CNNs (Gu et al., 2018) have become one of the most transformative architectures in artificial intelligence, largely due to their outstanding capabilities in image classification, pattern recognition, and object detection. Over time, their use has expanded far beyond visual perception, extending into fields such as natural language processing, biomedical imaging, and environmental modeling. The conceptual basis of CNNs draws inspiration from the hierarchical organization of the mammalian visual cortex, in which sensory information is processed through successive layers of increasing abstraction. In artificial models, this hierarchical mechanism is reproduced as the data move through multiple interconnected layers, where nonlinear activation functions, such as the rectified linear unit (ReLU), hyperbolic tangent (tanh), and sigmoid, allow the network to model complex nonlinear relationships among features.

A typical deep CNN is composed of several distinct types of layers: convolutional, activation, pooling, and fully connected layers. In the convolutional layer, a set of trainable filters (kernels) systematically traverse the input, performing localized dot-product computations between filter weights and corresponding input regions. The result is a group of feature maps that capture local patterns and spatial hierarchies. These feature maps are subsequently passed through activation layers, which introduce the nonlinearity necessary for learning complex dependencies. Among all activation functions, ReLU is the most widely used due to its computational simplicity and effectiveness in mitigating the vanishing gradient issue (Nair and Hinton, 2010).

The pooling layers perform spatial subsampling to reduce the dimensionality of the feature map while preserving the most important information. Max pooling, the most common approach, selects the highest value within each neighborhood, usually achieving a reduction of 70% to 80% in dimensionality without a considerable loss of relevant information. The abstract, high-level features obtained after a series of convolutional and pooling stages are finally processed by fully connected layers, which act as the decision-making component of the network, transforming learned features into the final class predictions.

CNNs have shown exceptional flexibility in a wide range of computer vision tasks (Bhatt et al., 2021), including face recognition (Budiman et al., 2023), document and handwriting analysis (Hasib et al., 2023), and medical image classification for diagnosis of diseases and clinical screening (Salehi et al., 2023; Purkovic et al., 2024). Beyond medical applications, CNN architectures have also been used successfully in climate and environmental studies, particularly to model global weather dynamics and predict extreme meteorological events (Kareem et al., 2021).

XGBoost (Extreme Gradient Boosting) is a machine learning algorithm based on high-performance gradient boosting (Chen and Guestrin, 2016). It constructs a ensemble of decision trees in a sequential manner, where each new tree corrects the errors of the preceding, resulting in enhanced predictive precision and model robustness. Recognized for its scalability and speed, XGBoost incorporates regularization to reduce overfitting and supports parallelized learning, making it well-suited for large, high-dimensional datasets. Its adaptability allows it to handle both classification and regression tasks, with several tunable hyperparameters that significantly affect performance. Thanks to its efficiency, reliability, and interpretability, XGBoost is widely adopted in cybersecurity, IoT data analytics, and other real-world applications that require fast and accurate data-driven predictions.

LightGBM (Ke et al., 2017), an open-source framework developed by Microsoft, is specifically designed for large-scale high-speed data processing. Its efficiency arises from techniques such as Gradient-based One-Side Sampling (GOSS), which preserves samples with larger gradient magnitudes to maintain accuracy, and Exclusive Feature Bundling (EFB), which combines mutually exclusive features to reduce dimensionality and computational load. These mechanisms allow LightGBM to train significantly faster and with lower memory consumption than traditional boosting algorithms, making it highly effective for massive datasets with numerous features.

This framework has proven reliable in a range of predictive problems, including classification, regression, and anomaly detection, and has found applications in structural analysis (Li et al., 2023), financial prediction (Wang et al., 2022), and defect identification (Lao et al., 2023). LightGBM also supports parallel and distributed computation, enabling seamless scalability in modern computing environments. Its main hyperparameters, such as the number of leaves per tree, the maximum depth of the tree, and the learning rate, play an essential role in determining overall model performance and predictive capacity.

A persistent and fundamental challenge in machine learning lies in the optimization of hyperparameters, a task widely acknowledged as NP-hard because of its immense combinatorial search space and computational complexity. This difficulty is further reinforced by the NFL theorem (Wolpert and Macready, 1997), which states that no single optimization approach can consistently outperform all others in all category of problems, as its effectiveness is inherently tied to the characteristics of the data set, the performance metrics, and the parameter configurations involved.

To mitigate these constraints, increasing attention has been focused toward metaheuristic optimization techniques. Metaheuristics, particularly those inspired by swarm intelligence, constitute a class of stochastic optimization strategies modeled after the collective behaviors observed in natural systems such as flocks of birds, swarms of insects, and herds of animals. These methods are particularly well-suited for solving complex, NP-hard problems because they maintain a dynamic balance between global exploration of the search space and local exploitation of promising regions. Nevertheless, population-based methods often face the drawback of overemphasizing one of these components, which can lead to premature convergence or suboptimal stagnation. To counteract this, hybrid approaches and adaptive mechanisms are frequently employed to preserve equilibrium and enhance the robustness of the search process.

Well-known members of this algorithmic family include particle swarm optimization (PSO) (Kennedy and Eberhart, 1995), genetic algorithm (GA) (Mirjalili, 2019), and numerous nature-inspired variants such as the reptile search algorithm (RSA) (Abualigah et al., 2022), whale optimization algorithm (WOA) (Mirjalili and Lewis, 2016), red fox algorithm (RFA) (Połap and Woźniak, 2021), sine cosine algorithm (SCA) (Mirjalili, 2016), artificial bee colony (ABC) (Karaboga and Basturk, 2007), firefly algorithm (FA) (Yang and He, 2013b), elk herd optimization (EHO) (Al-Betar et al., 2024), variable neighborhood search (VNS) (Mladenović and Hansen, 1997), and COLSHADE (Gurrola-Ramos et al., 2020). Together, these methods form a comprehensive and versatile set of tools capable of addressing diverse and computationally intensive optimization problems across scientific and engineering disciplines.

Metaheuristic approaches have shown strong performance in a variety of domains, including software engineering (Villoth J. P. et al., 2025; Villoth S. J. et al., 2025), medical diagnostics (Zivkovic et al., 2023, 2024), and a range of applied optimization scenarios (Bacanin et al., 2024; Lakicevic et al., 2024; Antonijevic et al., 2024; Petrovic et al., 2025; Bozovic et al., 2025). However, their use in the healthcare sector, particularly in the modeling of neurodegenerative disorders and the classification of stages of AD using neuroimaging, remains relatively underexplored (Antonijevic et al., 2024; Dobrojevic et al., 2024).

Drawing on their proven success in related areas, the integration of metaheuristic algorithms into neurodegenerative disease prediction represents a promising pathway toward enhancing diagnostic precision, model generalization, and individualized clinical evaluation. In this study, a cooperative dual-layer classification framework is proposed, in which a CNN performs hierarchical MRI feature extraction, followed by XGBoost and LightGBM classifiers for refined stage identification. Crucially, metaheuristic optimization is used to tune the hyperparameters in both phases, forming a unified and adaptive strategy that advances an automated and interpretable classification of AD progression.

Local search algorithms in combinatorial optimization improve an initial candidate solution by iteratively exploring its surrounding configurations and replacing it with a better alternative until no further enhancement of the objective function can be obtained. During each iteration, an improved solution x is selected from its neighborhood set N(x), and the search is completed once a local optimal point is reached. Unlike conventional local search methods that follow a single continuous search trajectory, VNS (Mladenović and Hansen, 1997) uses a structured diversification principle. Instead of restricting exploration to a single neighborhood, VNS systematically expands the search to progressively more distant neighborhoods, accepting a new solution only when it provides a measurable improvement. This strategy allows the algorithm to retain the beneficial properties of a near-optimal solution while simultaneously investigating unexplored regions of the search space that may yield superior outcomes. Each newly generated candidate solution is subsequently refined through a local search procedure to promote convergence toward a local optimum.

More precisely, VNS operates using a finite collection of neighborhood structures N_k, where k = 1, 2, …, k_max. The algorithm transitions between these neighborhoods through three main stages:

The algorithm terminates when the stopping conditions are met, such as when a predefined number of iterations is reached or the computational budget is exhausted.

Original VNS has been widely recognized as a powerful and adaptable modern generation optimization method that exhibits strong performance across a wide spectrum of application areas. However, despite its reliability and versatility, extensive empirical studies utilizing contemporary benchmark suites (Luo et al., 2022) have identified several limitations, particularly its relatively restricted exploratory capability during the early phases of the optimization process. In addition, the algorithm may occasionally suffer from premature convergence toward local optima, which can negatively impact its overall convergence efficiency under certain conditions.

To overcome these limitations, the first enhancement introduced in this work focuses on increasing population diversity during the initial optimization phase. This improvement is achieved through the integration of the Quasi-Reflexive Learning (QRL) mechanism (Rahnamayan et al., 2007) into the population initialization procedure. In this extended scheme, the initial population is divided into two complementary subsets: one generated using the standard VNS initialization process, and the other constructed through QRL-based diversification. The latter subset expands the spatial coverage of the search space from the outset, reducing the possibility of early clustering among agents and promoting a more uniform and comprehensive exploration of the solution landscape. The mathematical formulation of this quasi-reflexive generation procedure is given in Equation 1, which defines how mirrored solution vectors are produced to supplement their original counterparts.

In this formulation, lbj+ubj2 denotes the midpoint between the lower and upper boundaries of the j-th dimension in the search space, while rnd() produces a random value within the specified interval. QRL therefore generates complementary candidate solutions by probabilistically sampling between the midpoint of the search interval and the current solution, consequently enhancing population diversity during early exploration. A detailed mathematical analysis of this mechanism is provided in the original formulation (Rahnamayan et al., 2007).

The second improvement incorporated into the VNS algorithm introduces a soft rollback mechanism, designed in this research to alleviate convergence stagnation. This mechanism is triggered when the algorithm does not exhibit notable improvement over a defined interval of T/3 iterations, where T represents the total number of permitted iterations. The value of this threshold was determined empirically. When stagnation occurs, the population is partially reverted to its most recent productive configuration, allowing the algorithm to recover from unproductive search directions. To implement this mechanism, two auxiliary control parameters are introduced: the stagnation counter (s_count) and the stagnation threshold (s_tresh), initialized as s_count = 0 and s_tresh = T/3. The counter increases with every iteration that lacks an improvement in fitness, and when s_count reaches s_tresh, the rollback process begins.

This rollback strategy integrates an elitist preservation principle to safeguard the overall quality of solutions. Specifically, the best-performing individual, defined as the candidate who reaches the optimal fitness value, is retained, while the remaining members of the population are regenerated according to the original initialization procedure of the algorithm. This approach effectively restores population diversity without sacrificing the most promising solution identified so far.

To reflect these algorithmic refinements, the proposed variant is named the quasi-reflexive learning stagnation-aware VNS (QSAVNS). The complete step-by-step procedure of this modified method is presented in Algorithm 1.

Because elapsed runtime is heavily relying on hardware and implementation specifics, algorithmic complexity of metaheuristics is typically assessed in terms of fitness function evaluations, which is the standard and more reliable measure in metaheuristic optimization research. In each run, the fitness function evaluation (FFE), corresponding to model training and validation for one hyperparameter configuration, is the most computationally expensive operation and therefore dominates the overall runtime of the algorithm. From a computational standpoint, QSAVNS preserves the same fitness-evaluation complexity as baseline VNS. The QRL-based initialization and stagnation-aware rollback only alter solution generation/diversification, while maintaining N fitness evaluations within each of T iterations. Consequently, the overall complexity remains O(N×T) in FFEs, which is identical to baseline VNS.

The proposed method operates as the core optimization engine within a two-layer classification architecture. In this design, the hyperparameters of the classifiers' hyperparameters are represented as agent-specific variables, and optimization is carried out iteratively through repeated cycles of model training, parameter adjustment, and performance evaluation until a predefined convergence criterion is satisfied.

At the first level (L1), this iterative optimization is applied to CNNs. Once the most suitable CNN configuration is identified, its final output layer is removed, and the intermediate feature embeddings learned during training are extracted. These representations are subsequently passed to the second level (L2), where ensemble boosting classifiers are employed. In this second stage, the boosting models also undergo metaheuristic optimization, with their hyperparameters encoded as evolutionary traits of the agents within the population.

For this research, a dataset was used from the Kaggle platform.² The dataset was reduced to 10% of its original volume while preserving proportional representation between all classes to maintain balance. It is intended for the classification of AD stages and contains four distinct categories: No Dementia (class 0), Very Mild Dementia (class 1), Mild Dementia (class 2), and Moderate Dementia (class 3). The original dataset was already partitioned into training and testing subsets by class and was utilized in this study in its existing form, without any additional preprocessing or modification.

During the simulation phase, the performance of the model was assessed using a standard set of classification metrics, namely precision, precision, recall, and the F1-score, formally defined in Equations 2–5.

In the above equations, TP, TN, FP, and FN denote the numbers of true positives, true negatives, false positives, and false negatives, respectively.

In addition to conventional classification metrics, the Matthews correlation coefficient (MCC) (Matthews, 1975) was used as an additional evaluation measure. Due to its robustness in handling imbalanced class distributions, the MCC offers a more comprehensive and reliable indication of the overall performance of the model. Its calculation is formally defined in Equation 6.

Across all simulation experiments, the MCC was designated as the main optimization objective with the aim of maximizing its value to obtain the most balanced and accurate classification results.

A series of three experimental studies was conducted in which metaheuristic optimization algorithms were employed to fine-tune the parameters across both layers of the proposed dual-stage classification framework. The architecture consisted of a CNN as the first-layer module, followed by XGBoost and LightGBM classifiers that form the second-layer classification component. In each experimental scenario, the proposed QSAVNS metaheuristic served as the principal optimization algorithm, and its performance was systematically compared with several well-established optimization methods. The comparison group included the canonical VNS (Mladenović and Hansen, 1997), GA (Mirjalili, 2019), PSO (Kennedy and Eberhart, 1995), ABC (Karaboga and Basturk, 2007), BA (Yang and He, 2013a), SCHO (Bai et al., 2023), and EHO (Al-Betar et al., 2024), providing a representative balance between the classical and more recent optimization paradigms. All competing algorithms were executed using their standard parameter configurations as specified in the original studies. To maintain methodological consistency, identical experimental conditions were applied to each algorithm in all three experiments. To minimize the effect of stochastic variability inherent in metaheuristic processes, each method was independently executed 30 times.

Given the high computational cost of CNN training, the first-layer (L1) experiments used a reduced population of eight candidate solutions (N = 8) and a maximum of five iterations per run (max_iter = 5). For the optimization of XGBoost and LightGBM, the population size was set to ten (N = 10), with ten iterations per execution (max_iter = 10). Within the metaheuristic optimization procedure, each individual in the population encodes a unique configuration of a neural network or ensemble model (CNN, XGBoost, or LightGBM) along with its associated hyperparameters. Evaluating each configuration requires multiple training-validation cycles, which are computationally demanding. To alleviate this burden, the size of the population and the iteration count were deliberately constrained, thus reducing the total number of retraining operations. Furthermore, once the population size exceeds a certain threshold, additional expansion typically produces negligible improvements in optimization performance. Empirical evidence suggests that metaheuristic algorithms can often converge to near-optimal solutions even with moderate population sizes, providing an efficient and resource-conscious approach to solving high-cost optimization tasks. As previously stated, the optimization objective was defined as the maximization of the MCC.

In the first experimental setup, metaheuristic algorithms were applied to optimize the CNN component in the initial layer (L1) of the proposed framework. The tunable CNN hyperparameters, listed in Table 1, were intentionally limited to lightweight configurations to allow potential deployment on resource-constrained platforms such as ESP32 or Arduino. A batch size of 512 was used and an early stopping was triggered after one-third of the total training epochs. The target image resolution was fixed at (32, 32) using the RGB color mode and categorical label encoding. Within the cooperative dual-layer design, the optimized CNN from this stage provided the feature extraction foundation for the subsequent ensemble-based classification phase.

In the second experimental configuration, the XGBoost algorithm was applied within the classification layer (L2) of the framework. For this purpose, the intermediate feature embeddings generated by the optimized CNN from the first layer were extracted from the output of the dropout layer and saved for all data samples. Then these characteristic vectors were split into training and testing subsets following a 70%–30% ratio. The resulting feature representation was used as input for both the training and hyperparameter optimization of the XGBoost classifier. The specific parameters selected for tuning, along with their search intervals, are summarized in Table 1.

In the third experimental study, the LightGBM algorithm was integrated into the second layer (L2) of the proposed architecture. The classifier was trained and optimized using the same intermediate feature representations produced by the CNN in the preceding experiment. The LightGBM hyperparameters chosen for optimization, along with their defined search ranges, are also presented in Table 1.

Table 2 presents a comparative analysis of CNN models optimized using several metaheuristic algorithms, with the MCC serving as the primary objective metric. Among the evaluated methods, the proposed QSAVNS optimizer achieved the best overall result, achieving a maximum MCC of 0.287398. In comparison, the strongest worst-case performance was obtained by SCHO (0.239755), which also produced the highest mean MCC (0.251198) and the best median value (0.249601). Furthermore, it is worth noting that within this experimental configuration, the ABC algorithm exhibited the most consistent behavior, as evidenced by its minimal variance across multiple independent runs.

Table 2 also reports the results of the indicator function expressed in terms of the error rate for CNN models optimized by the same set of metaheuristic techniques. QSAVNS achieved the lowest absolute error rate of 0.554545, while SCHO recorded the best mean error rate (0.586742), median error rate (0.585606), and the most favorable worst-case result (0.589394). Although GA did not achieve the top-performing absolute score, it demonstrated notable stability across repeated executions, indicating high robustness despite slightly lower overall optimization effectiveness.

Table 3 provides a comprehensive overview of the evaluation metrics corresponding to the CNN classifiers that achieved the best performance under different metaheuristic optimization methods. The findings show that the proposed QSAVNS algorithm generated a robust CNN model, reaching an overall classification accuracy of 0.445455, accompanied by consistently solid precision, recall (sensitivity), and F1-scores in most categories. Nevertheless, a clear pattern emerged in all the models, each showing a limited ability to accurately differentiate among the four stages of AD. This limitation underscores the need for additional methodological refinements, which are explored in the following sections of this study.

Figure 1 shows the architecture of the L1 CNN model with the best performance, along with its truncated counterpart. The left diagram shows the full CNN architecture used for end-to-end training and L1 optimization. The right diagram illustrates the truncated CNN obtained by removing the final classification layers. This model outputs intermediate feature embeddings that are subsequently used as input for the L2 ensemble classifiers.

Table 4 presents a comparative evaluation of the XGBoost second-layer classifiers optimized using different metaheuristic algorithms, with the MCC serving as the primary evaluation metric. The proposed QSAVNS optimizer achieved the highest best-case result, achieving a peak MCC of 0.812047, while also demonstrating outstanding stability across other evaluation measures by recording the best mean values (0.796531) and median values (0.797621). These results highlight the robustness and reliability of QSAVNS as an optimization approach. Furthermore, QSAVNS achieved the strongest worst-case result (0.769870), while GA exhibited the lowest variability across repeated executions, indicating strong consistency in its optimization performance.

Table 4 also includes a comparative analysis based on the error rate indicator for the same XGBoost classifiers optimized with different metaheuristic methods. The most favorable result, corresponding to the lowest best-case error rate of 0.140909, was achieved by the proposed QSAVNS. In addition, QSAVNS outperformed competing algorithms by achieving the best mean and median error rates, measured at 0.152475 and 0.151515, respectively, confirming its high stability between independent runs. It also obtained the lowest worst-case error rate (0.172727) and demonstrated excellent consistency (second only to GA) in this evaluation scenario.

Table 5 provides detailed evaluation metrics for the top-performing L2 XGBoost classifiers optimized with different metaheuristic algorithms. Among them, the proposed QSAVNS achieved the best overall performance, yielding the most accurate CNN-XGBoost-based model with a maximum classification accuracy of 0.859091, while maintaining consistently high precision, recall (sensitivity), and F1-scores across all classes. An important observation from these results is that integrating XGBoost into the second layer of the framework significantly enhanced overall precision compared to standalone CNN models, notably improving the differentiation between AD stages. Nevertheless, as shown in the next subsection, the XGBoost classifiers were significantly outperformed by the LightGBM models implemented in the same layer.

Table 6 presents a comparative evaluation of the L2 LightGBM classification models optimized using several metaheuristic algorithms, with the MCC serving as the main objective function. Among the methods examined, the proposed QSAVNS once again proved to be the most effective optimizer, achieving the highest best-case MCC value of 0.860430 (tied with PSO) and achieving competitive results across other statistical indicators. The GA algorithm recorded the best worst-case performance (0.804565) and the highest mean (0.840211) and median (0.845163) MCC values. In addition, GA demonstrated exceptional consistency between independent runs, indicating minimal stochastic variability and high overall reliability.

Table 6 also reports a comparative analysis of L2 LightGBM classifiers optimized using different metaheuristic strategies, this time based on the indicator function represented by the error rate. Among all algorithms tested, the proposed QSAVNS achieved the best overall outcome, with the lowest absolute error rate of 0.104545. While QSAVNS also produced competitive results for the remaining metrics, GA achieved the strongest worst-case performance (0.146212), along with the best mean error rates (0.119545) and median error (0.115909). Although GA did not reach the lowest absolute error, it exhibited the greatest consistency across repeated runs, demonstrating outstanding stability despite slightly weaker optimization performance compared to QSAVNS.

Table 7 provides detailed evaluation metrics for the top-performing L2 LightGBM classifiers optimized using the examined metaheuristic algorithms. The findings show that the QSAVNS-optimized model produced the most effective CNN-LightGBM configuration, achieving the highest overall classification accuracy of 0.895455 (matched by PSO) and consistently maintaining high precision, recall, and F1-scores in all evaluated classes. An important conclusion drawn from these results is that the integration of LightGBM into the second layer of the framework substantially enhanced overall accuracy compared to the standalone CNN architectures, while also improving the classification of individual stages of AD. Moreover, the LightGBM-based models in the second layer clearly outperformed their XGBoost counterparts, confirming the superior performance and adaptability of LightGBM within this hierarchical framework.

Figure 2 provides a detailed comparative analysis of different metaheuristic optimizers applied to fine-tune both hierarchical layers of the proposed classification framework for the identification of stages of AD. The evaluation covers three experimental setups: L1 CNN optimization (top row), L2 XGBoost optimization (middle row), and L2 LightGBM optimization (bottom row). To ensure statistical robustness, the performance of each optimizer was assessed in 30 independent runs, with the distributions of the MCC values illustrated through box plots. Thirty separate runs were necessary to obtain statistically meaningful results and reduce the influence of randomness inherent in metaheuristic algorithms (Talbi, 2009). These visualizations emphasize central tendencies (medians), variability, and asymmetry in distribution, offering a clear perspective on the balance between stability and exploratory dynamics exhibited by each optimization approach.

The results reveal that the proposed QSAVNS consistently achieved the highest best-case MCC values in all three experimental stages, confirming its strong global search capability. Additionally, the distribution of its results shows stable median values combined with slightly wider variance, indicating effective exploration that prevents premature convergence to local optima. This broader dispersion in MCC outcomes reflects a deliberate design trade-off, where superior best-run performance was obtained at the expense of slightly lower overall stability.

The box plots also summarize the statistical behavior of error rates collected from 30 independent optimization runs, illustrating both the central tendency and variability for each algorithm. These graphs are particularly valuable for assessing model generalization, lower median error rates coupled with narrower interquartile ranges correspond to more consistent and reliable predictive outcomes. Across all configurations, the proposed QSAVNS algorithm consistently achieved the lowest error rates, confirming its ability to preserve population diversity while efficiently exploiting promising regions of the search space. This balance effectively minimizes the risk of premature convergence and reduces misclassification tendencies.

The complementary convergence plots shown in Figure 3 provide additional insight into the temporal progression of the optimization process, illustrating how each algorithm improves the objective function across successive iterations during their best-performing runs. The proposed QSAVNS demonstrates faster and more stable convergence behavior, which can be attributed to its adaptive features, including the QRL-based initialization and the integrated stagnation-aware rollback mechanism. These components foster a balanced interaction between exploration and exploitation, ensuring consistent progress throughout the search process. In contrast, alternative optimization algorithms often exhibit slower performance gains or early stagnation, reflecting reduced effectiveness in navigating complex, high-dimensional hyperparameter spaces.

In general, these findings highlight the decisive impact of the algorithmic structure on the efficiency of optimization in classification tasks. Approaches that maintain population diversity, enable structured exploration of neighboring regions, and dynamically regulate diversity during the search exert a significant influence on the convergence rate, the quality of the solution and the reproducibility. Such characteristics are particularly critical in real-world applications, where sensitivity to initialization settings and variations in input data can substantially affect predictive stability and reliability.

Figure 4 presents radar charts that summarize both macro and weighted-averaged results, offering a comprehensive depiction of classifier performance across multiple evaluation metrics. The macro-average treats all classes equally, making it particularly useful for assessing a model's ability to correctly recognize minority classes, an especially challenging aspect in scenarios characterized by class imbalance. In contrast, the weighted average accounts for the frequency of the classes, producing a metric that reflects the overall class distribution within the dataset and assigns greater importance to the performance of the majority classes.

Displaying these two perspectives side by side reveals the inherent trade-offs among the different optimization algorithms. Models that achieve high weighted-average values may still face challenges in generalizing to minority classes, whereas those demonstrating stronger macro-average results tend to exhibit greater resilience and robustness in imbalanced data contexts. Together, the radar plots provide a complementary means of analysis, supporting a more nuanced evaluation of generalization capability, fairness, and reliability of the classifiers optimized using the metaheuristic approaches examined.

In the first stage of the proposed framework, CNN functions as a feature extraction engine, capturing hierarchical and discriminative representations from MRI data. However, the conventional practice of relying on a dense output layer for classification within CNN architectures often fails to fully exploit the richness of the extracted features, resulting in suboptimal predictive performance. Replacement of this terminal layer with advanced ensemble classifiers substantially enhances the accuracy and robustness of the model. Following this principle, the proposed framework substitutes the CNN's dense layer with XGBoost and LightGBM classifiers, both of which demonstrate superior performance relative to the baseline of the dense layer. By integrating CNN-based deep feature learning with gradient enhancement techniques for classification and refining both levels through metaheuristic-driven hyperparameter optimization, the framework effectively combines the strengths of deep representation learning and ensemble-based decision making. This hybrid configuration leads to marked improvements in predictive accuracy and computational efficiency for the classification of stages of Alzheimer's disease, and both L2 models outperform the CNN of the baseline in terms of classification accuracy.

Analysis of the fitness function, expressed through the MCC, shows that models incorporating LightGBM in the second layer (L2) consistently outperform those utilizing XGBoost. Both ensemble-based configurations exceed the CNN baseline in the first layer (L1). The box plot analyzes further reveal that L2 LightGBM achieves the highest median and maximum MCC values, confirming its superior capacity to identify subtle and complex discriminative features critical for accurate stage differentiation. Additionally, the convergence patterns of LightGBM display smooth and stable optimization behavior across all metaheuristic algorithms. This effect is most evident when optimized using QSAVNS, where LightGBM attains the highest recorded MCC values, substantially reinforcing the discriminative capacity of the framework for this clinically important classification problem.

A similar trend is observed for the indicator function, represented by the error rate, where lower values correspond to better performance. Across all three experimental configurations, LightGBM in the L2 layer consistently achieves the lowest error rates, often by a significant margin. The best-performing LightGBM configuration, CNN-LGBM-QSAVNS, achieved the highest overall classification accuracy of 0.895455. Although XGBoost in L2 also produced strong and competitive results, LightGBM demonstrated superior stability and generalization among different metaheuristic optimizers. Taken together, these results establish LightGBM as the most suitable choice for the second layer of the proposed AD stage classification framework, combining high predictive accuracy, low error rates, and consistent performance, qualities essential for reliable clinical implementation.

From the perspective of general optimization theory, the coupling of metaheuristic optimization with ensemble learning aligns with the principles of adaptive search in complex, high-dimensional search spaces. Metaheuristic algorithms are particularly effective in navigating non-convex and discontinuous objective spaces, where gradient-based or deterministic tuning methods often fail. When metaheuristics are combined with ensemble models like XGBoost and LightGBM in this study (which themselves rely on aggregating multiple weak learners), the optimization process benefits from complementary mechanisms of exploration and exploitation at both the parameter-search and decision-fusion levels. This synergy is consistent with the NFL theorem, which suggests that performance gains arise not from universally optimal algorithms, but from well-matched combinations of optimization strategies and learning models tailored to a specific problem domain.

To facilitate reproducibility of experimental results, the hyperparameter configurations for the best-performing models, L1 CNN, L2 XGBoost, and L2 LightGBM, are summarized in Table 8.

To further evaluate the performance of the proposed framework, the best second-layer (L2) models were compared with a set of well-established benchmark classifiers. The benchmark suite included a multi-layer perceptron (MLP), decision tree (DT) (de Ville, 2013), k-nearest neighbors (KNN) (Kramer, 2013), random forest (RF) (Breiman, 2001), and several boosting algorithms, AdaBoost, CatBoost, plain LightGBM (Ke et al., 2017), and plain XGBoost (Chen and Guestrin, 2016), as well as a deep CNN (Gu et al., 2018). All baseline classifiers were trained and tested using their default hyperparameter configurations, and the resulting evaluation metrics are summarized in Table 9.

Although the benchmark models demonstrated generally solid accuracy, the proposed L2 architectures consistently outperformed them in all evaluation criteria, achieving superior class-wise results and substantially higher overall accuracy. The best performing model, CNN-LGBM-QSAVNS, achieved an accuracy of 0.895455, followed by CNN-XGB-QSAVNS with 0.859091. In comparison, the best-performing baseline models, plain LightGBM and random forest, reached considerably lower accuracies of 0.548485 under the same experimental conditions.

Although comparative analysis of optimization algorithms can offer valuable information, conclusions drawn from a single execution are inherently unreliable. The stochastic nature of metaheuristic methods introduces significant variability between runs, rendering single-instance results insufficient to accurately evaluate overall performance. To mitigate randomness and improve the robustness of the evaluation, each algorithm in this study was executed 30 times with independent random seeds. This procedure yielded comprehensive distributions of the results, providing a statistically sound foundation for comparison. Such a multi-run evaluation protocol not only strengthens statistical validity but also enables more accurate identification of performance trends. In addition, this methodology aligns with widely accepted best practices for benchmarking metaheuristic algorithms (LaTorre et al., 2021), thus improving both the credibility and reproducibility of the study's results.

Statistical procedures for determining the significance of performance differences among groups are generally divided into parametric and non-parametric tests. The choice between them depends on assumptions such as the independence of observations, normality of the data distribution, and equality of variances between groups (homoscedasticity) (LaTorre et al., 2021). Independence was ensured by initializing each algorithmic run with a distinct random seed, preventing inter-run dependencies. Homoscedasticity was examined using the Levene test (Schultz, 1985), which produced a p-value of 0.88 for all experimental results, indicating that there are no statistically significant variance differences between the groups. The assumption of normality was then tested with the Shapiro–Wilk test (Shapiro and Francia, 1972). Since all computed p-values were below the standard 0.05 threshold, the null hypothesis of normality was rejected, confirming that the data did not satisfy the conditions required for parametric statistical tests.

Given the violation of normality, subsequent analyzes employed non-parametric methods. Specifically, the Wilcoxon signed-rank test (Woolson, 2005) was applied to perform pairwise comparisons between the proposed QSAVNS and each of the competing optimization algorithms. The resulting p-values, listed in Table 10, were all below the conventional significance level of α = 0.05, confirming that QSAVNS achieved statistically significant improvements over all alternative approaches.

These results provide strong empirical evidence that the superior performance of QSAVNS is not due to random fluctuations or sampling bias. Instead, they confirm a consistent and meaningful advantage across all three experimental configurations, underscoring both the robustness and the practical effectiveness of the proposed enhanced optimization method.

The practical importance of machine learning classifiers extends beyond achieving high predictive accuracy to encompass the interpretability and transparency of their internal decision-making processes. Interpretability provides crucial insights into the mechanisms underlying algorithmic predictions, allowing the detection of hidden biases, the identification of key predictive features, and the refinement of analytical workflows. This transparency is especially valuable for improving data acquisition, feature engineering, and preprocessing procedures, ultimately contributing to the development of more reliable and trustworthy models. In image-based analysis, specifically, understanding which features exert the greatest influence on classification outcomes improves both the explanatory depth and the practical applicability of the model. However, as machine learning architectures, particularly DL systems, grow increasingly complex, achieving interpretability becomes substantially more difficult. The deeper and more intricate the model, the less transparent its internal reasoning tends to be, making it challenging to trace errors, identify sources of bias, or align algorithmic logic with human understanding. This opacity can erode trust in automated systems, particularly in high-stakes domains such as healthcare, where accountability and interpretability are essential.

To address these challenges, the present study employed SHAP (SHapley Additive exPlanations) (Lundberg and Lee, 2017) within the proposed two-tier classification framework. SHAP offers a unified and theoretically grounded approach to interpreting model predictions by quantifying the contribution of each input feature, thereby clarifying how specific factors influence decision outcomes. In this research, the standard SHAP methodology was applied directly to the output of models optimized with the QSAVNS algorithm, without any algorithmic modifications. This interpretive layer proved critical for identifying the most influential features that affect classification performance, an especially important consideration in clinical contexts, where understanding the rationale behind predictions is as vital as their accuracy. The kernel explainer variant of SHAP was used to examine the proposed multi-level system, effectively isolating the relative contributions of the CNN-based feature extraction stage, the ensemble classifiers, and the metaheuristic optimization process. This approach provided a comprehensive and transparent understanding of how the hybrid framework generates its final predictions.

For the interpretation of CNN-based models, the deep explainer variant of SHAP was used to identify and visualize the most influential features in the convolutional layers, offering a detailed representation of the internal reasoning of the model. The results of the multi-class classification analysis are illustrated in Figure 5, which contrasts interpretations obtained from the deep SHAP explainer with those generated using the kernel-based SHAP method applied to the XGBoost and LightGBM multi-tier frameworks. These comparative visualizations clarify how individual input features contribute across different layers of the models, providing a more comprehensive and transparent understanding of their underlying predictive mechanisms.

SHAP visualizations for the four classes of AD reveal distinct contribution patterns that evolve with disease progression. For the No Dementia class, the SHAP value distribution is relatively balanced, encompassing both positive and negative contributions. This balance suggests that the model's decisions for this class rely on a wide and diverse range of features, some reinforcing and others opposing the non-dementia classification, indicating that the decision-making process is based on varied and diffuse characteristics. In contrast, the Very Mild and Mild Dementia classes display more compact SHAP clusters, signifying that a smaller set of features exerts a stronger influence on the predictions. This concentration is in line with clinical expectations, as the early stages of Alzheimer's are marked by subtle, localized structural or functional alterations that serve as emerging differentiation signals. For the Moderate Dementia class, SHAP distributions become markedly polarized, revealing that a limited number of dominant features almost exclusively drive the model's predictions as the disease advances.

Together, these results illustrate a progression-dependent landscape of significance. During the earlier stages of the disease, the predictive reasoning of the model is based on a broad and heterogeneous collection of features, reflecting the inherent diagnostic ambiguity associated with early detection of Alzheimer's. As the condition progresses, the focus of the model narrows to a smaller group of highly discriminative features, consistent with the emergence of more distinct and stable pathological patterns. From a clinical perspective, this evolution mirrors real-world diagnostic challenges, while early-stage Alzheimer's detection depends on the recognition of subtle and diffuse anomalies, advanced stages present more pronounced and easily identifiable biomarkers. Consequently, SHAP-based interpretive analysis not only validates the predictive reliability of the proposed framework but also provides valuable clinical insight into which neuroimaging characteristics have the greatest diagnostic relevance in different phases of the progression of Alzheimer's disease.