Integrated Machine Learning Framework for Smart Food Systems Optimization in Aceh, Indonesia

1).DATA COLLECTION

The dataset employed in this study is obtained from the Aceh Food Agency (Dinas Pangan Aceh), which records the average annual retail prices of 12 strategic food commodities. The commodities include rice (premium and medium), dried soybeans, shallots, garlic, red chili peppers, beef, broiler chicken meat, chicken eggs, granulated sugar, packaged cooking oil, and wheat flour. The dataset spans from 2017 to 2024, as shown in Table II.

Table II. Annual average retail prices of strategic food commodities in Aceh (2017–2024)

2).MODEL TRAINING

Ridge regression is applied, and cross-validation is performed to determine the optimal penalty parameter (α), minimizing predictive bias and variance.

3).FORECASTING

The trained model is employed to project commodity prices for 2025–2028.

4).MODEL EVALUATION

Predictive performance is assessed using standard statistical indicators, including MSE and RMSE, as expressed in Equations (2) and (3), respectively:

In this formula, Yi denotes the observed value, Y^i is the predicted value, and n is the number of observations. A lower RMSE indicates higher forecasting accuracy and makes interpretation easier compared to MSE.

1).K-MEANS CLUSTERING

The K-means algorithm is applied through the following steps [27]:

• 1.Initialize centroidsRandomly select k initial centroids from the dataset to serve as starting points.
• 2.Assign districtsEach district i is assigned to the nearest centroid by minimizing the Euclidean distance, defined in Equation (4):
  ‖xi-μk‖(4)
  where x_i denotes the vector of vulnerability indicators for district i and μ_k is the centroid of cluster k.
• 3.Update centroidsRecompute each centroid μ_k as the mean of all points in cluster C_k.
• 4.Iterate until convergenceRepeat steps 2–3 until cluster assignments stabilize. The objective is to minimize the within-cluster sum of squares (WCSS), defined in Equation (5):
  WCSS=∑k=1K∑iεCk‖xi-μk‖2(5)
  where K is the number of clusters, Ck is the set of districts in cluster k, and μ_k is the cluster centroid.
• 5.Evaluate cluster qualityThe clustering performance was quantitatively evaluated using the CH index and SS, defined in Equations (6) and (7):
  CH=Tr(Bk)/(K-1)Tr(Wk)/(n-K)(6)
  Tr(B_k) is the trace of the between-cluster dispersion matrix, Tr(W_k) is the trace of the within-cluster dispersion matrix, K is the number of clusters, and n is the total number of observations. Higher CH values indicate more distinct and well-separated clusters:
  s(i)=b(i)-a(i)max{b(i)-a(i)}(7)
  a(i) is the average distance between observation i and other points in the same cluster, while b(i) is the minimum average distance to points in other clusters. The score ranges from −1 to 1, with higher values indicating more cohesive and well-separated clusters.

2).SAW-K-MEANS CLUSTERING

The SAW-K-means approach was implemented to enhance clustering stability and interpretability. By integrating SAW with K-means, cluster center initialization becomes more structured, reducing randomness, improving computational efficiency, and ensuring reliable clustering outcomes.

• 1.Compute Composite Vulnerability Scores.Each district i receives a composite score Si using SAW, defined in Equation (8) [28]:
  Si=∑j=1mwj.rij(8)
  where w_j is the weight of indicator, r_ij is the normalized value of indicator j for district i, and m is the total number of indicators. In this study, the weight w_j is automatically assigned using an equal distribution method, yielding a value of 0.027778 for each criterion. The weighting process follows an equal-weight approach, where the total weight is evenly divided among all identified criteria. This method ensures that each criterion contributes equally to the overall assessment, thereby promoting fairness and minimizing potential bias toward any specific attribute in the final ranking outcome.
• 2.Initialize Centroids.Districts with the highest Si scores are selected as initial centroids to ensure highly vulnerable regions are represented from the outset.
• 3.Apply K-Means Algorithm.Follow the standard K-means procedure (assignment, centroid update, and iteration) using SAW-based centroids.
• 4.Evaluate Cluster Quality.Cluster quality was evaluated using CH index and SS
• 5.Identify Food Vulnerable Districts.Districts belonging to the cluster with the highest average Si were designated as Food Vulnerable areas.

1).SUPPORT VECTOR MACHINE (SVM)

SVM is a supervised method designed to find the most effective hyperplane that distinguishes between classes [29]. For linearly separable data, the decision function is given in Equation (9):

For nonlinearly separable data, the kernel trick projects input features into a higher-dimensional space. Common kernels include the radial basis function (RBF), defined in Equation (11):

Here, γ controls the influence of individual samples. SVM was used to classify districts by mapping multidimensional food system features to an optimal decision boundary.

2).RANDOM FOREST (RF)

As an ensemble learning approach, RF strengthens classification performance through the integration of predictions from many individual decision trees [30]. Each decision tree is constructed using a bootstrap sample, with node divisions chosen from a randomly selected group of features. In this model, the concluding prediction is determined through a majority-vote mechanism across all decision trees, as represented in Equation (12):

In this equation, Y^ denotes the final predicted class label, where Y^ is determined based on the individual predictions h1(x),h2(x),…,hr(x) generated by each decision tree within the ensemble. The mode function identifies the most frequently occurring class label among these predictions, thereby determining the overall output of the RF model through a majority voting mechanism. The splitting criterion in each decision tree is typically based on Gini Impurity, defined in Equation (13):

1).STANDARD K-MEANS CLUSTERING RESULTS

Standard K-means is applied to classify food vulnerability across Aceh districts into three categories: Food Secure, Food Vulnerable, and Food Insecure, with results shown in Table VIII. Coastal urban districts such as Banda Aceh, Sabang, and Lhokseumawe were Food Secure, reflecting stable food access and infrastructure. Remote inland districts, including Gayo Lues, Aceh Tenggara, Simeulue, and Bener Meriah, were Food Insecure due to geographic isolation and limited productivity. Most other districts, such as Pidie, Aceh Utara, and Aceh Timur, were Food Vulnerable, indicating susceptibility to supply–demand fluctuations. Cluster distribution from 2017 to 2024 is shown in Fig. 5, with a corresponding heatmap in Fig. 6.

Table VIII. Standard K-means clustering results for food vulnerability in Aceh Province, Indonesia

Fig. 5. Food security cluster distribution in Aceh, Indonesia (2017–2024).

Fig. 6. Food security heatmap cluster distribution in Aceh, Indonesia (2017–2024).

To assess the performance and stability of the K-means algorithm, ten runs with different initial centroid selections were conducted. Convergence speed was measured by iteration count, while clustering quality was evaluated using the CH index and the SS. Results show that the CH index remained high (≈45.5) and the SS stable at 0.30, reflecting consistent cluster separability with moderate cohesion. Test 4 achieved the best outcome (CH = 45.75, 6 iterations), while Test 6 performed worst (CH = 35.35, Silhouette = 0.29). Overall, K-means proved robust, though centroid initialization influenced efficiency and cluster quality as shown in Table IX.

Table IX. Performance evaluation of K-means iterations with different initial centroids

2).SAW K-MEANS CLUSTERING RESULTS

The SAW-K-means method applies SAW to calculate feature weights, enabling more systematic centroid initialization and improving cluster distinction. This refinement addresses the key limitations of conventional K-means, namely its sensitivity to random centroid selection and the assumption of equal feature importance. The results are summarized in Table X.

Table X. SAW scores and rankings for the regions

Table X presents the top 10 results from a dataset of 184 regions ranked using the SAW method. In the SAW-K-means hybrid framework, centroid initialization was guided by SAW rankings, with one centroid each selected from the highest, middle, and lowest scores across 10 test iterations. Clustering performance was subsequently assessed using CH index and SS, demonstrating improved stability and quality through the integration of prior ranking information as shown in Table XI.

Table XI. SAW-K-means performance evaluation

Table XI presents the clustering performance of the SAW-K-means hybrid method across 10 iterations. Using SAW for centroid initialization enhances stability, with CH indices ranging from 31.85 to 45.72 and SSs mostly around 0.3. Iterations 3, 6, 9, and 10 achieve higher CH scores above 45, indicating clearer cluster separation, while iteration 8 records the weakest performance with the lowest CH (31.85) and Silhouette (0.2). These results confirm that SAW-based centroid selection improves consistency and reliability, with iteration counts (4–11) reflecting adaptive convergence. A comparison of average results with standard K-means is shown in Table XII and Fig. 7.

Table XII. Comparison of average performance metrics between standard K-means and SAW-enhanced K-means

Fig. 7. Comparison of average performance metrics: standard K-means vs. SAW-K-means.

The comparison between standard K-means and SAW-K-means shows that SAW-based centroid initialization improves convergence speed (7.5 vs. 8.7 iterations). While standard K-means achieves slightly higher CH (44.561 vs. 40.887) and SSs (0.299 vs. 0.288), the differences are marginal, indicating comparable clustering quality overall.

1).SVM RESULTS

SVM is applied to classify the stability of food supply chains by testing two kernel functions, namely RBF and sigmoid. Both kernels are selected to capture nonlinear relationships within the dataset, while variations of the penalty parameter C and kernel coefficient γ are analyzed to optimize performance. The results of SVM classification with the RBF kernel are summarized in Table XIII and Fig. 8.

Table XIII. Classification accuracy of SVM with RBF kernel for different values of C and γ

Fig. 8. Comparison of classification accuracy of SVM with RBF and sigmoid kernels for different values of C and γ.

SVM with RBF kernel showed strong sensitivity to C and γ, with accuracies below 85% at low γ (0.01–0.1) and improving above 90% for C = 100–200. The best accuracy of 94.59% occurred at C = 200 and γ = 50. SVM with sigmoid kernel was also evaluated across C and γ to assess its handling of nonlinear separability. In Table XIV, the SVM with a sigmoid kernel was evaluated across varying C and γ values to assess its capability in modeling nonlinear separability within the dataset.

Table XIV. Classification accuracy of SVM with sigmoid kernel for different values of C and γ

The sigmoid kernel performed poorly, reaching a maximum accuracy of only 46% (C = 100, γ = 0.01), with most results fluctuating between 30 and 40%, indicating instability and underfitting. In contrast, the RBF kernel consistently delivered superior performance, attaining 94.59% at optimal settings, thereby demonstrating its effectiveness in modeling food supply chain stability.

2).RF RESULT

The classification performance of the RF model across the three stability classes is presented in Table XV. This report provides a detailed overview of the precision, recall, and F1-scores, highlighting the model’s consistency in classifying Adequate, Deficit, and Surplus conditions.

Table XV. Classification report of random forest classifier

RF consistently classified food supply chain stability with high performance, achieving F1-scores of 0.985–0.995, a mean 10-fold accuracy of 98.89%, and low variability (0.75%). The RF model is configured with the hyperparameter n_estimators = 100, which specifies the number of decision trees in the ensemble. This value strikes an effective balance between model accuracy and computational efficiency, as adding more trees beyond this point typically yields diminishing performance improvements. The parameter random_state = 42 is applied to ensure the reproducibility of results across different runs. Other hyperparameters, including max_depth, min_samples_split, and min_samples_leaf, are retained at their default settings, allowing the model to adjust dynamically to the dataset’s characteristics. The chosen configuration is evaluated using 10-fold stratified cross-validation, which confirms stable and reliable model performance without the need for extensive hyperparameter optimization.

3).COMPARISON OF SVM AND RF CLASSIFICATION PERFORMANCE

As shown in Fig. 9, RF outperformed SVM, achieving 98.89% mean accuracy, low variability (std. dev = 0.75%), and high F1-scores (0.985–0.995), making it the more robust and reliable model.

Fig. 9. Comparative accuracy of SVM and random forest models in classifying regional food supply chain stability.

Beyond the comparison between SVM and RF in this study, other ensemble methods, such as LightGBM, modified KNN, and decision trees, can be explored in future work. While boosting-based models often achieve slightly higher accuracy, they remain more sensitive to hyperparameter tuning and demand greater computational resources. In contrast, RF offers a balanced trade-off between accuracy, stability, and interpretability, making it particularly well suited for policy-oriented analyses. Consequently, its selection in this framework is methodologically justified, with boosting-based ensembles proposed for subsequent evaluation.