (R2), Mean Squared Error (MSE), Akaike
Information Criterion (AIC), and Bayesian Information Criterion (BIC) are determinants for
evaluating the quality of kinetic model fitting by balancing accuracy and simplicity. R2 quantifies the
variance explained by the model, with higher values indicating better fit (De-Graft H., 2017), while
MSE measures the average squared residual error, with lower values reflecting improved accuracy
(Collenteur, 2021). AIC and BIC, on the other hand, penalize model complexity to prevent
overfitting, with AIC favoring models that balance fit and parameter usage and BIC imposing stricter
penalties to promote simplicity (Hoekstra et al., 2023; Corrales et al., 2015). Together, these metrics
ensure robust model selection, where R² and MSE assess goodness-of-fit, and AIC and BIC enhance
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interpretability and generalizability. The integrated use of these criteria has been theoretically
supported in model selection literature (Vrieze, 2012), and applied in food systems such as drying
kinetics modeling (Souza et al., 2019). More recently, their continued relevance has been
demonstrated in predictive modeling and longitudinal data analysis across various disciplines
(Hoekstra et al., 2023; Zhang & Meng, 2023).
Kinetic models, including zero-order, first-order, and second-order, are frequently used in food
science to understand and model quality product changes, allowing preservation optimization. Also,
these models enable describing the flavor development and evaluating nutrient stability (Contreras-
López et al., 2022; Hazrat et al., 2022; Buehler and Mesbah, 2016). While these models have broad
applications, traditional parameter estimation methods like ordinary least squares (OLS) face
limitations, including assumptions of error normality and challenges in parameter identifiability for
nonlinear systems (Chai et al., 2024; Manzhula et al., 2024). Advanced techniques, such as Bayesian
optimization, provide robust alternatives for addressing these challenges and improving model
validation (Luciano and Svoboda, 2024; Taylor et al., 2023; Jorayev et al., 2022). These techniques have
demonstrated significant predictive accuracy and efficiency advantages, particularly in systems with
complex or non-linear behaviors. For instance, Bayesian optimization has been shown to reduce the
number of required evaluations by over 90 % compared to grid or random search methods, while
improving convergence toward optimal solutions (Taylor et al., 2023). Additionally, in multi-
objective optimization scenarios, Bayesian approaches have increased parameter estimation
accuracy, such as conversion and yield in chemical processes, by up to 10–20 %, while reducing
processing times by several hours (Jorayev et al., 2022). These outcomes support the relevance of
Bayesian optimization in enhancing the reliability and performance of predictive models in food and
biological systems.
GAs are automated tools for kinetic model fitting in food science, offering advantages over
traditional methods like ordinary least squares (OLS). Inspired by natural selection, GAs evolve
populations of candidate solutions through operations such as selection, crossover, and mutation,
iteratively optimizing model parameters based on a defined fitness function (Xu, 2022; Fischer et al.,
2021). Unlike gradient-based approaches, which are often limited by local minima and sensitivity to
outliers such as OLS, GAs explore complex, multidimensional parameter spaces globally by
maintaining diverse solution populations and evaluating multiple performance metrics
simultaneously (Wrzecionek et al., 2021; Turgut, 2018; Umbarkar et al., 2015), ensuring a thorough
search for the global optimum (Wrzecionek et al., 2021; Zarejousheghani et al., 2016). This robustness
has enabled the successful application of GAs in modeling nonlinear and multistep reaction kinetics,
including optimized kinetic parameters for enzymatic biodiesel production (Zarejousheghani et al.,
2016)., and polycondensation and triglyceride epoxidation reactions (Kousaalya et al., 2019).
In food-related applications, GAs have been used to optimize fermentation kinetics in cocoa
processing, where they effectively estimated key parameters such as the maximum specific growth
rate (μmax) and saturation constants (Ks), yielding reliable predictions of metabolite production and
supporting process scale-up and control (López-Pérez et al., 2018). Additionally, they are
increasingly applied in food engineering tasks such as thermal degradation modeling, drying
optimization, and process control (Koop et al., 2024). GAs have also been employed to model the
polycondensation of citric acid with glycerol, a reaction relevant to developing edible coatings and
biodegradable food packaging matrices. These examples highlight the flexibility and robustness of
GAs in modeling complex reaction systems in food science (Wrzecionek et al., 2021).
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GAs and other predictive tools have been increasingly employed to model post-harvest changes’
kinetics in climacteric and non-climacteric fruits under controlled temperatures. These methods help
predict quality attributes, optimize storage protocols, and explore the genetic basis of post-harvest
traits. Tools such as artificial neural networks, fuzzy logic, adaptive neuro-fuzzy inference systems,
and GAs have been applied to model parameters like chilling injury, moisture loss, and firmness
(Salehi, 2020). Predictive models have also distinguished ripening behaviors in melons and tracked
changes in texture and physiology during storage (Tijskens et al., 2008). In blueberries, GAs have
supported breeding strategies by identifying traits linked to superior post-harvest quality (Casorzo
et al., 2024), while in barley, they have been used to monitor fungal development (Wawrzyniak,
2023). In climacteric fruits, strategies to delay ethylene-driven ripening have benefited from
physiological, molecular, and computational approaches, reinforcing the utility of predictive
modeling for quality control (Alonso-Salinas et al., 2024). Altogether, these studies highlight the
growing relevance of GAs and machine learning in post-harvest quality prediction across plant
systems.
It is hypothesized that the automation of kinetic model fitting using genetic algorithms enables more
efficient parameter estimation and allows for accurate modeling of TTA decreasing in bananas
during post-harvest ripening.
Based on the above, this study aimed to model the decrease in TTA in bananas (Musa paradisiaca L.)
by automating the fitting of zero-order, first-order, and second-order kinetic models. A Python script
was developed to implement GAs, which optimized the kinetic parameters—initial TTA (C₀) and
reaction rate constant (k)—by minimizing the MSE between experimental and predicted values.
Model performance was assessed using R², AIC, and BIC to explore a broader solution space and
enhance the predictive capacity of kinetic analysis.
2. Materials and methods
2.1 Samples
The bananas (Musa paradisiaca L., Cavendish variety) used in this study were sourced from the
central supply market of Pachuca de Soto, Hidalgo, Mexico. The fruits were selected based on visual
uniformity (color and size), corresponding to ripening stage 2 of the Von Loesecke scale
(Khodabakhshian and Baghbani, 2021), indicative of early post-harvest ripening, and were used
without prior washing, peeling, or chemical treatment. The samples were transported to the
laboratory in a tray without packaging or refrigeration, approximately five minutes after purchase.
2.2 Experimental conditions and storage setup
The experiment was conducted in the common-use laboratory of the Área Académica de Química
at the Universidad Autónoma del Estado de Hidalgo, Mexico. Whole, unpeeled bananas were placed
directly on clean laboratory work tables, maintaining a 30 cm separation between fruits to promote
adequate airflow and avoid physical contact. Although no specialized monitoring equipment was
installed, ambient temperature and relative humidity were recorded using publicly available
internet-based data corresponding to the study location. These environmental conditions averaged
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21 ± 1 °C and 57 ± 1 % relative humidity throughout the 16-day storage period. While direct
verification was not possible, the laboratory environment remained stable, and the primary objective
focused on modeling TTA degradation, making the referenced data appropriate for contextualizing
the storage conditions.
During the storage period, the fruits progressed naturally from ripening stage 2 to stages beyond 7
on the Von Loesecke scale. By the end of the 16-day period, the bananas exhibited brown to black
peels, a very soft pulp and signs of fermentation, such as an alcoholic odor. These characteristics are
consistent with late senescence under non-refrigerated conditions. Despite these advanced changes,
TTA was successfully measured at all time points, enabling a continuous and reliable kinetic analysis
throughout the study.
2.3 Total Titratable Acidity
The bananas’ TTA was measured in triplicate at specific time intervals: days 0, 1, 2, 3, 6, 7, 8, 9, 10,
13, 14, 15, and 16. These systematic measurements tracked changes in acidity over time, offering
valuable insights into the ripening process.
TTA was determined by titration with 0.01 mol/L NaOH after macerating the samples in distilled
water, following the procedure described in previous researches (García-Curiel et al., 2023; Barreto
Ferreira and Faria Freitas, 2019). The titration was performed using a 50 mL manual glass burette
(PYREX®, Corning Inc., USA, 2020) held in place with a burette clamp on a universal stand. The
Erlenmeyer flask (PYREX®, Corning Inc., USA, 2020) containing the sample and a magnetic stir bar
was placed on a magnetic stirrer with hot plate (Thermo Scientific® Cimarec™+, Waltham, MA, USA,
2020), operating at 400 rpm to ensure constant mixing under ambient conditions. All volumetric
glassware used was previously calibrated. The results were expressed as grams of malic acid per 100
grams of banana.
Although no separate reproducibility test was performed, all determinations were conducted under
uniform laboratory conditions using the same equipment and operator, ensuring procedural
consistency appropriate to the modeling scope of the study.
2.4. Kinetic modeling of total titratable acidity in bananas
2.4.1 Data preparation
The TTA data for bananas was collected and organized by time intervals. To ensure consistency
and reliability, the TTA measurements for each time point were averaged, resulting in a
representative dataset for kinetic modeling.
2.4.2 Kinetic models
Three kinetic models—zero-order, first-order, and second-order — were employed to describe the
changes in TTA over time (Table 1). In these models, Q(t) represents the critical quality attribute,
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which is the TTA at time t (in days), while Q0 denotes the initial TTA, and k is the rate constant
characterizing the speed of the reaction (Contreras-López et al., 2022). Each model was fitted to the
averaged dataset using the OLS method.
The observed TTA values were compared with the predictions generated by each kinetic model
through scatter plots of the experimental data overlaid with the corresponding model predictions.
For the zero-order model (Eq. (1)), TTA was plotted directly against time. In contrast, the first-order
model (Eq. (2)) used the natural logarithm of TTA (ln(Q(t)) plotted against time, and the second-
order model (Eq. (3)) represented the reciprocal of TTA (1/Q(t)) plotted against time.
Table 1. Kinetic models and their equations.
Tabla 1. Modelos cinéticos y sus ecuaciones.
Mathematical expression
Eq.
󰇛󰇜
(1)
󰇛󰇜 
(2)
󰇛󰇜
(3)
2.4.3 Model evaluation
The statistical summaries for each model were generated, including parameter estimates, standard
errors, and goodness-of-fit metrics such as R2.
2.5. Automated optimization and evaluation of kinetic models
2.5.1. Data splitting and optimization
The data preparation was carried out as described earlier, following the steps for calculating TTA
values from the experimental data. Subsequently, the kinetic models outlined in Table 1 described
the TTA changes over time, forming the basis for parameter optimization and model evaluation.
The dataset was divided into training (80 %) and test (20 %) subsets using random splitting to ensure
the robustness of the model evaluation process. The optimization of kinetic parameters, namely k
(reaction rate constant) and Q0 (initial TTA), was performed using a genetic algorithm implemented
with the DEAP library in Python. This algorithm aimed to minimize the MSE between the observed
and predicted TTA values. Initially, a population of candidate solutions, each representing potential
values of k and Q0, was generated. The fitness of each individual was evaluated through an objective
function based on the Eq. (4) (Dong et al., 2017).

 

Eq. (4)
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Subsequently, genetic operators, including selection, crossover, and mutation, were iteratively
applied to evolve the population over 100 generations or until convergence. This iterative process
enabled the exploration of a vast parameter space, ensuring the identification of the optimal set of
kinetic parameters for each model.
2.5.2. Model evaluation
The performance of each kinetic model was evaluated using multiple metrics to assess accuracy
and complexity. The MSE was calculated to quantify the average squared difference between the
observed (Qobserved) and predicted (Qpredicted) values, providing a measure of the model’s prediction
error (Eq. (4)).
The R2 was used to measure the proportion of variance in the observed data explained by the model,
indicating its goodness of fit. Higher values of R2 suggested better predictive performance.
The AIC was also computed to evaluate the trade-off between model fit and complexity. It was
calculated as described in Eq. (5) (Vaga et al., 2014; Zhang and Meng, 2023).
 󰇛󰇜 Eq. (5)
where n represents the number of data points, MSE is the mean squared error, and k is the number
of parameters in the model.
The BIC was also calculated to incorporate the effect of sample size on model complexity. The BIC
was calculated as described in Eq. (6) (Zhang and Meng, 2023; Brewer et al., 2016).
 󰇛󰇜 󰇛󰇜 Eq. (6)
These metrics allowed for a comprehensive and balanced evaluation of the models. While the MSE
and R2 assessed predictive accuracy, the AIC and BIC penalized unnecessary complexity (Brewer et
al., 2016; Corrales et al., 2015). They ensured simpler models were favored for comparable accuracy
and identified the most robust and efficient kinetic model for describing TTA dynamics.
The kinetic modeling and optimization procedures were implemented using the Python
programming language (version 3.12.2) within the Visual Studio Code integrated development
environment (IDE, version 1.96.2). Anaconda (version 25.1.1) was employed as the package and
environment manager to ensure compatibility and reproducibility across dependencies. The analysis
relied on several Python libraries: ‘pandas’ (2.2.3) for data handling, ‘numpy’ (1.26.4) for numerical
operations, ‘matplotlib’ (3.9.1) and ‘plotly’ (5.22.0) for data visualization, ‘scipy’ (1.15.1) and
‘statsmodels’ (0.14.2) for statistical modeling, ‘sklearn’ (1.6.1) for model evaluation metrics, and
‘deap’ (1.4) for implementing genetic algorithms.
The analysis was performed on a personal computer running Linux Mint 22 “Wilma” (Ubuntu 24.04
base) with Cinnamon desktop environment (version 6.2.9) and kernel 6.8.0-58-generic, using a 64-bit
x86_64 architecture and GCC compiler version 13.3.0. This configuration ensured the computational
efficiency and reproducibility of the modeling and optimization processes.
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The dataset, containing time and TTA values and the analysis scripts, will be publicly available on a
GitLab repository (https://gitlab.com/FoodChem-DataSci-Lab/kinetic-analysis-banana). This
repository will enable interested researchers and practitioners to download, analyze, and implement
the methodology for their studies or extend it to similar applications. This openness fosters
transparency, reproducibility, and collaborative kinetic modeling and optimization advancements.
2.6 Comparative analysis of model performance
To evaluate the effectiveness of the GAs-based optimization in improving kinetic model fitting, a
comparative analysis was performed between models fitted using traditional methods (Trad) and
those optimized with GAs. Four performance metrics were analyzed: R², AIC, and BIC.
Quantitative comparisons were conducted using percentage and absolute differences between the
values obtained by each fitting method. The percentage improvement in model accuracy was
assessed by changes in R² and MSE, calculated using Eqs. (7) - (9), as follows:
 


 Eq. (7)
   Eq. (8)
   Eq. (8)
3. Results and discussion
Fig. 1 presents the experimental data of TTA in bananas alongside the fitted curves for three
kinetic models: zero-order, first-order, and second-order. The zero-order model, shown in the left
panel, assumes a constant rate of TTA degradation over time, resulting in a linear decline in TTA.
This model provides the best statistical fit, with an R² value of 0.918 and an adjusted R² of 0.910
(Table 2). It exhibits the lowest AIC (−104.0) and BIC (−102.9), indicating that it is the most
parsimonious model. The estimated rate constant (k) is −0.0024 day⁻¹, suggesting a steady and
uniform decrease in TTA regardless of its initial concentration. This behavior, visible as a straight
line in Fig. 1a, is characteristic of zero-order kinetics and reflects a linear behavior, where the rate of
change remains constant over time. In this context, it suggests that the overall decrease in acidity, as
reflected by TTA, proceeds at a uniform rate regardless of the fruit’s evolving biochemical
composition.
The first-order model, shown in the middle panel, follows an exponential decay function, assuming
that the rate of change in TTA is proportional to its current value. This model also shows a strong
fit, with an R² of 0.913 and an adjusted R² of 0.905. However, its AIC (−47.67) and BIC (−46.54) values
are higher than those of the zero-order model, suggesting that it may be less efficient in explaining
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the observed variability. The estimated rate constant (k) is −0.0204 day⁻¹, indicating a more rapid
decline in TTA at the beginning of storage. As seen in Figure 1b, this behavior reflects a dynamic in
which the processes contributing to acidity loss are initially more active and gradually slow down,
as expected in a first-order process. The enzymatic conversion of organic acids such as malic or citric
acid into sugars or intermediate metabolites during ripening may explain this trend. Previous
studies have shown that enzymes like malate dehydrogenase are transcriptionally regulated
throughout ripening and contribute to the decline in TTA as part of a coordinated metabolic shift
(García-Gómez et al., 2020; Gao et al., 2018; González-Agüero et al., 2016).
The second-order model, presented in the right panel, was fitted using the inverse of TTA against
time. Although this model achieves a relatively high R² value of 0.899, it has the weakest fit among
the three, as indicated by the lowest adjusted R² (0.890). Furthermore, its AIC (10.13) and BIC (11.26)
are higher than those of the other models, making it the least suitable for describing TTA degradation
in bananas from a statistical standpoint. The positive rate constant (k = 0.1744 day⁻¹) suggests a
nonlinear behavior in which the decrease in TTA progressively slows over time. This deceleration
may reflect a cumulative or saturable pattern of acidity loss, potentially associated with the gradual
depletion of acid-related compounds and the downregulation of metabolic activity involved in acid
transformation. Although the model does not provide the best fit, its structure may be indicative of
a more complex physiological process. This interpretation is supported by studies in climacteric
fruits such as peach, mango, and tomato, which have shown that the decline in TTA during ripening
slows as a result of both substrate depletion and reduced activity of organic acid-related enzymes
(X. Jiang et al., 2023; Zhao et al., 2019; Batista-Silva et al., 2018; Rooban et al., 2016).
On the whole, the comparison of model performance indicates that the zero-order model best
represents the experimental data, supported by the highest R², the lowest AIC and BIC values, and
a consistent linear trend. Although the first-order model also shows a good fit, its higher information
criteria values suggest a less parsimonious description of the observed TTA changes. The second-
order model, despite offering a biologically plausible framework for complex degradation dynamics,
demonstrated a weaker statistical fit and higher prediction uncertainty. Therefore, a zero-order
kinetic model appears to provide the most appropriate and statistically robust representation of
titratable acidity degradation in bananas during ripening under the evaluated conditions. However,
to improve the precision of parameter estimation and overcome potential limitations associated with
traditional fitting methods, GAs were employed.
The experimental TTA values obtained in this study (ranging from 0.45 to 0.90 g of malic acid per
100 g of banana) are consistent with those reported in previous studies on climacteric fruits. For
instance, a comparable decline in malic acid content during postharvest storage of bananas under
physical treatments has been reported (Zhou et al., 2023), while TTA values between 0.60 and 1.20 g
of malic acid per 100 g of pulp have been documented for ‘Maçã’ bananas stored at room temperature
(Dos Santos et al., 2019). These comparisons support the physiological plausibility of the observed
data and validate the modeling approach applied in this study.
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Table 2. Kinetic model comparison for total titratable acidity.
Tabla 2. Comparación de modelos cinéticos para la acidez total titulable.
Model
R²
Adjusted R²
F-statistic
AIC
BIC
Intercept (C0)
Rate constant (k)
Zero Order
0.918
0.91
122.6
−104
−102.9
0.1385
−0.0024
First Order
0.913
0.905
114.9
−47.67
−46.54
−1.9699
−0.0204
Second
Order
0.899
0.89
98.28
10.13
11.26
7.1008
0.1744
Figure 1. Kinetic model fitting for total titratable acidity (TTA) in bananas using classical models. TTA: Total
titratable acidity, expressed as g of malic acid per 100 g of banana. Error bars represent the standard deviation
of three replicates.
Figura 1. Ajuste del modelo cinético para la acidez titulable total (TTA) en plátanos utilizando modelos clásicos.
TTA: Acidez titulable total, expresada como g de ácido málico por 100 g de plátano. Las barras de error
representan la desviación estándar de tres réplicas.
Fig. 2 shows the predictive performance of three kinetic models—zero-order, first-order, and second-
order fitted to the TTA in bananas using genetic algorithms. This provides a more reliable assessment
of model generalization, avoiding over-fitting to the training data. The left panel represents the zero-
order model, which maintains a linear decline in TTA with a train R2 of 0.9120 and a test R2 of 0.9126.
Despite exhibiting a low MSE in the training set (1.1874×10−5), its test MSE increases to 2.6915×10−5,
suggesting a slight decrease in predictive accuracy (Table 3).
The middle panel presents the first-order model, where the decay follows an exponential trend. This
model demonstrates improved predictive performance, with a test R2 of 0.9246, outperforming the
zero-order model in predictive capacity. The test MSE decreases to 2.3204×10−5, further supporting
its higher predictive reliability. Additionally, the first-order model has a slightly higher AIC
(−108.5263) and BIC (−107.9211) than the zero-order model, indicating a modest increase in model
complexity without significant over-fitting.
The right panel illustrates the second-order model with the highest test R2 (0.9349) and the lowest
test MSE (2.0029×10−5), indicating that it provides the best predictive performance among the three
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models. Although its train R2 (0.8933) is slightly lower than the other models, the improved test
results suggest better generalization. However, its AIC (−107.4819) and BIC (−106.8768) are higher
than those of the zero- and first-order models, indicating that this model is statistically less
parsimonious despite its predictive strength.
These results highlight the importance of train-test validation when evaluating kinetic models for
decreasing TTA. This step allows the model’s generalization ability to be assessed beyond the dataset
used for calibration. Without this step, a model may exhibit excellent statistical fit (e.g., high R², low
AIC) but fail to predict unseen data reliably, potentially leading to over-fitting and poor real-world
applicability. In this study, validation revealed that although the zero-order model fitted the training
data best, the second-order model showed superior predictive performance, emphasizing the need
for this evaluation step (Sivakumar et al., 2024; Pandey et al., 2020). The initial analysis (Fig. 1)
suggested that a zero-order kinetic model best represented TTA loss. However, when tested on
unseen data, the second-order model demonstrated superior predictive performance. This indicates
that the degradation of TTA may follow a more complex mechanism than a simple linear or
exponential decay, warranting further exploration of higher-order or mechanistic models.
Table 3. Predictive performance of kinetic models for total titratable acidity.
Tabla 3. Rendimiento predictivo de modelos cinéticos para la acidez total titulable.
Model
Train MSE
Test MSE
AIC
BIC
Train R²
Test R²
Optimized k
Optimized C₀
Zero Order
1.1874×10−5
2.6915×10−5
−109.4115
−108.8064
0.912
0.9126
0.0024
0.1372
First Order
1.2973×10−5
2.3204×10−5
−108.5263
−107.9211
0.9039
0.9246
0.02
0.1382
Second
Order
1.4401×10−5
2.0029×10−5
−107.4819
−106.8768
0.8933
0.9349
0.167
0.1391
Figure 2. Kinetic model fits for total titratable acidity (TTA) in bananas using genetic algorithms: Training and
test data. TTA: Total titratable acidity, expressed as g of malic acid per 100 g of banana. Error bars represent the
standard deviation of three replicates.
Figura 2. Ajustes del modelo cinético para la acidez titulable total (TTA) en plátanos mediante algoritmos
genéticos: datos de entrenamiento y prueba. TTA: Acidez titulable total, expresada como g de ácido málico por
100 g de plátano. Las barras de error representan la desviación estándar de tres réplicas.
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The results in Figs. (1) and (2) emphasize the necessity of selecting an appropriate kinetic model to
describe the decreasing of TTA in bananas. While the zero-order model initially exhibited the best
statistical fit based on R2, AIC, and BIC values (Fig. 1), its predictive performance on unseen data
was lower than that of the other models, as indicated by an increase in test MSE (2.6915×10−5) (Table
3), which suggests that although the zero-order model is parsimonious, it may not fully capture the
complexity of TTA degradation.
The first-order model demonstrated improved predictive performance, with a higher test R2 (0.9246)
and a lower test MSE (2.3204×10−5) than the zero-order model, indicating that an exponential decay
assumption better reflects the initial decline in TTA. However, the second-order model achieved the
best predictive results, with the highest test R2 (0.9349) and the lowest test MSE (2.0029×10−5),
suggesting that the degradation process involves more complex mechanisms. Nevertheless, its
higher AIC and BIC values indicate an increased model complexity that may limit its practical
application.
To quantify the improvement achieved through GAs-based optimization, a comparative analysis
was conducted using R², AIC, and BIC values from the traditional and optimized models. The first-
order model showed the most significant increase in explanatory power, with a 1.27 % increase in R²
(from 0.913 to 0.9246), while the second-order model exhibited a 3.99 % improvement (from 0.899 to
0.9349). Although the R² of the zero-order model decreased slightly by 0.59 % (from 0.918 to 0.9126),
it still retained strong performance.
In terms of model parsimony, all three models showed clear improvements after optimization. The
AIC was reduced by 5.41, 60.86, and 117.61 units for the zero-, first-, and second-order models,
respectively. Similarly, the BIC values were lowered by 5.91, 61.38, and 118.14 units, confirming that
GA optimization enhanced the balance between model fit and complexity across all models.
Among the models evaluated using GAs optimization, the second-order model yielded the highest
coefficient of determination (R² = 0.9349) and the lowest MSE on the test data, suggesting that its
nonlinear structure better captured the dynamics of TTA decline over time. This is also evident in
Fig. 2, where the fitted curve for the second-order model closely follows the experimental points
throughout the ripening period.
The kinetic parameters obtained in this study, particularly the initial TTA (C₀ = 0.1391 g of malic
acid/100 g) and the rate constant for the second-order model (k = 0.167 day⁻¹), fall within the ranges
reported in previous studies on banana ripening under ambient conditions. For instance, titratable
acidity values ranging from 0.60 to 1.20 g of malic acid per 100 g of pulp have been documented for
‘Maçã’ bananas (Dos Santos et al., 2019), while values between 0.34 and 0.73 % have been reported
for different banana cultivars depending on ripening stage (Aquino et al., 2017). Additionally, acidity
values in ‘Prata Anã’ bananas showed similar declining patterns during storage at 23 ± 2 °C
(Aquino et al., 2017). The observed decrease in acidity in these studies aligns with the nonlinear decay
pattern captured by the second-order model in this work. These similarities support the
physiological plausibility of the fitted model and reinforce the value of GAs-based parameter
optimization for capturing complex postharvest transformations in climacteric fruits.
Results highlight the advantages of GAs in kinetic fitting, as they facilitate a more robust exploration
of the parameter space and mitigate local minima issues associated with traditional methods like
OLS (Lei et al., 2018; Zarejousheghani et al., 2016). The ability of GAs to optimize multiple
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performance metrics, including R2, MSE, AIC, and BIC, provides a comprehensive framework for
model selection (Xue et al., 2023). Furthermore, their automated nature enhances efficiency and
reproducibility, allowing for a systematic evaluation of complex kinetic models without extensive
manual intervention (Chakrabarti et al., 2013).
The observed discrepancy between statistical fit and predictive performance underscores the
necessity of train-test validation in kinetic modeling. While the zero-order model may appear
optimal based on training data, its reduced accuracy in test predictions suggests it oversimplifies the
degradation process. Conversely, despite its greater complexity, the second-order model provides a
more accurate representation of TTA degradation, reinforcing the need for robust optimization
techniques like GAs to improve parameter estimation reliability (Razdan et al., 2023).
Thus, integrating GAs in kinetic modeling enhances parameter estimation accuracy and model
reliability. Although the zero-order model remains a practical option due to its simplicity, the
predictive superiority of the second-order model suggests that TTA degradation follows a more
intricate mechanism. Future studies could explore hybrid or mechanistic models to refine this
understanding, leveraging GAs’ adaptability to gain deeper insights into food degradation kinetics.
From a chemical perspective, while a zero-order kinetic model accurately describes the observed
TTA degradation in the dataset, a second-order approach may better capture the underlying
biochemical complexities when applied to unseen data. This discrepancy suggests that the apparent
linear decline in TTA could arise from the interplay of multiple biochemical processes, which, when
analyzed individually, exhibit nonlinear behavior. Banana ripening is a complex process driven by
various biochemical reactions, including the degradation of organic acids, influenced by factors such
as enzymatic activity, cellular respiration, and ethylene production (Zhou et al., 2023; Thakur et al.,
2019).
Enzymatic activity plays a central role in TTA decreasing, with malic enzymes facilitating the
breakdown of malic acid, the predominant organic acid in bananas (Zhou et al., 2023). This
contributes to the overall decline in acidity, particularly in the early stages of ripening. Ethylene, an
autocatalytic hormone, further accelerates acid degradation by regulating the transcription of genes
associated with organic acid metabolism, including those coding for malate dehydrogenase and
NADP-malic enzyme (Wei et al., 2023; Cordenunsi-Lysenko et al., 2019). Additionally, ethylene
modulates other ripening-related processes such as starch-to-sugar conversion, softening, and
changes in pigment synthesis, all of which influence the biochemical environment in which acid
degradation occurs. Cellular respiration also consumes organic acids to generate energy, reducing
TTA levels and reinforcing the link between ripening intensity and acidity loss (Ton Nu and
Kobayashi, 2020). Together, these factors suggest that the degradation process is not strictly linear,
but rather results from multiple overlapping reactions operating at different rates throughout
ripening. The superior predictive performance of the second-order model in validation tests
reinforces the idea that TTA decreasing follows a more intricate pattern, consistent with a dynamic
and evolving metabolic context (X. Jiang et al., 2023; Zhao et al., 2019).
While the experimental data’s statistical analysis is a zero-order kinetic model for TTA degradation
in bananas, predictive validation suggests that a second-order approach may better represent the
biochemical processes’ complexity. Further studies incorporating mechanistic models or hybrid
approaches may provide deeper insights into the dynamic changes in acidity during banana
ripening.
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Integrating GAs into kinetic modeling refines parameter estimation and broadens the applicability
of predictive models in food science. By leveraging these advanced optimization techniques,
researchers can develop more robust models that account for variability in storage conditions and
biochemical interactions (Zhong and Tian, 2011). Future research should explore combining data-
driven machine-learning methods with mechanistic models to enhance predictive accuracy and
adaptability (Kousaalya et al., 2019). Such advancements will contribute to more effective post-
harvest management strategies, ultimately improving food quality and reducing economic losses in
the industry (Zhong and Tian, 2011).
These results underscore the methodological contribution of this study. Although genetic algorithms
(GAs) have been previously applied in food-related modeling tasks, such as optimizing parameters
in reaction kinetics or enhancing classification accuracy (Nirere et al., 2023; Ozbuyukkaya et al., 2021;
Rivera et al., 2020), to date, no studies have been found that focus on their application to model
acidity changes in climacteric fruits. In this study, the use of GAs led to improved fitting of the kinetic
models, particularly in the second-order model, where the predictive R² increased to 0.9349 and the
AIC and BIC values decreased significantly compared to traditional methods. These improvements
align with the broader literature that highlights the ability of GAs to explore complex parameter
spaces and reduce prediction error in non-linear systems. Thus, the present results contribute novel
evidence supporting the integration of GAs in postharvest acidity modeling and reinforce their
potential for improving the reliability of kinetic predictions in perishable fruit systems.
4. Conclusion
This study successfully automated the fitting of kinetic models to describe TTA degradation
in bananas using GAs. Among the three evaluated models, the zero-order kinetic model exhibited
the best statistical fit on training data (R² = 0.9120; AIC = −109.41; BIC = −108.81). However, test
validation revealed that the second-order model achieved superior predictive performance (test R²
= 0.9349; test MSE = 2.00×10⁻⁵), suggesting that the degradation process follows a more complex
mechanism than initially assumed.
These results emphasize the value of train-test validation to avoid overfitting and highlight the
ability of GAs to enhance parameter estimation and generalization in food kinetic modeling. Despite
the promising results, the study is limited by the scope of the data (single temperature, fixed ripening
stage, and no cross-validation), which could be addressed in future studies.
Future research should consider expanding the experimental design to include varying temperature
and humidity conditions, extended storage periods, and larger datasets to improve model
robustness and generalizability. Additionally, although this study was conceptual and
methodological, focused on developing a replicable optimization framework, the practical
usefulness of the GA-optimized models could be further strengthened through experimental
validation using independent samples or external post-harvest conditions. Future work should also
explore hybrid modeling approaches, such as those combining mechanistic kinetic equations with
machine learning techniques (e.g., neural networks or support vector regression), better to capture
the biochemical processes underlying banana acidity changes. Moreover, applying this methodology
to other perishable fruits or complementary biochemical quality markers, such as texture, soluble
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solids, or vitamin degradation, represents a promising avenue for advancing postharvest quality
modeling and supporting data-driven decision-making in the food industry.
Acknowledgments
The authors thank the Sistema Nacional de Investigadoras e Investigadores (SNII-
CONAHCyT) and the Universidad Autónoma del Estado de Hidalgo (UAEH) for supporting this
research. They also dedicate this work to the memory of Engineer Cástulo Pérez Cabañas (1960–
2005), whose legacy continues to inspire.
Conflict of Interest statement
The authors declare no conflicts of interest.
5. References
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
17
Méndez-Castillo et.al
TECNOCIENCIA CHIHUAHUA, Vol. XIX (Special Issue): e1847 (2025)
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
18
Méndez-Castillo et.al
TECNOCIENCIA CHIHUAHUA, Vol. XIX (Special Issue): e1847 (2025)
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
19
Méndez-Castillo et.al
TECNOCIENCIA CHIHUAHUA, Vol. XIX (Special Issue): e1847 (2025)
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
20
Méndez-Castillo et.al
TECNOCIENCIA CHIHUAHUA, Vol. XIX (Special Issue): e1847 (2025)
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
21
Méndez-Castillo et.al
TECNOCIENCIA CHIHUAHUA, Vol. XIX (Special Issue): e1847 (2025)
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
22
Méndez-Castillo et.al
TECNOCIENCIA CHIHUAHUA, Vol. XIX (Special Issue): e1847 (2025)
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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