# A digital twin integrating multi-objective optimization to support fryer operators in managing potato crisps production

Manon Perrignon, Mathieu Emily, Mélanie Munch, Paul Debuire, Romain Jeantet, Thomas Croguennec

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Manon Perrignon, Mathieu Emily, Mélanie Munch, Paul Debuire, Romain Jeantet, et al.. A digital twin integrating multi-objective optimization to support fryer operators in managing potato crisps production. Journal of Food Engineering, 2026, 406, pp.112800. 10.1016/j.jfoodeng.2025.112800. hal-05247019

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A digital twin integrating multi-objective optimization to support fryer operators in managing potato crisps production

Manon Perrignon, Mathieu Emily, Mélanie Munch, Paul Debuire, Romain Jeantet, Thomas Croguennec

PII: S0260-8774(25)00335-8

DOI: https://doi.org/10.1016/j.jfoodeng.2025.112800

Reference: JFOE 112800

To appear in: *Journal of Food Engineering*

Received Date: 17 March 2025

Revised Date: 29 August 2025

Accepted Date: 3 September 2025

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Please cite this article as: Perrignon, M., Emily, M., Munch, M., Debuire, P., Jeantet, R., Croguennec, T., A digital twin integrating multi-objective optimization to support fryer operators in managing potato crisps production, *Journal of Food Engineering*, https://doi.org/10.1016/j.jfoodeng.2025.112800.

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© 2025 Published by Elsevier Ltd.
1 **Title:** A digital twin integrating multi-objective optimization to support fryer operators in managing potato crisps production

2 **Authors:** Manon Perrignon¹, Mathieu Emily², Mélanie Munch³, Paul Debuire⁴, Romain Jeantet¹ and Thomas Croguennec¹*

5 ¹L'Institut Agro, INRAE, STLO (Science et Technologie du Lait et de l'œuf), Rennes, France

6 ²L'Institut Agro, Université de Rennes, CNRS, IRMAR (Institut de Recherche Mathématique de Rennes)-UMR 6625, Rennes, France

8 ³INRAE, STLO (Science et Technologie du Lait et de l'œuf), Rennes, France

9 ⁴ALTHO - Brets, Saint Gérand, France

10 *Corresponding author

11 **Keywords:** Digital Twin, Multi-objective optimization, Machine Learning, Potato crisps, Decision-support tool

13 **Abstract:**

14 The production of potato crisps currently relies on the expertise of human operators, known as fryers, whose training is long and demanding. With the decline in fryer vocations and the increase in consumer quality expectations, it is now essential to develop decision-support tools to make fryer work easier and better control product quality. This study proposes a digital twin (DT) approach that incorporates multi-objective optimization to assist fryers in managing their crisp production line. Data from crisp production is collected and used to model key crisp physicochemical indicators (Fat content, Moisture content, and Lightness) using a Machine Learning approach, specifically the Random Forest method. Then, a multi-objective optimization is carried out using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm, which identifies optimal adjustments to enhance the three crisp physicochemical indicators. The optimization is tested on 2 batches of potatoes as inputs. The algorithm generates a set of optimal solutions, from which a final solution is selected using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) multi-criteria decision-making method. This solution provides practical recommendations for adjusting production parameters according to a given potato batch quality. The results show that physicochemical parameters of the crisps are similar after optimization, regardless of the quality the potato batch. Variation in potato batch quality is compensated by appropriate adjustments of the crisp manufacturing process parameters ensuring consistent and optimal production. In conclusion, this digital twin, integrating multi-objective optimization, proves to be a valuable tool for improving fryer decision-making and optimizing production line management.

33 **Graphical abstract:**
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# 1 Introduction

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The manufacturing process of potato crisps is a complex process, which is monitored by skilled operators called fryers, who adjust the various parameters of the production line. The fryers have extensive technical expertise they have developed through rigorous and specialized training. However, the dwindling number of qualified candidates due to the demanding nature of the training underlines the urgent need to offer new support tools to the fryers. The fryers must control the process to meet several crisps quality criteria in terms of texture, visual appearance, and taste (Salvador et al., 2009). These objectives are linked to specific physicochemical indicators of potato crisp, among which fat and moisture contents of the crisps, and crisp lightness (Zhang et al., 2024). Fat content contributes to both flavor and texture. Moisture content influences crisps shelf life and texture, particularly its crispiness (Glassey et al., 2017). If the moisture content is too high or too low, it can lead to either soggy or overly dry crisps, respectively. Crisp lightness plays a critical role in the visual appeal of the crisps. Deviations in crisp lightness can lead to non-conformity, particularly if the crisps appear excessively brown. This browning is primarily due to Maillard reaction, which also generates small amount of acrylamide, a carcinogen compound formed during the high-temperature cooking of starchy foods and aroma compounds that affects the sensory properties of the crisps (Martinez et al., 2019). The lightness is evaluated as a percentage of lightness (L*). In the CIELAB color space, lightness quantifies the visual perception of color brightness on a scale from 0 (black) to 100 (white), where higher values correspond to lighter surface coloration. A higher value is correlated with lower acrylamide content (Viklund et al., 2007) and more appealing crisps.
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These indicators represent key measures of the industry's performance, which fryers must optimize while adapting to the variability of potatoes (Peñalver-Soto et al., 2022). However, optimizing this performance is particularly challenging, as it involves balancing multiple conflicting objectives (Drofenik et al., 2023), such as crisp lightness and moisture content. To address this complexity, multi-objective optimization (Gunantara, 2018) (Wari and Zhu, 2016) helps solve such food process optimization problem by simultaneously dealing with multiple performance objectives, identifying trade-offs, and providing the ideal parameters to reach the objectives set (Konak et al., 2006). The multi-objective optimization of processes is a well-defined procedure, but the implementation of the different steps depends on the specific problem to be solved and the application domain (Perrignon et al., 2024). For instance, the step of modeling objectives can be approached in various ways. One option is the use of available mathematical equations, known as mechanistic modeling, while another is data-driven model (Madoumier et al., 2019). There are no global equations to describe the entire process of potato crisp manufacture. The process is controlled by setting/measuring various manufacturing parameters but the relationships between these parameters are often complex justifying the use of data-driven methods, such as Machine Learning. These methods allow for establishing relationships between collected manufacturing parameters to predict the defined objectives (Garre et al., 2020). However, their effectiveness relies on the availability of sufficient and relevant data. Currently, a large amount of data is collected throughout the potato crisp production process, providing an opportunity to apply these methods. It has been shown that data collected from complex food transformation processes can be leveraged to better manage food processing performance indicators and gain a deeper understanding of the influencing process parameters (Perrignon et al., 2025).

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These data can also be integrated in virtual replicas of food processes providing innovative solutions for managing food processes in real-time, while optimizing performance and product quality (Henrichs et al., 2022). These so-called digital twins (DT) (Shankarrao Patange and Bharatkumar Pandya, 2022) are running in parallel to the real food manufacturing process through a continuously updated data flow (Verboven et al., 2020). By integrating data from sensors installed all along the food process, DT enable continuous performance monitoring and facilitate rapid, data-driven decision-making. When a change is measured in the food manufacturing process, DT integrates the information and sends updated instructions to the real food process (Kritzinger et al., 2018). This technology can be leveraged to optimize production lines, enhance product quality and reduce costs (Barricelli et al., 2019). It has therefore the potential to improve the management of crisps manufacturing process, assisting fryers in making decisions towards constant crisps quality achievement, simplifying their training and making their role more accessible.
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The aim of this paper is to propose a Digital Twin approach incorporating a multi-objective optimization and data-driven method to provide a decision support tool to the fryers. To achieve this, the data collected through the whole process from the potato batches to the crisps before salting and packaging were used to model crisp physicochemical indicators that were then used for multi-objective optimization. To illustrate the optimization approach two batches of potato of different quality (A and B) were used as inputs. The optimization returns the manufacturing parameters to be implemented by the fryers for the two batches of potatoes to meet the crisps quality objectives. This study showed that, depending on the quality of the potatoes, the process has to be managed differently, and implementing this approach through a Digital Twin could assist and guide fryers in setting the process parameters for optimizing crisp quality.

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## 2 Methodology

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### 2.1 Manufacturing process overview

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The potato crisp manufacturing process under study is illustrated in Figure 1. The potatoes in batches are stored in hoppers. A batch represent a defined volume of potatoes. For each batch, the dry matter content and the size of the potatoes are measured. The potatoes are classified as very small, small, medium or big. The potatoes are then sent to an optical sorter to identify any appearance defects: bruises, deformations, percentage of burnt, rotten, spotted and green, sprouts on the potatoes. They are washed before being sent to a Pulsed Electric Field (PEF) system, which helps reducing the final acrylamide content in crisps (Bruno et al., 2024). The potatoes are then peeled, calibrated, and possibly cut to achieve a uniform size. A buffer zone is added to regulate the potato flow before they pass through an elevator to be sliced. The slats of potatoes are washed, drained, and then sent to the fryer. The fryer consists of three belts circulating the potato slats through the frying oil. After exiting the fryer, the crisps go through an optical sorter and an infrared spectrometer to remove non-conform crisps and measure the indicators that define the crisps (fat and moisture contents, lightness). The crisps are then sent to the salt shaker before being placed in a buffer zone before packaging. Each red star in Figure 1 represents a data collection point.

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### 2.2 Data collection and preprocessing

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The data come from two years of production (2022-2023) of one production line of a crisp manufacturing industry. Throughout the production process, from potato storage to crisp packaging, various manufacturing parameters are recorded using automated sensors (red stars in Figure 1) and collected in a data file. These parameters include those defining the raw material (quality criteria of
the potato batches), production conditions (peeling time, frying temperature, crisp thickness, etc.), as well as physicochemical indicators of the potato crisps. The data file is composed of 135,849 individuals (potato batches) and 47 variables (manufacturing parameters). A simplified form of the dataset is shown in Figure 2 and a detailed summary of the variables is provided as supplementary material (Supplementary material Table S2).

A batch of potatoes, which is defined by quality variables, is processed under uniform conditions. This means that in the dataset, each batch of potatoes is defined by 47 variables, specifically comprising 19 potato quality variables, 25 process parameters and 3 crisp physicochemical indicators (fat and moisture content, and lightness). This dataset links the quality of the potatoes, the setting of the manufacturing process parameters and the physicochemical indicators of the potato crisps.

Variables have different roles in the process and can be classified into three categories. The first category gathers the 3 performance indicators (fat content (%), moisture content (%) and lightness (%)) that constitute the crisp quality objectives. The second category gathers 9 decision variables that refer to actionable parameters in the process, meaning they can be directly adjusted by the fryers to influence the course and performance of the process. These variables represent the levers on which the DT will provide decision-making support. The identified variables, listed in chronological order along the crisp process, are: Peeling Time, Elevator drive sprocket frequency, Slat Thickness, Water Supply, Boiler Temperature, Fryer Temperature, Time Belt 1, Time Belt 2 and Belt 3 drive sprocket frequency. The third category includes 35 informative variables, which are non-actionable parameters defining the process trajectory (e.g., potato quality variables, other process variables) (Figure 2).

A data preprocessing phase is undertaken to transform raw data into an exploitable database. This phase allows for data cleaning by removing missing values, duplicates, or errors, standardizing formats and measurement units, and structuring information consistently. Without this preparation, results may be biased or unreliable, since their quality directly depends on the quality of the input data. This data preprocessing phase is divided into three steps.

The first step consists of detecting outliers. To achieve this, data visualization techniques such as box plots or distribution graphs were used. This filtering is performed using expert knowledge based on acceptance thresholds (Supplementary material, Figure S1). These thresholds were established for each parameter, defining the standard operating range of the manufacturing process. Experts are again consulted to determine whether the detected outliers provide useful information or are simply data entry errors. Their knowledge allows for evaluating the nature of these outliers. Data collection problems (automatic data recording when manufacturing is stopped) were considered as outliers. Individuals in the dataset presenting outliers were removed. The second step consists of removing redundant variables, as some variables may be represented with different units (for example, minutes
or seconds), or variables that do not fall within the scope of the study (for example, final product traceability). The final step consists of transforming the initial dataset. For this study, we chose to normalize the data by centering and scaling the data so that all variables have the same weight.

## 2.3 Definition and modeling of the performance indicator with Random Forest

The three crisp performance indicators (fat and moisture contents and lightness) were modeled using several methods of machine learning (details of methods are provided in supplementary material). For each method and each performance indicator, the complete dataset was divided into two parts: 80% of the data was used to train the model and optimize the hyperparameters (train set), while the remaining 20% was used to validate the model's performance (test set). Model performance was optimized through hyperparameter tuning. A grid search approach was employed to adjust key hyperparameters, including learning rate and number of trees. To prevent overfitting, fivefold cross-validation was applied to evaluate different hyperparameter combinations (Münch, 2023). The optimal hyperparameter set was selected based on minimizing root mean square error (RMSE), ensuring robust performance on unseen data.

Following hyperparameter optimization, model predictions were generated using the test set to assess performance indicators. To establish 95% confidence intervals for predictions, this evaluation process was repeated 100 times using bootstrap sampling. The dataset was randomly partitioned into training and test subsets 100 times, with each bootstrap sample created through random sampling with replacement from the original dataset. This methodology enables comprehensive evaluation of model performance across diverse samples, providing robust estimates of predictive accuracy and associated uncertainty. The resulting 95% confidence intervals offer reliable prediction ranges for each performance indicator (Perrignon et al., 2025).

Each model was trained using all the decision variables and informative variables from the database. Its performance was then evaluated using the Root Mean Square Error (RMSE) and the R² metric. The RMSE measures the deviation between the predicted values and the actual analytical measurements of the objectives, providing an indication of the model's accuracy. The R² metric quantifies the proportion of variance in the response variable (performance indicator) that is explained by the model. A low RMSE and high R² value indicate a good model accuracy. Random Forest (RF) achieved the best results, for the RMSE and R², explaining it is selected for the study (Supplementary material, Table S1). RF is a machine learning model built using an ensemble of decision trees, which are built from the collected data. RF algorithm (Breiman, 2001) selects subsets of data and variables for tree construction randomly, to obtain a diversity of trees (Garre et al., 2020; Speiser et al., 2019). Each tree returns a prediction of the output variables and the final prediction is calculated by
averaging the predictions of each tree (Koay et al., 2022; Ma and Cheng, 2016). RF and others methods were implemented in Python, using the scikit-learn library.

## 2.4 Formulation of the multi-objective problem and constraints

Three objectives were defined based on performance indicators defined previously:

- Minimize the fat content (% w/w) with a minimal value higher than 34% w/w

- Minimize the moisture content (% w/w) with a minimal value higher than 1.7% w/w

- Maximize crisp's lightness (%)

In order to structure the algorithm's search space and ensure that the results are realistic and applicable, all the constraints associated with the crisps manufacturing process were listed. Equality constraints are parameters that cannot be modified. They refer to the 19 quality attributes of the potato batches. Fryers do not control these parameters that remain fixed during the optimization problem. The process parameters are optimized based on them. Inequality constraints correspond to parameters boundaries defined by minimum and maximum values. The boundaries are the minimum and maximum values of each process variable listed in the dataset. The objectives also have their own boundaries that need to be set. These boundaries delimit the target values to be achieved and are set by the industry. The lower boundary for fat content is set at 34% w/w, and for moisture content at 1.7% w/w, which are the minimal values to achieve. The objective is to get as close as possible to these boundaries without going below them. Regarding the lightness, the objective is to maximize this variable. By default, optimization algorithms minimize the indicator; therefore, to maximize it, a negative sign must be placed in front of the value.

The multi-objective optimization problem of the potato crisp manufacturing process can be formulated and solved once the boundaries and equality constraints are defined (1):

$$ \text{Minimize } f(x) = [f_{\text{Fat content}}(x), f_{\text{Moisture content}}(x), -f_{\text{Lightness}}(x)] \quad (1) $$

subject to
Fat content ≥ 34 and Moisture content ≥ 1.7

$$ x_i^{\min} \le x_i \le x_i^{\max}, \forall i \in \{1, ..., n\}, $$

with $x_i$ = $i^{th}$ process variable

and $n$ = number of process variables

and fixed potato quality attributes

## 2.5 Presentation of potato scenarios

To illustrate the multi-objective approach and understand how to adjust the process based on potato quality, two scenarios corresponding to two potato batches characterized by different quality
attributes (Table 1) were set up. The first scenario (Scenario 0) corresponds to a potato batch A. The second (Scenario 1) corresponds to a potato batch B. The quality attributes of the potato batches are representative of potato batches handled by the crisp manufacturing industry. Table 1 do not list all the quality attributes of the potato batches A and B but only the quality attributes having a value other than 0 are indicated. Potato batch A represents the most common scenario encountered in crisp manufacturing, where potatoes meet standard quality requirements with minimal defects. In contrast, potato batch B represents an unusual scenario that occurs when potatoes present significant quality issues, such as appearance defects or suboptimal characteristics. Processing such batches are challenging because they require specific adjustments to the process that can significantly impact product quality and yield if not properly managed. These two contrasting scenarios were chosen to demonstrate the adaptability of the multi-objective optimization approach across a large spectrum of potato quality variations encountered in industrial crisp manufacturing. The 19 variables corresponding to the quality attributes of the two batches of potatoes are fixed as inputs for the optimizations.

## 2.6 Solving the multi-objective problem using Nondominated Sorting Genetic Algorithm II

The multi-objective problem was solved by the genetic algorithm Nondominated Sorting Genetic Algorithm II (NSGA-II) proposed by (Deb et al., 2002). NSGA-II is based on non-dominated sorting, designed to solve multi-objective optimization problems with quantitative decision variables. The algorithm is divided into several steps (Figure 3). The first step involves generating randomly an initial population P0 of size 100 (The population size is a parameter that can be modified by the user. Here, the size has been arbitrarily set to 100). Then, a child population (Q0), also of size 100, is generated from the initial population using tournament selection, crossover (to combine solutions and explore new possibilities) and mutation (to introduce small random changes and maintain diversity). The new population P1 is then selected by comparing P0 and Q0 through non-dominated sorting, which ranks solutions based on their dominance, selecting the solutions that improve the performance of all objectives and by comparing the crowding distances between solutions. These steps are repeated 1000 times. This value corresponds to the number of generations of the algorithm and is set by the user. The tests conducted in this study showed that the results remained unchanged for a number of generations higher than 1000. This method was implemented in Python using the *pymoo* library. The algorithm returns a set of 100 acceptable solutions obtained after 1000 iterations.
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## 2.7 Identification of the best solution using Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)

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To select a solution from the set of solutions proposed by the algorithm, multi-criteria decision support methods are required. Several methods exist in this family, including AHP (Analytic Hierarchy Process), ELECTRE (ELimination and Choice Translating REality), and PROMETHEE (Preference Ranking Organization METHod for Enrichment Evaluation). In this study, the TOPSIS method developed by Hwang and Yoon (1981) was chosen for its ability to rank solutions efficiently and its particular suitability to contexts where objectives are numerous and heterogeneous. TOPSIS is also easy to implement, well documented and available in several computer languages.

The selected Pareto-optimal solution is the one with the greatest Euclidean distance from the negative ideal solution and simultaneously the smallest Euclidean distance from the positive ideal solution (Supplementary material, Figure S2). The TOPSIS method allows for indicator weighting, meaning different weights may be assigned to indicators when they hold different economic or regulatory importance. In this study, equal weights were assigned to all objectives in collaboration with industrial experts to ensure a balanced evaluation of all performance indicators. This selected solution provides the best trade-off between all objectives. The method was implemented in Python using the *topsispy* library.

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# 3 Results

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## 3.1 Overview of the decision variables in the dataset

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The 9 decision variables are the process parameters involved in crisp quality optimization. They are adjusted directly by the fryers to influence the process flow. Figure 4 illustrates the frequency distribution of the decision variables observed in the database that corresponds to the different levels and frequency of adjustment of these variables in the process by the fryers. The frequency distribution of the variables Peeling time, Slat thickness, Water supply, and Time Belt 1, indicates that some levels are preferentially used by the fryers while other levels have never been tested during the crisp manufacturing process. For Water supply, one level is mainly applied, while four other levels have been tested sporadically. The frequency distribution of slat thickness shows some untested values due to constraints related to the design of the cutting head, which limits the number of available options for this variable. This information will need to be considered in the constraints of the optimization step, and the obtained values should be assessed in light of the technical capabilities of the process. For the variables Elevator drive sprocket frequency, Fryer temperature, Time Belt 2 and Belt 3 drive sprocket frequency, large ranges of levels have been explored indicating that the fryers preferentially
tune these variables to control the quality of the crisps. In summary, figure 4 shows that both operational preferences and technical constraints influence the setting of the decision variables. These results highlight the interest of using a multi-objective optimization approach to assess whether the levels implemented for the decision variables are optimal or not with regard to the crisp quality criteria. Indeed, the algorithm can suggest new combination of levels for the decision variables, provided they fall within the defined boundaries.

## 3.2 Evaluation of model performance

For the modeling of each crisp physicochemical indicator, 80% of the dataset, representing 120,127 individuals, is used to train and optimize the model's hyperparameters. The model of each crisp physicochemical indicator is then validated on the test set to assess its performance using the RMSE and $R^2$ evaluation metric. The performance of the model for each crisp physicochemical indicator using RF is shown in Figure 5. It shows the predicted values from the trained model as a function of the observed values from the test set as well as the evaluation metrics (RMSE and $R^2$) for each indicator.

The RMSE is expressed in the same unit than the indicator. This metric simply provides an indication of the quality of the approximation. The closer the value is to 0, the better the model's approximation. RMSE result shows that the predictions of the indicator “fat content” are off by 0.46% from the observed values. RMSE result shows that, on average, the predictions of the indicator “moisture content” are off by approximately 0.09 from the observed values and by approximately 0.40 for the “lightness” indicator. To compare the performance of the models, the $R^2$ was examined. The predictive model for crisp “fat content” achieved a $R^2$ of 0.96, indicating an excellent predictive capability. Similarly, the model for “lightness” reached an $R^2$ of 0.94, also reflecting very good performance. In contrast, the model predicting “moisture content” yielded an $R^2$ of 0.71, which demonstrates lower performance compared to the other two models. Nevertheless, all these three models were then used for the optimization step.

## 3.3 Comparison of objectives achieved after optimization and best solution selection

For the two potato batches, 100 solutions that satisfy the crisp quality objectives were obtained. The Pareto front for the three crisp quality objectives after processing potato batch A and B are represented in Figure 6 and 7, respectively. Each point represents a solution. “Fat content” (%) is represented on the X-axis, “Moisture content” (%) on the Y-axis, and “Lightness” (%) is represented by the lightness gradient. Both Pareto fronts have the same profile. The optimization algorithm successfully obtained solutions close to industrial targets for fat content and moisture. Indeed, fat values ranged between
313 34% and 34.25%, which remains very close to the set target (Figure 6). For moisture, the results fell between 1.7% and 1.8%, with a target of 1.7%, demonstrating excellent precision while fully meeting industrial requirements (Figure 6).
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316 Regarding lightness, values ranged from 64% to 70% (Figure 7), with the majority of the solutions clustering around 69%. Since the aim was to maximize this indicator, and the average value was approximately 65% in the database, these results appear highly satisfactory. Solutions with lower lightness values were mainly associated with a fat content of 34% (Figure 7) suggesting a correlation between decreased fat content and reduced lightness demonstrating the algorithm effectively balances the three performance criteria. With targets met for fat content and moisture content, and consistently high lightness values, the proposed solutions can be considered fully satisfactory for industrial applications.
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324 Optimization enables the identification of a set of solutions that balances trade-offs between the three performance indicators. The aim is then to select the best compromise from these solutions based on the industry's guidelines. For this purpose, the TOPSIS method was applied, assigning equal weight to each objective to avoid bias. The solution obtained using the TOPSIS method is highlighted in red in Figure 6 and 7. For Scenario 0 (potato batch A), the selected solution for the crisp physicochemical indicators is a fat content of 34%, a moisture content of 1.7% and a lightness of 70%. For Scenario 1 (potato batch B), the selected solution is for a fat content of 34%, a moisture content of 1.7%, and a lightness of 69.8%. The obtained solutions can then be compared to those actually achieved in the industry, as both batches of potatoes have already been produced. The results are presented in Table 2. The objectives obtained after optimization are closer to the target value than those achieved in the industry. Indeed, the industrial targets set for fat content and moisture content are met through optimization, whereas in the industry, the values are close but do not exactly match the target. For lightness, the results after optimization are close to 70%, while in the industry, they are 66.4% for potato batch A and 67.2% for potato batch B. Comparing the industry results with those obtained through optimization demonstrates that the optimization identifies solutions that lead to improved objective values.
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340 All these results for the two potato batches indicate that regardless of the quality of the potatoes, the optimization algorithm succeeds in achieving similar objectives. This suggests that the variability in potato quality is corrected during the process, enabling comparable quality objectives for the crisps to be reached. To confirm this hypothesis, it is necessary to closely examine the values of the decision variables for each potato quality.
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345 **3.4 Scenario comparison and decision support for fryers**

346 The methodology integrated into the DT (modeling and optimization) provides a set of solutions for
347 achieving the target crisp quality objectives from a potato batch characterized by specific quality
348 attributes. The set of solutions is a guide for the fryers to better manage their crisp manufacturing
349 lines, by providing the level of the decision variables to be implemented in order to optimize the
350 manufacturing process. The results for the two scenarios are displayed in Figure 8 in the order of
351 appearance of the decision variables in the process. The distribution of the process parameter levels
352 of the database is represented with boxplot and the red circles and the blue triangles indicate the levels
353 selected by the TOPSIS method. Red circles correspond to the solution for scenario 0 (potato batch
354 A), while blue triangles represent the solution for scenario 1 (potato batch A). This figure shows the
355 levels returned after optimization in the light of the range of levels set in the industry, as well as the
356 difference between the levels obtained after optimization for the two scenarios.

357 For the variables "Elevator drive sprocket frequency", "Slat Thickness", "Boiler Temperature",
358 "Fryer Temperature" and "Time Belt 1", the levels of the process parameters obtained after
359 optimization lie within the distribution of levels already set by the fryers. This means that these levels
360 have already been set for crisp manufacture and, in the opinion of the fryer, do not pose a problem
361 for the correct operation of the process. Conversely, the optimization returns levels outside the
362 distribution of levels observed in the plant for the process parameters "Peeling Time", "Water
363 Supply", "Time Belt 2" and "Belt 3 drive sprocket frequency". In order to assess the relevance of
364 these levels, the opinion of the fryer is required. For "Peeling Time," the result for Scenario 0 (potato
365 batch A) falls within the range of values already used in the industry. For Scenario 1 (potato batch B),
366 the peeling time is nearly twice the mean value used in the industry but remains feasible and
367 acceptable for production. For the "Water Supply" variable, the level obtained after optimization for
368 Scenario 1 (potato batch B) is lower than those set in the industry. This suggests that the operator
369 could reduce by a factor of near 4 the mean amount of water used to wash the potato slats. This
370 solution does not appear to be out of place and would be advantageous for the company from an
371 economic and environmental point of view. With regard to time spent on belt 2, the levels obtained
372 after optimization suggest an increase of "Time Belt 2", mainly for Scenario 0. Increasing the time
373 spent in the fryer means longer cooking times which in turn improves crisp quality. Finally, for the
374 variable "Belt 3 drive sprocket frequency", the level obtained after optimization suggests an increase
375 of the speed. The level of this parameter, which influences the fat content of potato crisps, is currently
376 modified within a restricted range of levels by operators. The level obtained after optimization could
377 be of interest as this variable impacts the crisp quality objectives, but in-plant trials are necessary to
378 validate the new setting of the variable "Belt 3 drive sprocket frequency".
The level of decision variables "Slat Thickness", "Boiler Temperature" and "Fryer temperature" remained unchanged between Scenario 0 and Scenario 1, indicating that the quality differences between the potato batches A and B do not require any adjustment of these parameter settings. In contrast, the level of the variables "Water supply", "Time Belt 1" and "Time Belt 2" is higher in scenario 0 (potato batch A). This indicates that for potato batch A (without appearance defect), both the conveyor belt times at the fryer inlet and the water supply should be increased. While the difference for "Time Belt 1" between the two scenarios is minimal, "Time Belt 2" requires a significant reduction of 30 s for potato batch B (potato with appearance defects). This indicates that when potatoes have less defects, the potato slats need to spend more time at the second belt in fryer, which is achieved by slowing down the speed of belt 2. For "Water supply", a higher volume of water is used to wash potato slats for Scenario 0 (potato batch A) compared to Scenario 1 (potato batch B) indicating that slats from potatoes with less appearance defects require more water to meet crisp quality objectives. This variation may also be related to the potatoes size distribution between the 2 batches. Indeed, potato batch A contains a higher proportion of smaller potatoes (Table 1), coming with smaller and more numerous slats, which could affect the amount of water needed for the potato slat's washing. This insight demonstrates that quality of the potato batch can affect the water usage.

The level of the process parameters "Peeling Time", "Elevator drive sprocket frequency" and "Belt 3 drive sprocket frequency" should be increased for potato batch B (Scenario 1) compared to potato batch A (Scenario 0). The peeling time of potatoes having defects such as blemishes, deformities, or green spots, etc. must be longer than for potatoes without defects in order to obtained uniformly peeled potatoes with no more traces of defects. The speed of the elevator determines the process throughput because this constitutes the limiting step of the crisp manufacturing process. However, the difference of Elevator drive sprocket frequency between the two potato batches remains small.

The increase of the speed of the final conveyor belt in the fryer (variable "Belt 3 drive sprocket frequency") is higher for potato batch B, meaning the potato slats spent less time in the final section of the fryer (Belt 3) for having the same oil content.

As with the objectives in the previous section, the values of the decision variables implemented in the industry for these potato batches can be compared with those suggested by the optimization. This comparison helps to understand the decisions made by the fryers and identify necessary adjustments (Supplementary material, Figure S3).

## 4 Discussion

The illustration of the methodology applied to two batches of potatoes having different qualities reflects the day-to-day reality of food industry processing raw materials with quality attributes that
varies with phenotypes, seasons, etc (Yee and Bussell, 2007). To overcome this variability, the food industries have two strategies, depending on the raw material being processed. The first one is to standardize the raw material, as many dairy industries do, in order to process a milk of constant composition under constant processing conditions all year round (Soodam and Guinee, 2018). The second strategy is to adapt the process according to the variability of the raw material since it cannot be standardized (Bourquard, 2018). In the field of crisp production, fryers constantly adjust process parameters to variabilities in the quality of potato batch while maintaining regular objectives in terms of crisp qualities. This requires a long training and expertise for the fryers on their crisp manufacturing lines. The methodology developed in this study offers the possibility of adapting to this variability by training machine learning models on a dataset collected over several years. The results obtained for both potato batches demonstrate the necessity of adapting the process based on raw material quality to achieve similar objectives. Table S2 in the supplementary materiel summarizes the different adjustments to be made on the production line along with the associated expert evaluation for each proposed modification. This expert validation proves essential since the developed tool aims to provide decision support to fryer operators. The acceptance and adoption of this approach by end users directly conditions its industrial success; it is therefore crucial to integrate their feedback to validate and refine the methodology, particularly by adjusting variable bounds or process-related constraints. For example, regarding the “Water supply” variable, the recommendation for one scenario is significantly lower than current industrial practice. While this recommendation makes it possible to reduce crisp line water consumption, it remains questionable as this drastic reduction could impact performance indicators not yet integrated in the optimization. This observation raises several improvement perspectives for the method, such as the integration of additional performance indicators in the optimization or the revision of bounds to better reflect actual operational constraints. Models presented in this article have been studied in two ways. A training phase, on the whole database, ensures its genericity and adaptability to new data (evaluated through a cross-validation). Thanks to the richness of the historical database (two complete years of process between 2022 and 2023), the trained models are thus easily transferable to new applications. Retraining them would only be necessary in case of an evolution of the raw material (different sizes, shapes, ...), causing a drift between the predicted and actual values. A validation phase has been done on two distinct batches in order to illustrate two different real-life situations. In a first case, we consider a batch of standard quality potatoes (batch A), without any defect, typical of those processed daily by the fryers. In a second time, an extreme scenario has been processed (batch B) to test the limit of the predictive models. In this case, the potatoes presented many defects in order to represent the most difficult cases
to process. While these two batches do not cover the whole range of possible scenarios, they allow
us to demonstrate the adaptability of our models in a context of a DT approach.

The quality of the models is crucial for the subsequent steps of the multi-objective optimization
approach (Madoumier et al., 2019). Indeed, the results of the optimization will be biased and
unrealistic if a model does not predict the indicator correctly or if its prediction error is too high. In
the context of crisp production, it was shown above that the performance of the "moisture content"
model was lower than the two other models, with an R² of 0.71 compared to 0.96 and 0.94 for fat
content and lightness models, respectively. While this model remains satisfactory given its overall
performance metrics (RMSE and R²) and can be used for the optimization step, its lower prediction
accuracy introduces uncertainty into one of the three objectives. This limitation could potentially
affect the reliability of optimization outcomes. The reduced model performance may lead to
suboptimal solutions or increased variability in the recommended process parameters. Beyond model
accuracy, understanding model interpretability is also essential for building confidence in the
optimization results. Machine learning models often operate as "black boxes" with numerous
interdependent parameters, limiting the interpretation of results and understanding of the model's
decision (Przybyl, 2024). There are several methods to help interpret models (Ali et al., 2023),
including the SHapley Additive exPlanations (SHAP) (Lundberg et al., 2018) and Local Interpretable
Model-agnostic Explanations (LIME) (Ribeiro et al., 2016) methods. Both model-agnostic methods
help explain how models make their predictions and improve understanding of model behavior.
Understanding how this model uncertainty propagates through the optimization process and impacts
the final optimal solutions represents an important area for future investigations. Methods such as
uncertainty quantification, sensitivity analysis of optimization results to model prediction errors and
model interpretability methods such as SHAP and LIME analysis could provide valuable insight into
the reliability of the methodology and strengthen user confidence in the optimization
recommendations.

Another aspect to consider is the computational cost associated with this methodology. The training
phase of the models is particularly demanding in terms of computing time (few hours, depending on
the amount of training data). Unlike mechanistic modeling based on known equations, data-driven
modeling requires a preliminary training phase before using the models for the optimization step
(Khan et al., 2022). This training process must be conducted in advance to ensure real-time results.
In the case of potato crisp production, the model training phase (including hyperparameter
optimization) requires 1 hour on a dedicated server, while the optimization step to determine the
parameters to implement for a given potato batch takes only a few seconds (less than 40 in our case).
This rapid optimization enables real-time actions to be taken on the process: as soon as a new potato
batch is qualified, fryer operators instantly obtain the optimal parameters to be implemented and they control the line according to these recommendations. However, prior model training presents a limitation: once trained, models cannot integrate new parameters or updated data that were not present in the initial training dataset. In this case, models can be retrained to refine future predictions. To overcome this limitation, dynamic model training could be directly integrated into the digital twin. This approach would enable continuous model improvement by incorporating new data collected from the crisps line (Kreuzer et al., 2024). This dynamic training can be performed in parallel without interfering with ongoing optimization processes, allowing newly trained models to be integrated into the DT framework once ready. However, integrating dynamic training requires careful management of computational resources and timing. A practical solution involves implementing a scheduled update framework (whether daily, weekly, or monthly) to systematically retrain models and deploy updated versions in industrial operations (Metcalfe et al., 2025).

The computing time of the optimization step is directly influenced by two main parameters: the number of generations and the population size used in the algorithm. A high number of generations ensures a high-quality Pareto front but also results in significant computational costs, sometimes for solutions that could be obtained for a lower number of generations. Conversely, if the number of generations is too low, the Pareto front may not be stabilized, leading to suboptimal solutions. Therefore, fine-tuning these parameters is necessary to maximize optimization efficiency while minimizing computational cost (Zakaria et al., 2011). The combination of parameters is specific to each problem. Indeed, depending on the number of objectives to be optimized, the number of generations will need to be optimized to ensure the quality of the Pareto front (di Pierro et al., 2007).

In the case of the crisp process optimization, the number of generations was set to 1000 and the population size to 100. This combination of parameters was sufficient in this case study to achieve a stable Pareto front, but it could be optimized to reduce computation time. Currently, the computation time for optimization is short enough to allow for the consideration of potato quality and to send the information back to the fryers. Thus, while the developed methodology demonstrates strong adaptability and generalization potential, its computational cost must be carefully considered, particularly for efficient industrial implementation. The integration of dynamic training strategies and the optimization of the trade-off between computing time and solution quality represent promising outlook for future improving this methodology.

To sum up, several perspectives emerge from this work to further enhance the proposed optimization framework. First, the generalization of this data-driven methodology to other food manufacturing processes represents a promising avenue (Datta et al., 2022; Mavani et al., 2022), though success will inherently depend on the quality and representativeness of the available industrial datasets. The
adaptability of the approach across different production contexts will require careful consideration of
513
514 data characteristics, process specificities, and the nature of process parameters (continuous vs.
515 discrete variables), which is crucial for selecting the appropriate optimization methodology. Second,
516 integrating uncertainty quantification into both the machine learning models and optimization process
517 constitutes a stimulating research direction. Addressing model prediction uncertainties and their
518 propagation through the optimization algorithm would provide more robust and reliable solutions for
519 industrial decision-making. Third, industrial deployment and validation of the process parameter
520 predicted by the algorithm remains essential for establishing its practical value. To date, the proposed
521 methodology operates in offline mode, meaning it is not applied in real-time on production lines.
522 However, the definition of a digital twin states that these systems run in parallel to the real food
523 manufacturing process through a continuous data flow. For our approach to be fully qualified as a
524 digital twin, it must be implemented in the industry to provide real-time recommendations.

5 Conclusion

The study presented in this article demonstrates the potential of the digital twin, coupled with a multi-
526
527 objective optimization approach, as a tool to assist fryers in managing potato crisp production lines.
528
529 By exchanging a continuous flow of information, the tool integrates collected data throughout the
530 crisp manufacturing process to build models, optimize process parameters, and provide instructions
531 to the fryers to reach crisp quality objectives. The results obtained for potato batches with two
532 different qualities show that the production line needs to be managed differently depending on the
533 quality of the potatoes. This validates the relevance of the present approach in providing real-time
534 specifications on the process parameter settings to be implemented to guarantee optimal crisp quality
535 objectives.
536

Once implemented, it will be able to process real-time data on potato quality and return instructions
535
to the fryers on the level of process parameters to control potato crisp manufacturing process. One of
536
the advantages of the proposed approach is its modularity and its ability to evolve in line with
537
industry's guidelines. While the current optimization focused on three objectives, future
538
developments represent a key opportunity to incorporate environmental sustainability metrics,
539
including water consumption, energy usage, and waste reduction, thereby enabling optimization
540
frameworks that simultaneously address economic and environmental performances. Consequently,
541
the development of digital twins holds promise for addressing current industrial challenges while
542
anticipating future needs, particularly in terms of environmental impact.
543
544 **Funding sources**

545 This project was supported by Fondation Institut Agro

546 **Acknowledgements**

547 The authors thank Romuald Rituit, Laurent Mollard and Geoffrey Ruiz from Altho for sharing the
548 data and for their expertise in interpreting the results. The authors would also like to thank Manon
549 Gaudin, Océane Frayssinet and Nolwenn Poulain for their assistance in collecting and pre-
550 preprocessing the data.

551 **Author contributions: CRediT**

552 Manon Perrignon: Conceptualization, Investigation, Methodology, Visualization, Writing – original
553 draft; Mathieu Emily: Supervision, Conceptualization, Methodology, Writing – review and editing;
554 Mélanie Munch: Methodology, Writing – review and editing; Paul Debuire: Methodology; Romain
555 Jeantet: Supervision, Conceptualization, Project administration, Funding acquisition, Writing –
556 review and editing; Thomas Croguennec: Supervision, Conceptualization, Writing – review and
557 editing

558 **Abbreviations**

559 DT = Digital Twin

560 RF = Random Forest

561 RMSE = Root Mean Square Error

562 NSGA-II = Nondominated Sorting Genetic Algorithm II

563 TOPSIS = Technique for Order of Preference by Similarity to Ideal Solution

564 **Conflicts of Interest**

565 The authors declare no conflicts of interest.

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<table><caption>Table 1: Presentation of the two potato quality scenarios defined for optimization. Scenario 0 represents a batch of potatoes A without appearance defect, while Scenario 1 represents a batch of potatoes B with appearance defects (burnt, spotted, green).</caption><thead><tr><th>Scenario</th><th>Dry matter<br>(% w/w)</th><th>Small<br>size (%)</th><th>Medium<br>size (%)</th><th>Quality<br>index</th><th>Tuber<br>weight (g)</th><th>Burnt<br>(%)</th><th>Spotted<br>(%)</th><th>Green<br>(%)</th></tr></thead><tbody><tr><td>Scenario 0:<br>potato batch A</td><td>21,2</td><td>77,31</td><td>21,99</td><td>7,5</td><td>134,06</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Scenario 1:<br>potato batch B</td><td>20,7</td><td>18,16</td><td>71,96</td><td>6</td><td>245,37</td><td>1,28</td><td>2,17</td><td>5,73</td></tr></tbody></table>
<table><caption>Table 1: Comparison of optimized values for TOPSIS-selected solutions with actual industry results for potato batches. The values in green represent the best results for each indicator and potato batch. The optimization suggests better objectives than actual objectives</caption><thead><tr><th></th><th></th><th>Fat content<br>(%)</th><th>Moisture content<br>(%)</th><th>Lightness<br>(%)</th></tr></thead><tbody><tr><td rowspan="2">Potato batch A</td><td>Actual objectives<br>achieved in the industry</td><td>34.9</td><td>1.8</td><td>66.4</td></tr><tr><td>Optimized objectives</td><td>34</td><td>1.7</td><td>70</td></tr><tr><td rowspan="2">Potato batch B</td><td>Actual objectives<br>achieved in the industry</td><td>34.6</td><td>1.8</td><td>67.2</td></tr><tr><td>Optimized objectives</td><td>34</td><td>1.7</td><td>69.8</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>Figure 1: Schematic representation of the potato crisps production. The red stars represent the data collection points.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 2: Simplified version of the dataset used in this study and different variable categories. Each column corresponds to a measured process parameter, classified into a specific category (e.g., performance indicators, decision variables and informative variables). Each row represents a batch of potatoes processed in the system. The complete dataset consists of 135,849 rows (individuals) and 47 columns (variables). The informative variables include potato quality variables and process variables.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 3: NSGA-II procedure for creating one generation. P_n represents the initial population and Q_n represents the child population generated by P_n through mutation, crossover and tournament selection.

The population size has been set to 100 solutions.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 4: Histograms illustrating the distribution of decision variables observed in the dataset</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 5: Performance of the three RF models for predicting crisp physicochemical indicators, determined on the test set. Each graph shows the comparison between predicted and observed values, along with performance metrics RMSE (Root Mean Squared Error) and R² (coefficient of determination). Graph (A): Model performance for the *fat content* indicator. Graph (B): Model performance for the *moisture content* indicator. Graph (C): Model performance for the *lightness* indicator.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Figure 6: Representation of the Pareto front for the 3 objectives of the potato crisp process after optimization by the NSGAII algorithm (number of generations = 1000 and population size = 100) for Scenario 0 (potato batch A). “Fat content” is represented on the X axis, “Moisture content” is represented on the Y axis and “Lightness” is represented by the lightness scale. The red frame represents a zoomed-in view of the area near the targets for fat and moisture contents. The red circle represents the solution selected from the Pareto front by the TOPSIS method.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure 7: Representation of the Pareto front for the 3 objectives of the potato crisp process after optimization by the NSGAII algorithm (number of generations = 1000 and population size = 100) for Scenario 1 (potato batch B). “Fat content” is represented on the X axis, “Moisture content” is represented on the Y axis and “Lightness” is represented by the lightness scale. The red frame represents a zoomed-in view of the area near the targets for fat and moisture contents. The red circle represents the solution selected from the Pareto front by the TOPSIS method</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 8: Violin graphs of the process decision variables based on data from the database. Red circles indicate the optimal values obtained for each variable after optimization for scenario 0 (potato batch A), blue triangles represent those for scenario 1 (potato batch B). These optimal values determine the settings to be implemented in the industry to achieve the target objectives.</figcaption></figure>
**Highlights:**

* Digital twin integrating multi-objective optimization for crisp manufacturing

* Machine learning models predict fat, moisture and lightness performance indicators

* Optimization delivers optimal solutions proving differential control necessity between potato batches

* Process parameters must be adjusted based on potato quality to meet crisp standards

* Framework provides a decision-support tool for process control by fryer operators
**Declaration of interests**

[x] The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

[ ] The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

<figure><img src="image_13.png" /></figure>