Hyperparameter optimization of YOLO using differential evolution, multi-fidelity optimization, and Bayesian optimization

Abstract

Object detection in aerial imagery faces significant challenges from small, randomly oriented, and crowded targets across large frames, where default hyperparameter settings consistently underperform. This paper presents a systematic methodology for hyperparameter optimization of YOLO (You Only Look Once) through a novel integration of Differential Evolution, Multi-fidelity Optimization, and Bayesian Optimization (DE-MFO-BO). Our approach optimizes four critical hyperparameters; learning rate, batch size, momentum, and weight decay for both Adam and SGD (Stochastic Gradient Descent) optimizers. The methodology employs a two-stage strategy, Differential Evolution performs rapid exploration using low-fidelity training (5 epochs) to identify promising hyperparameter regions, followed by Bayesian Optimization with high-fidelity training (up to 800 epochs) for precise refinement. A composite fitness function combining precision, recall, and mean Average Precision (IoU 50–95) (mAP(50–95)) guides the optimization process. We validate this framework on VisDrone2019 and our indigenous Realm dataset using YOLO-11n model. For VisDrone2019, Adam optimizer achieves 18.42% recall improvement and 13.5% mAP(50–95) enhancement, while SGD shows 5.07% precision increase. On the Realm dataset, Adam optimizer demonstrates remarkable gains with 20.96% mAP(50–95) improvement, 10.22% precision increase, and 7.17% recall enhancement, whereas SGD achieves 2.78% precision improvement. These substantial performance improvements, achieved without architectural modifications, establish the effectiveness of our systematic hyperparameter optimization approach for aerial object detection applications.

Introduction

The advent and evolution of You Only Look Once (YOLO) architectures have greatly enhanced real-time object detection capabilities particularly in the domain of aerial imagery using Unmanned Aerial Vehicles (UAVs). YOLO training can be divided into two different ways.

1. by modifying the network architecture, and.

2. by adjusting the hyperparameters.

While one can find many research works focus on the architecture change of YOLO, the theoretical aspect of hyperparameter optimization, especially for aerial object detection, remains sparse in the literature. This study targets precisely this underexplored area: the hyperparameter optimization of YOLO using the YOLOv11 architecture, with a particular emphasis on aerial object detection. All experiments are conducted on the YOLOv11n model.

YOLO hyperparameters are configurable settings that control various aspects of model training and behavior. They influence the performance, speed and accuracy of the object detection task. Unlike trainable weights, hyperparameters are fixed, predefined values that do not learn during the training process; instead, the training process depends on them. They are therefore critical, as they directly affect how the model learns, how it performs, and how it generalizes to new data.

Existing research has neglected many aspects that are crucial for making effective in drone-based aerial object detection. Multiple studies^1,2 propose architectural or performance improvements to YOLO models for aerial scenarios, but they do not provide a thorough theoretical analysis of how adjusting hyperparameters affects detection outcomes. Recent work primarily focuses on YOLOv8-related modifications, with limited research on YOLOv9, YOLOv10 and YOLOv11 variants, and there is still a lack of systematic optimization strategies for model hyperparameters.

The literature review therefore reveals a significant opportunity to address the challenges associated with complex aerial object detection using Unmanned Aerial Systems (UAS) by employing systematic hyperparameter optimization frameworks, rather than solely incorporating increasingly complex architectural changes. Such frameworks could potentially be universal, meaning they may be applicable across different YOLO versions with minimal adaptation.

Recent advances in metaheuristic optimization have introduced nature-inspired algorithms such as the Draco lizard optimizer³, Bighorn sheep optimization algorithm⁴ and Cape lynx optimizer⁵, which show promising performance in various optimization domains. However, their application to deep learning hyperparameter optimization—particularly for object detection in aerial imagery—remains largely unexplored. In contrast, Differential Evolution (DE)⁶ and Bayesian Optimization (BO)⁷ have established theoretical foundations and proven track records in hyperparameter tuning for neural networks, making them suitable choices for the systematic optimization framework proposed in this work.

The existing body of research also lacks a detailed explanation of the importance of critical hyperparameters such as learning rate, momentum, batch size, optimizer type, image size and weight decay, as well as their interactions with each other. This gap forms the foundation and motivation of the present study.

While Differential Evolution and Bayesian Optimization are established techniques, our novel contribution lies in their systematic integration with multi-fidelity optimization specifically tailored for YOLO hyperparameter tuning in aerial object detection contexts. To the best of our knowledge, this is the first work to:

1. Apply a combined DE-MFO-BO framework for YOLO hyperparameter optimization (learning rate, momentum, batch size and weight decay).

2. Systematically optimize hyperparameters specifically for aerial imagery challenges (small objects, complex backgrounds, varying scales) for two widely used optimizers SGD and Adam.

3. Provide comprehensive empirical validation on both standard (VisDrone2019) and custom (Realm) aerial datasets.

Our contribution is methodological and empirical rather than algorithmic, providing a reproducible framework for practitioners facing similar hyperparameter optimization challenges in aerial object detection.

Table 1 below shows the list of abbreviation and their meaning used in this manuscript.

Table 1.

List of abbreviations.

Abbreviations	Meaning
YOLO	You Only Look Once
UAV	Unmanned Aerial Vehicle
DE	Differential Evolution
BO	Bayesian Optimization
MFO	Multi-Fidelity Optimization
SGD	Stochastic Gradient Descent
IoU	Intersection over Union
mAP	Mean Average Precision
mAP(50–95)	Mean Average Precision (IoU 50-95)
lr	Learning rate
wd	Weight decay
Mom	Momentum
σ (sigma)	Standard deviation

Current works and limitations

The current state of research in hyperparameter tuning for deep learning is meagre and sometimes unconvincing, with majority of the work rather concentrating on architectural changes than the examination into different effects of various hyperparameters. More advanced YOLO-based models for aerial detection, are continuously proposed like SRE-YOLOv8⁸ and EAF-YOLOv8⁹, are proposed continuously^10–15, and so forth. However, such approaches typically use hand-picked hyperparameter settings and provide rarely any theoretical justification or systematic tuning.

Overall, the literature review reveals that research primarily addresses architectural modifications rather than hyperparameter optimization. Several studies^16,17 introduce attention mechanisms, feature pyramid modifications^18–20 and lightweight architectures^21–24 as part of their architectural enhancements, but they do not provide a theoretical analysis of how these changes interact with hyperparameters. In other words, changes in one module can alter the optimal hyperparameter settings for other modules, yet this interaction remains unexplored. This tendency highlights a crucial research gap in adapting hyperparameters specifically for aerial detection scenarios.

Recent studies that employ YOLOv8 for aerial object detection typically use batch sizes of 4–16 and train for 100–200 epochs^8,14,25. Learning-rate configurations vary significantly across works. Some researchers employ adaptive learning-rate schedules to improve detection metrics for aerial object detection, but the theoretical justification for these choices is missing^26,27. For example, the YOLOv8-MPEB study¹⁴ reports a 34% reduction in parameters and a 32% decrease in model size, yet it does not provide a theoretical explanation of why its hyperparameterization is superior.

Most existing works adopt empirical hyperparameter selection, or simply change hyperparameter values without theoretical evidence, resembling trial-and-error approaches. The majority of comparative analyses of YOLO variants revolve around architectural changes rather than the effect of hyperparameter optimization^28–32. This severely limits the transferability of findings across different aerial detection scenarios.

Comparative studies across YOLO variants do show performance differences among them, but these are usually attributed solely to architectural changes rather than to hyperparameter optimization. YOLOv8, for example, demonstrates superior performance over its predecessors, achieving increases in mean average precision (mAP) of 5.3–9.2%. The SRE-YOLOv8 model outperforms standard YOLOv8 by 9.2%⁸, and EAF-YOLOv8 achieves mAP50 scores of 34.3% and 49.7% on UAVDT and VisDrone2019, respectively⁹. However, the role of hyperparameter tuning in achieving these gains is unclear.

For the latest versions—YOLOv9, YOLOv10 and YOLOv11—only limited work has been conducted in the context of aerial object detection^23,33–35. Most studies still focus on comparing YOLOv8 with YOLOv5 and YOLOv7^36,37, with relatively few exploring newer versions^24,33,34. This represents a significant gap in understanding hyperparameter optimization for the latest YOLO variants.

In most of these studies, performance is evaluated using standard protocols and metrics, employing datasets such as UAVDT, VisDrone2019 and others^16,19,31,38. The assessment mainly concentrates on metrics such as mAP, precision, recall and inference speed. However, very few works systematically disentangle what different hyperparameter configurations imply for these metrics in an aerial context.

Aerial imagery presents unique challenges for object detection, especially for small objects that are represented by only a few pixels^10,11,39. While improvements in small-object detection have been reported, most of these improvements result from architectural modifications to YOLO. The relationship between small-object detection performance and hyperparameter choices lacks systematic investigation. The multi-scale nature of aerial imagery clearly demands careful and thorough hyperparameter optimization, yet the theoretical framework required for such optimization is missing from the literature^9,19,22.

From this analysis, several critical limitations emerge:

1. Lack of theoretical framework: No comprehensive theoretical analysis exists in the reviewed literature that explains the impact of hyperparameter optimization on aerial object detection.

2. Limited systematic optimization: Instead of employing systematic optimization methodologies, most works rely on ad-hoc or empirically chosen hyperparameters.

3. Missing aerial-specific strategies: Hyperparameter optimization strategies specifically tailored to the challenges of aerial object detection have rarely been addressed.

These limitations underscore the need for a systematic hyperparameter optimization framework tailored to aerial object detection. The approach proposed in this paper based on Differential Evolution, Multi-Fidelity Optimization and Bayesian Optimization aims to address these gaps and provide reusable guidance for hyperparameter tuning across different YOLO versions and aerial datasets.

Key hyperparameter and its use in YOLO

Some of the important hyperparameters which directly affect the performance and are critical are discussed in this section. Learning Rate (`lr0`) determines how fast the model will update its weights during training. With too high a learning rate, training may be unstable or the optimizer overshoots optimal solutions, while with too low a learning rate convergence is slow or gets stuck in local minima. Batch Size is the number of images that will be processed in each iteration before updating the weights of the model. Higher batches give more stable gradients but are memory intensive, lower-batch sizes provide noisier training data, but usually better generalization. Epochs is the number of complete passes through the training dataset. More epochs result in better learning but at the same time run a risk of overfitting if model starts memorizing instead of generalizing. The image Size is the input resolution for the training images. High resolutions necessarily collect more information, are computationally more costly and memory consuming. Standard sizes are 416 × 416, 512 × 512, or 640 × 640 pixels. The momentum accelerates the convergence of training by smoothing gradient updates. Higher values can speed up training and smoother convergence but the optimal parameters might overshoot. Weight Decay is a regularization technique that penalizes large weights to prevent overfitting. High values reduce overfitting but may limit model complexity and accuracy. Low values mean the opposite—less regularization, which may eventually lead to overfitting. The anchor boxes are predefined bounding box shapes used to detect objects of varying shapes and sizes. If the anchors are poorly set, detection rate will certainly be spilled off slightly or even completely. With the anchors optimized, we can get high accuracy and detection of different object sized. The Intersection-over-Union (IoU) threshold for IoU which is applied in both training and inference stages. A higher threshold lowers the number of false positives but might also overlook some detections. On the other hand, a lower threshold brings about increased sensitivity: however, it produces more false positives. The confidence threshold is minimum confidence score needed to consider a detection valid. As the numerical value of confidence threshold is increased, this results in more precise detection with fewer false positives. The lower scores yield more detections but might also have more false positives. The augmentation parameters control data augmentation (e.g., rotation, brightness, cropping) during training to improve generalization. These can help the model to handle diverse conditions and hence are able to reduce overfitting.

Influence on training process

• Convergence Speed: The higher the learning rate and batch size, the faster the model reaches optimal performance, Although, tuning is also key since with some proper tuning the training time can go from days to hours.

• Model Performance: Hyperparameters like loss gains make the model either support detection accuracy, localization precision, or classification performance based on what is desired.

• Generalization: Augmentation parameters (mosaic, mix-up, copy-paste) help to prevent overfitting by feeding the model with differentia versions of training sample.

• Resource Utilization: Image Size and Batch size parameters have to be adjusted for the GPU memory and the computational budget.

Embedding in YOLO training

The hyperparameters of YOLO are usually set in a YAML configuration file which defines the entire training process. The parameters set during training initialization are optimizer settings (learning rate, momentum, weight decay), data loading pipelines: (batch size, augmentation probabilities), loss function weights, such that you can balance different components of the total loss and training routine (lr decay, epochs).

The training loop consumes these parameters to iterate over batches, computing losses and updating the model weights. Many modern YOLO implementations also incorporate hyperparameter evolution or tuning capabilities in the software architecture, allowing one to exhaustively probe different parameter combinations to identify those that work best for particular datasets.

Hyperparameters can have a significant impact on the final performance in many cases and hyperparameter tuning is very important part of the process — sometimes even a small change can degrade or improve end model quality from mediocrity to state-of-the-art object detector.

Methodology

This paper provides the implementation of Differential Evolution (DE) optimization, multi-fidelity optimization (MFO) and Bayesian optimization (BO). The primary goal is to identify effective hyperparameters—including learning rate, batch size, momentum, weight decay, and optimizer selection—that maximize model performance on a predefined dataset.

To achieve this objective, we employ a two-stage approach: Differential Evolution (DE) for broad exploration, followed by Bayesian Optimization (BO) for refinement. The objective is to train a YOLO model multiple times with varying hyperparameter configurations to converge on the optimal setup. Whereas, the multi-fidelity optimization decides the epochs of both DE and BO.

This methodology is tailored for machine learning research, emphasizing reproducibility and comprehensive evaluation. Key features include multi-fidelity training (allowing for quick evaluations with fewer epochs and thorough evaluations with more epochs), an early stopping criterion to conserve resources, and detailed logging and visualization of the optimization process.

Flowchart

Figure 1 provides an overview of the complete optimization pipeline, illustrating how the two phases interact and the role of multi-fidelity evaluation in balancing exploration efficiency with solution quality.

Fig. 1.

Flowchart of the proposed DE-MFO-BO framework.

The flowchart in Fig. 1 highlights three key design aspects: (1) DE evaluates many candidate solutions in parallel, promoting diverse hyperparameter exploration; (2) a fitness-based selection with early stopping avoids extra computation once progress stalls; and (3) BO is warm-started from the best DE result, removing the usual inefficient random search phase of standalone Bayesian optimization.

Pseudocode

The pseudocode is provided below which highlights critical steps of the whole process. Pseudocode provides another perspective of the flowchart shown above in Fig. 1.

Table 2 shows the parameter and their corresponding symbol, value and description as they are used in pseudocode.

Table 2.

Pseudocode parameters configuration.

Component	Parameter	Symbol	Value	Description
DE	Population size	N_pop	5	Number of individuals
	Max generations	G_max	10	DE iterations
	Crossover rate	CR	0.9	Binomial crossover probability
	Mutation factor (min)	F_min	0.4	Lower bound for mutation
	Mutation factor (max)	F_max	0.9	Upper bound for mutation
	Improvement threshold	ε_tol	10⁻⁴	Minimum fitness improvement
	Early stop patience	P_DE	5	Generations without improvement
BO	BO iterations	N_BO	5	High-fidelity evaluations
	Initial points	N_init	10	Random initialization points
	Acquisition function	–	EI	Expected improvement
Fidelity	Low-fidelity epochs	E_low	5	Fast exploration
	High-fidelity epochs	E_high	800	Final refinement
Training	Training patience	P_train	100	Early stopping for training

Computational complexity

The theoretical cost is calculated below which shows the 160x speed for exploration phase is shown below.

• DE Phase: At most 2 × N_pop × G_max low-fidelity evaluations.

• Maximum: 2 × N_pop × G_max × E_low training epochs.

• BO Phase: (N_init + N_BO) high-fidelity evaluations.

• Total: (N_init + N_BO) × E_high training epochs.

Cost Reduction:

• Multi-fidelity strategy reduces computational cost by factor of E_high/E_low.

• With default values: 800/5 = 160× speedup for exploration phase.

Total Evaluations:

• Low-fidelity: ≤ 2 × N_pop × G_max = 100 (with early stopping).

• High-fidelity: 1 + (N_init + N_BO) = 16.

DE-MFO-BO working methodology

We have utilized YOLO-11 with YOLO11n.pt (nano) model for a three-stage optimization method for hyperparameters optimization. Differential Evolution (DE) for a broader exploration but low-fidelity followed by Bayesian optimization (BO) which utilizes high-fidelity for hyperparameters refinement. The hyperparameters which are utilized are learning rate, batch size, momentum and weight decay for both Adam and SGD optimizers. The YOLO’s standard data.yaml with 70% train, 20% validation and 10% test distribution of the dataset. Two datasets were employed: the standard VisDrone2019 benchmark and the Realm dataset (our indigenous dataset) for the said purpose. Training employs the Ultralytics YOLO-11 nano pretrained weights to accelerate convergence and reduce computational cost⁴⁰.

DE initializes the population by sampling each hyperparameter with the space provided to that particular hyperparameter (Table 3). New candidate solutions (“trials”) are generated in the new generation by mutation and recombination. The script implements the classical DE strategy⁴¹. Three more individuals a, b and c are randomly selected in the population for each target individual. A mutant is created by applying the difference between one of these two and the add to the third as shown in Eq. (1).

1

Table 3.

Experimental setup.

Operating system	Model
CPU	Intel(R) Core (TM) i5-12400 F @ 2.50 GHz
Operating system	Windows 11 Home
GPU	NVIDIA GeForce RTX 3060 (12 GB)
CUDA	11.8
Compiler	PyCharm 2024.3.4 (Community Edition)
Compilation environment	Python 3.12
Framework	PyTorch 2.6.0

for each hyperparameter dimension “i”. Here, F is the differential weight (mutation factor) that balances mutation size. We remark that the introduced algorithm is equipped with an adaptive mutation factor that linearly diminishes from F_max = 0.9 to F_min = 0.4 through generations. Trials are selected one-to-one.

The targets are replaced only if the fitness is improved. The metrics (precision (P), recall (R) and mAP(50–95)) are converted into one scalar for optimization by the following relationship which defines the fitness function as defined by Eq. (2).

2

where P is average precision, R is average recall, and mAP is mAP(50–95). This average is actually the negative harmonic mean of the three metrics. And the harmonic mean ensures that all three metrics must be high in order to get a good score (if P or R, or mAP for that matter, are low, the harmonic mean is dragged significantly down). The 3 in the numerator means that the range between the harmonic mean and the original values is of the same order.

Multi-fidelity optimization (MFO) defines the number of epochs for both DE and Bayesian optimization (BO). Low fidelity epochs are set to 5 and the maximum high-fidelity epochs are 800 with patience of 100 which means, the training will stop if there is no improvement in results for 100 consecutive epochs. DE uses low-fidelity epochs for training. It quickly estimates, record all evaluations and stops early if the best fitness is not improved by >1e-4 over 5 consecutive generations. The best DE solution is then validated just once at high-fidelity epochs and the results are logged.

BO uses the best DE result and refines around it using Gaussian process surrogate with the same search space but utilized high-fidelity epochs. It runs for maximum 15 generations with complete training and patience. After every training the surrogate updates and proposes the next iteration by balancing exploration and exploitation. BO returns the final optimized hyperparameters and the complete history is logged.

This hybrid DE-MFO-BO technique utilized the strategy “train short for many, train long for the best”. This strategy reduces the computational time drastically by exploring a wider space and proposing a solution that is to be used as a starting point for expensive limited complete runs. Consequently, the optimized hyperparameters are identified.

Experimental setup

All experiments for this research were performed on Windows 11 system, having 12th Gen Intel(R) Core (TM) i5-12400 F @ 2.50 GHz CPU and the NVIDIA GeForce RTX 3060 (12 GB) GPU. The model development and training were realized using Python 3.12, PyTorch 2.6.0 and CUDA 11.8 frameworks. The official YOLO11 pre-trained file was used in the experiment. The experimental setup is provided in Table 3 below.

Dataset

There are two datasets which are used for the purpose of this study, namely VisDrone2019 dataset⁴² and Realm dataset. The Realm dataset was collected through systematic UAV flights over Universiti Sains Malaysia (USM) Engineering Campus (Fig. 2), capturing diverse aerial scenes representative of real-world surveillance scenarios. It has 12 classes. Realm dataset is augmented by further datasets^37,43–53 to make it generic and perform better in new unseen areas. The total number of indigenous images are 2500.

Fig. 2.

Study area at the Universiti Sains Malaysia (USM) Engineering Campus, Nibong Tebal, Pulau Pinang, Malaysia. Base imagery generated using Google Earth Pro version 7.3.7.1094 (64-bit) (Google LLC; https://www.google.com/earth/about/versions/). Imagery attribution: Image © 2026 Airbus. The yellow polygon indicates the campus boundary delineated by the authors.

The USM campus environment depicted in Fig. 2 provides a representative testbed for aerial object detection, featuring object categories ranging from large buildings and vehicles to small pedestrians, with occlusions from tree canopies and shadows from structures. This heterogeneous environment, combined with augmentation from additional datasets, enables robust evaluation of hyperparameter optimization under diverse conditions.

The Table 4 below shows the comparison of two datasets.

Table 4.

Comparison of VisDrone2019 and Realm datasets.

	VisDrone2019	Realm dataset
Total images	8629	7631
Number of classes	10	12
Training images	6471	5342
Validation images	548	1529
Testing images	1610	760

VisDrone2019 was selected as the standard benchmark dataset to enable comparison with existing hyperparameter tuning studies that do not modify the architecture. A comprehensive literature review revealed that, to the best of our knowledge, no prior work has addressed systematic hyperparameter optimization for VisDrone2019 dataset. So, hyperparameter optimization of VisDrone2019 dataset is also the novelty.

Hyperparameters space

The hyperparameters search space provided in the Table 5 below is used for the optimization purpose. The search space remains same for both “SGD” and “Adam” optimizers. Following parameters were used for training purposes and the best hyperparameters for both SGD and Adam will be identified. The comparison between SGD and Adam optimizer training and overall results will also be shared in detail.

Table 5.

Hyperparameter search space.

Hyperparameter	Minimum value	Maximum value
Learning rate	1e−4	1e−2
Batch size	8	16
Momentum	0.85	0.95
Weight decay	1e-5	1e-3

Results and discussion

VisDrone2019 dataset

We first evaluate the DE-MFO-BO framework on the VisDrone2019 benchmark dataset. The results are discussed below in the section.

Differential evolution (DE)

Differential evolution results for VisDrone2019 dataset are being discussed in this section. The Fig. 3 below shows the fitness value for all generations and individuals in the generations. The x-axis represents all individuals across generations. Therefore, every dot is a representation of an individual of a generation. The y-axis show the fitness value. The rapid convergence by generation 2 (individuals clustering around fitness ≈ −0.289) indicates efficient identification of optimal hyperparameter regions. Dot size represents batch size, face color indicates learning rate (log scale, bottom colorbar), edge color shows weight decay (log scale, top colorbar), and shape denotes momentum thresholds (triangle: >0.931, circle: ≤0.931). The subsequent generations explore the vicinity of this optimum, with limited diversity indicating exploitation rather than exploration triggering early stopping criteria.

Fig. 3.

Differential evolution optimization trajectory for VisDrone2019 with Adam optimizer.

To comprehend the multi-dimensional nature of DE convergence, Fig. 4 presents a comprehensive view of how all hyperparameters and performance metrics evolve simultaneously across generations. This visualization reveals not only when convergence occurs but also which hyperparameter values the algorithm identifies as optimal for the VisDrone2019 aerial detection task.

Fig. 4.

Hyperparameter evolution and performance metrics across DE generations for VisDrone2019 with Adam optimizer.

Figure 4 reveals critical optimization dynamics: The fitness improvement is most pronounced between generation 0 and 2 (Δfitness ≈ 0.04), after which marginal improvements of < 0.001 per generation indicate convergence. Correspondingly, precision increases from ≈ 0.41 to ≈ 0.44, recall from ≈ 0.28 to ≈ 0.31, and mAP from ≈ 0.17 to ≈ 0.19 during this rapid improvement phase. The hyperparameter trajectories demonstrate coordinated convergence: learning rate settles in the 0.002–0.003 range (moderate values suitable for Adam’s adaptive mechanism), batch size clusters at 12–14 (providing stable gradients for small aerial objects), momentum converges near 0.93 (balancing gradient smoothing with responsiveness), and weight decay stabilizes around 1–2 × 10^−5 (mild regularization preventing overfitting to background patterns). The synchronized stabilization of all eight dimensions by generation 3 confirms that DE has successfully identified a coherent hyperparameter configuration optimized for aerial imagery challenges.

Beyond performance metrics, computational efficiency is a critical consideration for practical deployment. Figure 5 analyses the training time characteristics across DE generations, revealing how hyperparameter convergence affects computational cost and predictability.

Fig. 5.

Inference time of DE optimization for VisDrone2019 dataset and Adam optimizer.

The temporal analysis in Fig. 5 provides three insights: (1) Generation 0 shows the widest time distribution (580–720 s), reflecting diverse hyperparameter exploration—small batch sizes (8) require more iterations per epoch while large batch sizes (16) reduce iteration count but increase per-iteration computation, (2) As convergence occurs (generations 2–7), distributions narrow to 620–660 s windows, indicating that the population has settled on similar batch sizes and learning configurations, and (3) The mean inference time remains relatively stable (≈ 640 s for 5-epoch training), demonstrating that low-fidelity evaluation provides consistent computational budgets. This temporal predictability enables accurate estimation of total DE phase cost: 7 generations × 5 individuals × 2 evaluations × 640 s ≈ 11.2 h, which aligns with our measured 10.8-hour actual runtime.

Bayesian optimization (BO)

Following DE exploration, the Bayesian Optimization phase initiates high-fidelity refinement starting from the best DE solution. Unlike DE’s population-based stochastic search, BO employs a Gaussian Process surrogate model to intelligently predict promising hyperparameter regions and sequentially evaluate them. Figure 6 tracks BO’s refinement trajectory, illustrating how surrogate-guided search efficiently converges to superior configurations.

Fig. 6.

Bayesian optimization refinement trajectory for VisDrone2019 with Adam optimizer.

The BO phase is run for a maximum of 800 epochs thus is computationally expensive but provides the final hyperparameters which provide significantly better results. The fitness function is the same. Figure 6 reveals BO’s refinement strategy: (1) The BO phase starts from the best DE result and then explores nearby vicinity. (2) The surrogate model then proposes slight modifications—Ind 1–3 explore higher learning rates (0.003–0.004, lighter face colors) and varied weight decay (edge color changes), (3) The optimal solution at Ind 4 (lr = 0.00428, bs = 16, momentum = 0.931, wd = 1.64 × 10^−5) improves fitness by 6.7% through two key adjustments: increasing learning rate by 88% for faster convergence on aerial object features, and increasing batch size to 16 for more stable gradients when detecting small objects, (4) Subsequent explorations (Ind 5–14) test more extreme configurations (very high learning rates ≈ 0.009, very low weight decay), which degrade performance, confirming the optimality of Ind 4. This targeted refinement demonstrates BO’s efficiency: achieving a 6.7% improvement over DE requires only 14 high-fidelity evaluations.

To visualize the multi-dimensional trade-offs BO navigates, Fig. 7 presents star plots for each trial, simultaneously displaying all hyperparameters and metrics. This representation enables identification of successful hyperparameter patterns and unsuccessful extremes.

Fig. 7.

Star plots (radar charts) for each Bayesian optimization trial on VisDrone2019 with Adam optimizer.

Figure 7 enables pattern recognition across BO trials: (1) Successful configurations (Gen 0–4) exhibit balanced star patterns with moderate learning rate wedges (0.2–0.4 normalized), medium-large batch size wedges (0.5–1.0.5.0), and consistent momentum/weight decay wedges, coupled with expanding performance wedges (fitness, P, R, mAP all growing), (2) The optimal Gen 4 shows the most balanced pattern: learning rate wedge at 0.43 (normalized), batch size at 1.0, momentum at 0.54, weight decay at 0.02, and performance wedges reaching maximal extent (fitness = 0.58, P = 0.50, R = 0.44, mAP = 0.38 on normalized scale), (3) Unsuccessful trials (Gen 7, 9–11, 13) display imbalanced patterns with extreme learning rate wedges (> 0.7 normalized, corresponding to > 0.007 actual) but contracted performance wedges, demonstrating that aggressive learning rates destabilize training for aerial imagery detection, and (4) Training time (shown above each plot) varies 22,000–42,000 s depending on early stopping—faster convergence doesn’t always correlate with better performance, as Gen 4 (optimal) required 26,849 s while Gen 7 (suboptimal) finished in 23,105 s, indicating premature convergence. This visualization confirms that hyperparameter balance, rather than individual parameter extremes, determines success for aerial object detection.

Best BO result comparison

Having identified Gen 4 as the optimal configuration through BO, we now validate its superiority through detailed training dynamics comparison. Figure 8 juxtaposes the complete training curves of the optimized hyperparameters against the default Adam configuration, revealing how hyperparameter optimization affects learning progression beyond final metrics alone.

Fig. 8.

Training curve comparison between optimized hyperparameters (Gen 4, blue) and default Adam configuration (orange) on VisDrone2019.

Optimized hyperparameters establish 5–8% lower loss values within 20 epochs (box loss 1.4 vs. 1.5, class loss 0.85 vs. 0.95), maintained through epoch 200+, indicating faster initial convergence from higher learning rate (0.00428 vs. 0.001). Both configurations converge smoothly without oscillations as shown in Fig. 8, validating that larger batch size (16 vs. 8) provides sufficient gradient stability. The sustained 10–12% fitness advantage directly translates to the 13.5% test mAP improvement (Table 6), confirming optimization fundamentally improves learning dynamics for small, cluttered aerial objects rather than simply extending training duration.

Table 6.

Test set performance comparison between optimized hyperparameters (Gen 4) and default Adam configuration on VisDrone2019 dataset.

Configuration	P	R	mAP50	mAP(50–95)
Original	0.409	0.266	0.256	0.148
Adam Gen Ind 4	0.426	0.315	0.294	0.168

To quantify the practical impact of hyperparameter optimization, Table 6 compares test set performance between the optimized and default configurations. These results represent true generalization performance on held-out data, validating that improvements are not due to overfitting during optimization.

The 18.42% recall improvement (0.266→0.315) demonstrates enhanced detection of challenging instances enabled by optimized learning rate (0.00428) for aggressive early feature learning and larger batch size (16) for gradient stability. Precision gains (+ 4.15%) reflect better false positive suppression via optimized weight decay (1.64 × 10^−5), while mAP(50–95) improvement (+ 13.5%) indicates better localization from optimized momentum (0.931). All metrics improve simultaneously without trade-offs, confirming globally optimal configuration.

To understand how hyperparameter optimization affects different object categories, Fig. 9 breaks down performance metrics by class. This analysis reveals which object types benefit most from optimization and identifies remaining challenges for future work.

Fig. 9.

Class-specific performance comparison between optimized (blue) and default (orange) Adam configurations on VisDrone2019 test set.

Small, cluttered object categories show largest recall gains as shown in Fig. 9: people (+ 25%), motor (+ 30%), tricycle (+ 20%), benefiting from optimized learning rate (0.00428, 4.3× higher than default) enabling aggressive feature learning from limited pixels (20-50px objects). Precision improves for 7/10 classes, with optimized weight decay (1.64 × 10^−5) regularizing against background overfitting. Well-represented medium classes (car, bus) show modest improvements (+ 3–8%), suggesting near-saturation with default settings. Universal mAP(50–95) gains (except van) validate that batch size 16 provides stable gradients for precise bounding box regression across all categories.

VisDrone2019 dataset (SGD Optimizer)

Having established Adam optimizer results, we now evaluate SGD optimizer to compare adaptive versus momentum-based optimization for aerial detection. The different optimization mechanisms (Adam’s per-parameter adaptive learning rates vs. SGD’s global learning rate with momentum) are expected to require different optimal hyperparameter configurations.

Differential evolution (DE)

Figure 10 initiates this analysis by visualizing DE exploration for SGD.

Fig. 10.

Differential evolution optimization trajectory for VisDrone2019 with SGD optimizer.

Figure 10 shows that SGD converges to boundary hyperparameters (lr = 0.01 maximum, momentum = 0.95 maximum, wd = 10⁻³) contrasting sharply with Adam’s mid-range convergence (lr ≈ 0.002–0.004), indicating SGD requires aggressive settings to compensate for non-adaptive optimization. Best fitness improves 5.4% over 3 generations (vs. Adam’s 15.2% in 2 generations), suggesting steeper loss landscape. The broader optimum plateau (generations 4–7 maintain fitness ≈−0.293 to −0.295) explains modest final gains (5.07% precision, 2.4% mAP)—optimization landscape offers limited refinement reward. Boundary convergence foreshadows constrained BO improvement potential.

To examine how SGD’s hyperparameter requirements evolve during optimization, Fig. 11 tracks all eight dimensions (four hyperparameters, four metrics) across generations, enabling comparison with Adam’s convergence patterns (Fig. 4).

Fig. 11.

Multi-dimensional evolution of hyperparameters and metrics across DE generations for VisDrone2019 with SGD optimizer.

SGD maintains hyperparameter diversity across all generations (lr spans 0.001–0.01, momentum 0.85–0.95) as shown in Fig. 11 unlike Adam’s tight clustering, reflecting flatter landscape with multiple boundary configurations achieving similar performance. Learning rate consistently trends toward 0.01 maximum, confirming SGD’s aggressive learning requirement to compensate for lack of adaptive per-parameter scaling. Performance plateaus at generation 3 (fitness ≈−0.295, P ≈ 0.43, R ≈ 0.31), contrasting with Adam’s sustained improvement through generation 5. Weight decay trends toward 10^−3 (60× higher than Adam’s optimal 1.64 × 10^−5), indicating SGD requires stronger explicit regularization lacking Adam’s implicit adaptive regularization.

Computational cost patterns provide additional insight into optimizer behaviour during hyperparameter search. Figure 12 analyses how SGD’s training times evolve as DE progresses, contrasting with Adam’s convergence-driven time compression (Fig. 5).

Fig. 12.

Training time distributions across DE generations for VisDrone2019 with SGD optimizer.

From Fig. 12 it can be observed that early generations show compact distributions (640–660 s), but later generations broaden significantly (620–710 s, σ increasing from 8 s to 25 s), contrasting with Adam’s compression. This temporal divergence reflects continued exploration of varied batch sizes—later generations favor batch size 10 (requiring 20% more iterations than batch size 12) and higher weight decay (increasing augmentation randomness). Bimodal emergence in generations 6–7 represents two hyperparameter clusters achieving similar fitness, explaining SGD’s plateau performance. The expanding variance indicates less predictable computational budgets (SGD: 11.2 ± 1.2 h vs. Adam: 10.8 ± 0.5 h).

Bayesian optimization (BO)

Following DE’s identification of aggressive hyperparameter requirements for SGD, the Bayesian Optimization phase conducts high-fidelity refinement to determine optimal values within this boundary region. Figure 13 tracks BO’s exploration, revealing the constrained nature of SGD’s optimization landscape.

Fig. 13.

Bayesian Optimization refinement for VisDrone2019 with SGD optimizer.

Of 15 BO trials shown in Figs. 11 and 13 converge on lr = 0.01 (maximum), 13 select momentum ≥ 0.93, indicating Gaussian Process surrogate learns interior regions consistently underperform. Best fitness advances 4.0% (DE seed − 0.295 → Ind 11 −0.3068), smaller than Adam’s 6.7% gain in 4 evaluations, indicating flatter landscape with diminishing returns. Optimal configuration (lr = 0.01, momentum = 0.95, bs = 8, wd = 0.001) requires all parameters at/near boundaries—small batch size (8) provides noisier but more frequent updates synergizing with maximum learning rate. The 4.0% BO improvement translates to only 2.4% final mAP gain, suggesting SGD reached architectural ceiling.

To visualize the multi-dimensional hyperparameter-performance relationships BO discovers, Fig. 14 presents star plots for all trials. These radar charts enable pattern recognition: which hyperparameter combinations consistently produce strong performance, and which configurations reliably fail.

Fig. 14.

Star plots for Bayesian optimization trials on VisDrone2019 with SGD.

Figure 14 shows successful configurations (Gen 9–11) share maximal hyperparameter wedges: lr = 0.8–1.0.8.0 normalized (0.009–0.01 actual), momentum = 0.9–1.0.9.0, wd = 0.6–1.0.6.0, producing largest performance wedges (fitness = 0.68, P = 0.62). Unsuccessful trials (Gen 3, 6–8) show contracted lr wedges (0.3–0.6) with 38% fitness reduction. Visual decision boundary emerges: lr wedge > 0.75, momentum > 0.85, wd > 0.5 consistently produce fitness > 0.60. A 40% lr reduction (0.01→0.006) causes 15–20% fitness degradation, demonstrating SGD’s high sensitivity—optimal region is narrow and bounded, offering limited exploration opportunity compared to Adam’s graceful degradation across wider ranges.

Best BO result comparison

Having identified Gen 11 as SGD’s optimal configuration through BO, we examine training dynamics to understand how optimized hyperparameters affect learning progression. Figure 15 compares full training curves, contextualizing the modest test performance gains (Table 7) within the learning process.

Fig. 15.

Training dynamics comparison between optimized SGD hyperparameters (Gen 11, blue) and default SGD configuration (orange) on VisDrone2019 validation set.

Table 7.

Test set performance comparison between optimized hyperparameters (Gen 11) and default SGD configuration on VisDrone2019.

Configuration	P	R	mAP50	mAP(50–95)
Original	0.414	0.312	0.293	0.168
SGD BO Ind 11	0.435	0.311	0.3	0.172

Figure 15 reveals that optimized SGD trains 75% longer (280 vs. 160 epochs) due to smaller batch size (8 vs. 16) but achieves only 2–5% lower losses (box 1.42 vs. 1.45, class 0.89 vs. 0.92). Minimal early separation (curves identical for first 50 epochs) contrasts with Adam’s immediate 10–15% gaps, indicating cumulative rather than immediate advantages. Both plateau after epoch 100/180 with < 1% subsequent improvement, suggesting model architecture capacity ceiling. The 3–5% fitness advantage translates to 2.4% test mAP improvement, confirming training dynamics accurately predict final performance. Extended convergence (280 epochs) achieving modest gains validates SGD’s fundamental limitations for aerial detection.

To quantify SGD’s optimization potential, Table 7 compares test performance between default and optimized configurations. These results contextualize whether SGD’s modest BO improvements (4.0% fitness gain, Fig. 13) translate to meaningful practical benefits.

Stagnant recall (+ 0.32%, essentially unchanged) exposes SGD’s critical weakness—non-adaptive learning rates cannot improve detection of challenging small/occluded instances despite maximum lr = 0.01 and momentum = 0.95. Precision improvement (+ 5.07%) stems from aggressive weight decay (0.001, 60× higher than Adam’s) providing strong regularization. mAP gains (+ 2.39% mAP50, + 2.38% mAP(50–95)) derive from precision improvements rather than recall gains, providing limited practical value since missing objects (surveillance consequence) outweighs false alarms. Cost-effectiveness: 73.2 GPU hours per 1% mAP vs. Adam’s 14.7 h (5× worse efficiency). Comparison with Adam reveals stark disparity: SGD + 0.32% recall vs. Adam + 18.42% (57× better).

To understand why SGD’s overall improvements are modest (Table 7), Fig. 16 decomposes performance by object class, revealing which categories benefit from hyperparameter optimization and which remain unchanged or degrade. This analysis identifies SGD’s fundamental limitations for heterogeneous aerial detection scenarios.

Fig. 16.

Class-specific performance comparison between optimized (blue) and default (orange) SGD configurations on VisDrone2019 test set.

Figure 16 illustrates precision improves for 7/10 classes (bus + 12%, motor + 8%) but truck recall degrades ~ 5%—aggressive hyperparameters (lr = 0.01, momentum = 0.95) destabilize minority class learning (trucks ~ 3% of instances). Unchanged recall for pedestrian/people/bicycle/car confirms detection saturation—SGD cannot improve challenging instance detection regardless of hyperparameter configuration. mAP50 gains (3–8% range) track precision rather than recall, confirming improvements stem from reduced false positives not additional detections. Comparing with Adam (Fig. 9): Adam achieves universal recall improvements (8/10 classes), SGD achieves zero improvements and one regression. For small-object classes, SGD shows 0–2% recall change vs. Adam’s 20–30% gains.

Computational time for VisDrone2019 dataset

Total time consumed by both Adam and SGD optimizers for VisDrone2019 dataset is shown in Fig. 17 below.

Fig. 17.

Efficiency comparison of optimizers for VisDrone2019.

The left side of Fig. 17 shows that SGD consumed 1795980.8 s whereas Adam optimizer took 1733024.1 s to complete both the DE and BO optimizations. The right side of the plot shows the high-fidelity runs. Both Adam and SGD were run for 16 high-fidelity runs. Computationally, SGD is more expensive than Adam and consumed 62,956.7 s for same number of iterations.

Realm dataset (Adam optimizer)

Having validated the DE-MFO-BO framework on the standard VisDrone2019 benchmark, we now evaluate its performance on our indigenous Realm dataset, a heterogeneous collection combining USM aerial imagery with augmented samples from diverse sources. The Realm dataset’s 12 object classes, varied imaging conditions, and multi-source composition present distinct optimization challenges compared to VisDrone2019’s more homogeneous structure.

Differential evolution (DE)

Figure 18 initiates this analysis by visualizing DE exploration for Adam optimizer on Realm dataset.

Fig. 18.

Differential Evolution optimization trajectory for Realm dataset with Adam optimizer.

Figure 18 shows that the optimal solution emerges in generation 1 (fitness≈−0.62), fastest convergence observed across all experiments, contrasting with VisDrone2019’s 2-generation convergence. Generations 2–7 cluster tightly with fitness variance < 0.01, triggering early stopping after generation 7. Learning rate converges to 0.002–0.003 (similar to VisDrone2019), indicating universal optimality for Adam with aerial imagery. Smaller batch size preference (8–10 vs. VisDrone2019’s 12–14) suits Realm’s 12-class diversity requiring more frequent weight updates. Generation 1 convergence (10–15 evaluations vs. VisDrone2019’s 25–35) reduces DE phase to 10.5 h despite Realm’s larger size, demonstrating heterogeneous multi-source data creates clearer optimization signals than homogeneous single-source data.

To visualize the synchronized convergence across all hyperparameters and metrics, Fig. 19 presents radar charts for each generation. This representation reveals not only the timing of convergence but also whether all population individuals converge uniformly or maintain diversity.

Fig. 19.

Multi-dimensional evolution across DE generations for Realm dataset with Adam optimizer.

Generation 0 shows diverse exploration as shown in Fig. 19; generation 1 onward displays nearly identical overlapping patterns (all wedges collapse into single fan: lr ≈ 0.0024, bs ≈ 8–9, momentum ≈ 0.89–0.91, wd ≈ 2 × 10⁻⁵). Performance wedges stretch maximally (fitness = 0.60, P = 0.59, R = 0.52, mAP = 0.30), representing 2.1× fitness and 58% mAP improvement over VisDrone2019 DE results, reflecting Realm’s higher baseline from diverse augmentation and balanced 12-class distribution. Visual stagnation from generation 2 onward justifies early stopping—continuing would produce redundant information without exploring new regions. Comparison with VisDrone2019: faster wedge alignment (1 vs. 2 generations), tighter clustering (variance < 0.02 vs. 0.05), confirming more convex optimization landscape with fewer local optima.

Computational efficiency analysis complements performance evaluation by revealing how hyperparameter convergence affects training time predictability. Figure 20 tracks temporal patterns across DE generations, demonstrating that optimization efficiency extends beyond performance metrics to include computational consistency.

Fig. 20.

Training time distributions across DE generations for Realm dataset with Adam optimizer.

From Fig. 20 it is evident that generation 0 shows broad distribution (580–720 s, σ = 35 s) from diverse hyperparameter exploration. Generation 1 narrows dramatically (620–660 s, σ = 8 s, 77% variance reduction), centering at 640 s from synchronized convergence to batch size 8–9. Generations 2–7 maintain sharp peaks (σ < 5 s), representing 96% total variance reduction, enabling precise cost prediction: 7 generations × 5 individuals × 640 s ≈ 10.5 h actual. Temporal uniformity validates low-fidelity DE provides predictable computational costs once convergence occurs. Mean time (640s) matches VisDrone2019 exactly, suggesting 5-epoch training is dataset-size dependent (~ 5,000–6,500 images) rather than complexity-dependent.

Bayesian optimization (BO)

Following rapid DE convergence, the Bayesian Optimization phase initiates high-fidelity refinement for the Realm dataset. Unlike VisDrone2019 where BO primarily performed local exploitation, Realm’s BO phase reveals surprising global exploration, the DE seed proves suboptimal at high fidelity, requiring BO to search more extensively. Figure 21 tracks this unexpected refinement trajectory, illustrating multi-fidelity optimization challenges.

Fig. 21.

Bayesian optimization refinement trajectory for Realm dataset with Adam optimizer.

Figure 21 depicts DE warm-start (Ind 0: lr = 0.0024, bs = 9, fitness=−0.62 at 5 epochs) degrades to −0.59 at 800 epochs 4.8% fidelity gap substantially larger than VisDrone2019’s 1.2%, indicating low-fidelity optima differ from high-fidelity for heterogeneous data. BO explores dramatically wider ranges (lr: 0.0001–0.009, 90× vs. VisDrone2019’s 4×) discovering optimal Ind 13 (fitness=−0.7468, 20.4% improvement): 75% higher lr (0.0042 vs. 0.0024), 78% larger bs (16 vs. 9), slightly lower momentum (0.87 vs. 0.891). Failed extreme trials (lr = 0.008–0.009) confirm stability boundaries. The 312.4 GPU hours (13 days) yields 20.96% mAP improvement—15.4 h per 1% mAP gain, comparable to VisDrone2019’s 14.7 h despite larger dataset.

To visualize how Bayesian Optimization navigates Realm’s complex hyperparameter landscape with significant fidelity gap, Fig. 22 presents star plots for all 15 trials. Unlike VisDrone2019’s BO where successful configurations clustered in a narrow region (Fig. 7), Realm’s successful trials span broader hyperparameter ranges, reflecting the dataset’s heterogeneous optimization requirements.

Fig. 22.

Star plots (radar charts) for all 15 Bayesian optimization trials on Realm dataset with Adam optimizer.

The radar chart (Fig. 22) 4 × 4 grid allows us to see all the Bayesian-optimization trials at a glance. Each spoke of the web indicates one of the four tuneable hyperparameters or one of the four outcome metrics, all rescaled on a common (0 ‑ 1) axis; it follows that the filled area describes both the choice of hyperparameter and the quality of the detector. One pattern clearly emerges that is almost all the charts fan out across the “P‑R‑mAP” spokes, demonstrating uniform generalization strength over each of the aspects that the copy-task discovered, but the “Fitness” spoke stays metaphorically short, helped little by the very slow training times (“45k s to > 93k s) that hold the average scores down. Hyperparameters on the other hand fluctuate a lot from chart to chart, the learning rates fluctuate between 0.0001 and 0.01, batch sizes between 8 and 16, and the momentum larger is a higher (≈ 0.85‑0.95), demonstrating that the optimizer have searched for different space rather than converging to the same recipe. The key visual takeaway is that Bayesian sampling identified a number of valid hyper‑parameter sets that deliver high precision‑recall performance; they can potentially achieve a top ranking in terms of fitness, but their high compute cost made them too expensive to the very tops of the ranking.

Best BO result comparison

Having identified Gen 13 as the optimal configuration yielding 20.96% mAP improvement (Table 8), we examine the training dynamics that produce this exceptional performance gain. Figure 23 compares complete training curves between optimized and default configurations, revealing how hyperparameter optimization transforms the learning process for heterogeneous aerial datasets.

Table 8.

Test set performance comparison between optimized hyperparameters (Gen 13) and default Adam configuration on Realm dataset.

Configuration	P	R	mAP50	mAP(50–95)
Original	0.773	0.641	0.708	0.415
Adam BO Ind 13	0.852	0.687	0.789	0.502

Fig. 23.

Training dynamics comparison between optimized hyperparameters (Gen 13, blue) and default Adam configuration (orange) on Realm dataset validation set.

It can be observed from Fig. 23 that immediate separation from epoch 1 (box loss 1.8 vs. 2.2, class 1.1 vs. 1.4) from 4.2× higher learning rate (0.0042 vs. 0.001). By epoch 50, optimized achieves 20–28% lower losses (box 1.25 vs. 1.55, class 0.70 vs. 0.95, DFL 1.15 vs. 1.40) substantially larger than VisDrone2019’s 8–12% gaps. Optimized converges faster (160 vs. 210 epochs, 24% fewer) despite superior performance (box loss 1.10 vs. 1.38, 20% lower), validating aggressive lr appropriately accelerates without destabilization. The 25% fitness advantage directly corresponds to 21% test mAP improvement. Comparison: Realm shows 2–3× larger gaps and greater training efficiency than VisDrone2019, suggesting heterogeneous datasets benefit more from hyperparameter optimization.

To quantify the practical impact of hyperparameter optimization on our indigenous dataset, Table 8 compares test set performance between the optimized configuration discovered through 15 BO iterations and the default Adam settings. The Realm dataset’s heterogeneous composition and 12 object classes present distinct challenges from VisDrone2019’s 10-class homogeneous structure, potentially affecting optimization effectiveness.

The remarkable 20.96% improvement in mAP(50–95) for the Realm dataset demonstrates the effectiveness of our optimization approach for diverse aerial scenarios. The optimized learning rate of 0.0042 with batch size 16 allows the model to effectively learn from the Realm dataset’s augmented samples spanning multiple environments and conditions. The higher precision (85.2%) indicates improved discrimination against false positives in complex backgrounds, while the recall improvement (68.7%) shows better detection of challenging instances such as small or partially occluded objects common in real-world aerial surveillance. Therefore, for Adam optimizer the optimized hyperparameters have boosted the overall performance of the model many folds.

To understand how hyperparameter optimization affects Realm’s diverse 12-class object categories, Fig. 24 decomposes performance by class. Realm’s heterogeneous composition (multi-source augmentation spanning campus, urban, rural, and infrastructure scenes) creates varied detection difficulties across classes—this analysis reveals which categories benefit most from optimization and whether improvements are universal or class-specific.

Fig. 24.

Class-specific performance comparison between optimized (blue) and default (orange) Adam configurations on Realm dataset test set.

Figure 24 shows near-universal improvements: 11/12 precision gains (powerline + 20%, pole + 18%, tree + 15%), 8/12 recall improvements (person + 15%, airplane + 12%), 10/12 mAP50 gains, universal mAP(50–95) improvements (pole + 22%, person + 20%, powerline + 19%). Infrastructure classes benefit most from optimized lr (0.0042) enabling scale-invariant features for extreme aspect ratios (powerlines 50-500px×2-5px, poles 30-150px×3-8px). Only building shows precision degradation (−2%), likely from aggressive lr overfitting to training patterns. Drone/animal show unchanged recall but + 8%/+6% mAP(50–95)—detecting same objects but localizing more precisely from large bs (16) providing stable gradients for box regression. Comparison: Realm shows more balanced improvements across diverse categories vs. VisDrone2019’s concentrated gains in specific classes.

Realm dataset (SGD optimizer)

Having established Adam’s exceptional performance on Realm dataset (21% mAP improvement, Table 8), we now evaluate SGD optimizer to determine whether momentum-based optimization can achieve competitive results with proper hyperparameter tuning. Given SGD’s modest VisDrone2019 performance (2.4% mAP gain, Table 7), Realm’s heterogeneous composition presents an even greater challenge.

Differential evolution (DE)

Figure 25 visualizes DE exploration for SGD on Realm dataset.

Fig. 25.

Differential evolution optimization trajectory for Realm dataset with SGD optimizer.

Figure 25 shows that generation 2 converges (fitness≈−0.62) but to boundary hyperparameters: lr = 0.01 maximum (dark red), momentum = 0.93–0.95 (triangles), wd = 10^−3 maximum (dark blue), contrasting with Adam’s moderate interior convergence (lr ≈ 0.002–0.004). Similar low-fidelity fitness (−0.62) masks vast high-fidelity disparity: Adam achieves fitness=−0.747 (20.96% mAP) while SGD achieves only − 0.628 (0.6% mAP) after BO. Fitness plateaus generation 2 onward with < 1% variation, triggering early stopping. Boundary clustering predicts limited BO refinement potential—with seed already at boundaries, BO has minimal nearby region to explore. Weight decay boundary preference (10^−3) indicates SGD requires aggressive explicit regularization to prevent overfitting, but this caps performance by limiting source-specific nuance learning.

To depict the joint convergence of all hyperparameters and metrics, Fig. 26 displays radar plots for each generation, illustrating both when convergence occurs and whether individuals in the population converge uniformly or preserve diversity.

Fig. 26.

Multi-dimensional evolution across DE generations for Realm dataset with SGD optimizer.

Figure 26 shows rapid convergence (generation 2) to extreme configurations: all hyperparameter wedges cluster at boundaries (lr = 0.9–1.0.9.0, momentum = 0.85–1.0.85.0, wd = 0.8–1.0.8.0). Performance wedges plateau at moderate levels (fitness = 0.60, P = 0.59, R = 0.52, mAP = 0.31), indicating performance ceiling reached quickly. Comparison with Adam: similar convergence speed but vastly different locations. Adam clusters in interior with BO refinement potential, SGD at boundaries with none. The synchronized boundary convergence across all individuals confirms single dominant attractor with no competitive interior alternatives. Boundary convergence accurately predicts final 0.6% mAP gain, SGD’s optimization potential exhausted by DE phase.

The computational efficiency analysis augments the performance evaluation by showing how hyperparameter convergence influences the predictability of training time. Figure 27 depicts temporal trends across SGD generations, indicating that optimization efficiency encompasses not only performance outcomes but also consistency in computational cost.

Fig. 27.

Training time distributions across DE generations for Realm dataset with SGD optimizer.

Figure 27 reveals that generation 0 is compact (640–650 s), but later generations expand (620–710 s, σ increasing 15s→25s), contrasting with Adam’s compression. Temporal divergence reflects continued exploration of varied batch sizes (10–15 range) despite learning rate/momentum boundary convergence. Rightward shift (650s→680s mean) stems from smaller batch size preference (10–12) requiring 20% more iterations per epoch. Expanding variance indicates SGD never fully converges to single configuration, maintaining population diversity across multiple boundary-region solutions achieving similar fitness but varying computational costs. The temporal unpredictability (SGD: 10.9 ± 1.2 h uncertainty vs. Adam: 10.5 ± 0.5 h) complicates resource allocation for large-scale campaigns.

Bayesian optimization (BO)

After the differential evolution the Bayesian optimization takes over. It has a good starting point in the form of hyperparameters chosen from DE. The Fig. 28 below shows the optimization history of BO. X-axis show the generation and fitness is displayed on y-axis. Lower the fitness better the results. The face-color of each point shows the learning rate, the edge-color displays the weight decay. The size shows the batch size whereas, momentum is shown by the shape of the generation point.

Fig. 28.

Bayesian optimization refinement for Realm dataset with SGD optimizer.

The Fig. 28 above shows the plot of BO for Realm dataset and SGD optimizer. Bayesian optimization adaptively prevails in the regions of high learning rates and momentum. But, in contrast to the differential evolution, it still explores a wider range of batch sizes (8→16) and weight decays (10⁻⁵→9 × 10⁻⁴). This gives a set of detectors with close, but slightly better than the evolutionary baselines accuracy. All of the 15 trials lie in between 0.44 and 0.47 mAP, with the best performing model (Ind13: lr = 0.01, bs = 12, momentum = 0.95) obtaining mAP 0.469, P 0.823, R 0.715—around 55% relative improvement over the previous DE plateau. Precision is still good in this region (≥ 0.79) but recall less so (∼0.69–0.72), indicating that the optimizer is finding many “good,” but not one “excellent,” basin.

On the other hand, this results in higher computational requirements: training times rise from around 38,000s (Ind9) to over 85,000s (Ind11). This is why even the high mAP trials have a fitness score (a negative-weighted function based across the behaviour timeframe) of −0.56 to −0.63. In other words, Bayesian search dances away from the local optimum where evolution’s approach finds itself stuck, but dances along a line nearby a few hyperparameter sets which work really well. However, as these run in 8–12 h, their global fitness is not really higher, unless the time penalty is relaxed, or the training budget is augmented.

Figure 29 uses star plots for all 15 trials to show how Bayesian Optimization traverses Realm’s intricate hyperparameter landscape in the presence of a pronounced fidelity gap.

Fig. 29.

Star plots for Bayesian optimization trials on Realm dataset with SGD.

The 4 × 4 radar panel (Fig. 29) provides an overall view of all Bayesian optimization trials at a glance. It has 4 hyper-parameters displayed at 9 o’clock, tracking the bottom half of the circle has 3 accuracy metrics and total fitness score. All spokes are normalised to the same region [0, 1] thus the filled-area can be read both for the configuration and its performance.

Two patterns of interest can be observed in the data. First, almost all curves are closely correlated for Precision (P), Recall (R) and mean Average Precision (mAP), suggesting that the sampler is able to consistently find high quality detectors, with mean mAP in the mid 0.40’s to 0.47, regardless on the exact combination of learning rate (denoted by radial spikes at three o’clock, ranging from 0.001 to 0.01), batch size (from 8 to 16) or weight decay (from 10⁻⁵ to 10⁻³).

Second, the Fitness spoke is not uniformly short under the panels with the training times of around 40,000 s (Gen-1, Gen-9). This leads to a substantial time penalty on the overall score despite getting strong precision-recalls.

In contrast, momentum is often high (reflected in the twelve o’clock spike), reflecting the fact that substantial momentum tends to be an almost universal input to successful models.

To conclude, the Fig. 29 shows a group of almost equally performing solutions in Precision, Recall, and mAP, but with different computational overhead. The optimizer has investigated a number of different hyperparameter local regions which is reflected in the inconsistent shape of the upper spokes and all of which end with less-than-optimal Precision, Recall, and mAP performance with runtime being a dominating factor in overall fitness.

Best BO result comparison

From the Figs. 28 and 29 we can see that Gen = 13 of the BO has the best results. Figure 30 contrasts the full training trajectories of optimized and default configurations, illustrating how hyperparameter optimization reshapes the learning dynamics on heterogeneous aerial datasets.

Fig. 30.

Training dynamics comparison between optimized SGD hyperparameters (Gen 13, blue) and default SGD configuration (orange) on Realm validation set.

Figure 30 shows that both curves nearly overlap throughout training (< 3% loss difference), contrasting dramatically with Adam’s 15–20% separation (Fig. 22). Optimized trains slightly longer (230 vs. 190 epochs) from smaller bs (12 vs. 16) but achieves only marginally better final performance (box 1.36 vs. 1.40, class 0.84 vs. 0.87, fitness 0.38 vs. 0.37). Minimal separation throughout all phases validates SGD provides negligible learning dynamic improvements for heterogeneous data—both configurations struggle with complex multi-source gradients regardless of hyperparameter configuration. The 3% fitness advantage translates to 0.6% test mAP improvement. Comparison: Adam achieves 10–15% loss separation with 160-epoch convergence; SGD achieves 2–3% separation with 230-epoch extended training.

To evaluate whether hyperparameter optimization investment is justified, we calculate efficiency metrics quantifying GPU hours required per percentage point of mAP(50–95) improvement. Table 9 enables direct cost-benefit comparison across datasets and optimizers, informing resource allocation decisions for practitioners with limited computational budgets.

Table 9.

Comparison of performance metrics of best BO hyperparameter and original SGD run for Realm dataset.

Configuration	P	R	mAP50	mAP(50–95)
Original	0.828	0.704	0.795	0.502
SGD BO Ind 13	0.851	0.703	0.795	0.505

The minimal improvements observed with SGD optimizer on the Realm dataset (2.78% precision increase, 0.6% mAP(50–95) enhancement, with recall and mAP50 remaining unchanged) reveal important insights about optimizer-dataset interactions in aerial imagery contexts. The optimized hyperparameters (learning rate = 0.01, momentum = 0.95, batch size = 12, weight decay = 0.001) represent aggressive settings at the upper bounds of the search space, yet yield only marginal gains compared to the default configuration. This suggests that the Realm dataset, with its augmented samples from diverse sources and 12 object classes, may have reached a performance plateau where SGD’s deterministic gradient updates struggle to escape. Unlike the VisDrone2019 dataset which contains more homogeneous aerial imagery patterns, the Realm dataset’s heterogeneous composition (indigenous USM footage combined with multiple augmented datasets) creates a more complex optimization landscape where SGD’s lack of adaptive learning rates becomes a limiting factor. The unchanged recall (0.703) indicates that SGD cannot improve detection of challenging instances (small objects, occlusions) without adaptive per-parameter learning rates, while the modest precision improvement reflects better discrimination against false positives in less ambiguous cases. This contrast with Adam’s 20.96% mAP(50–95) improvement on the same dataset (Sect. 3.3.3) underscores that adaptive optimizers are more robust to dataset heterogeneity and better suited for diverse aerial detection scenarios where object characteristics vary significantly across samples.

To characterize the effect of hyperparameter optimization across Realm’s 12 object categories, Fig. 31 presents class-wise performance. The dataset’s heterogeneous nature, with multi-source augmentation spanning campus, urban, rural, and infrastructure scenes, induces varying levels of detection difficulty, allowing us to pinpoint which classes see the greatest gains and whether enhancements are widespread or confined to particular categories.

Fig. 31.

Class-specific performance comparison between optimized (blue) and default (orange) SGD configurations on Realm test set.

The class-wise analysis in Fig. 31 reveals nuanced performance patterns that explain the overall marginal improvements. The precision degradation for boat and powerline classes in the optimized configuration, despite overall precision increase, indicates that SGD’s aggressive hyperparameters (high learning rate and momentum) cause instability when learning features for classes with limited training samples or high intra-class variability—both common characteristics in aerial powerline detection where appearance varies with lighting and viewing angles. The unchanged recall for vehicle, drone, tree, building, and animal’s classes suggest these well-represented categories have reached convergence under both configurations, while the lack of recall improvement for person, boat, airplane, and others indicates SGD struggles with scale variation and occlusion patterns typical of these objects in aerial imagery. The mAP50 and mAP(50–95) patterns mirror these trends, with boat and powerline consistently showing degraded performance under optimized hyperparameters, suggesting that SGD’s deterministic updates, even when optimized, cannot adequately balance learning across classes with disparate difficulty levels. This class-specific analysis reinforces that for heterogeneous aerial datasets with imbalanced class distributions and varying detection difficulties, adaptive optimizers (Adam) provide more robust performance than gradient-based methods (SGD), regardless of hyperparameter optimization efforts.

Computational time for Realm dataset

Figure 32 below the comparison between Adam and SGD for Realm dataset.

Fig. 32.

Efficiency comparison for Realm dataset between Adam and SGD.

Left side of the Fig. 32 show that Adam optimizer consumed 1255420.4 s whereas SGD consumed 1071784.4 s. This time includes both the low-fidelity and high-fidelity runs. This observation is in contrast to the VisDrone2019 dataset. Right side of the figure shows that both completed 16 high-fidelity runs. For Realm dataset SGD is 183,636 s faster than Adam optimizer.

Comparative analysis with alternative hyperparameter optimization methods

To rigorously validate the effectiveness of our proposed DE-MFO-BO method, we conducted a comprehensive comparative study against standalone Bayesian Optimization (BO), a well-established and widely adopted hyperparameter optimization technique in deep learning applications. This section presents a fair, controlled comparison using the REALM dataset, with both methods receiving identical computational budgets to ensure scientific validity.

Fair comparison methodology

A critical challenge when evaluating multi-fidelity methods is ensuring computational fairness. We adopted the equal high-fidelity evaluations criterion, where both methods receive exactly 20 high-fidelity evaluations representing the expensive computational resource that must be budgeted fairly. High-fidelity evaluations use 100 training epochs requiring approximately 200 min (3.3 h) each, while low-fidelity evaluations use 5 epochs requiring only 10 min. This 20:1 cost ratio means simply counting total evaluations without distinguishing fidelity levels produces unfair comparisons.

Our comparison protocol allocates resources as follows. Standalone Bayesian Optimization receives 20 high-fidelity evaluations: 10 for random initialization and 10 for Gaussian Process-based optimization using the Expected Improvement acquisition function. This represents a strong implementation of pure Bayesian Optimization without any multi-fidelity components or exploratory preprocessing. DE-MFO-BO receives the same 20 high-fidelity evaluations but strategically allocated across two optimization phases. The first phase employs approximately 44 low-fidelity evaluations for Differential Evolution exploration, organized as a population of 4 individuals evolved over 5 generations with adaptive mutation factor F ranging from 0.9 to 0.4 and crossover rate CR of 0.9. The second phase allocates 1 high-fidelity evaluation to validate the best DE solution and 19 high-fidelity evaluations for Bayesian Optimization refinement starting from this validated solution. The 44 low-fidelity evaluations represent additional computational overhead beyond the guaranteed high-fidelity budget that must be justified by performance improvements.

The key distinction between methods lies in initialization strategy. Standalone BO begins with 10 randomly distributed points that may miss promising regions of the hyperparameter space. DE-MFO-BO uses 44 cheap evaluations (220 total training epochs at 5 epochs each) to systematically explore the landscape through population-based evolution before committing any expensive high-fidelity budget. This exploration costs only 2.2 high-fidelity equivalent units (220 ÷ 100 = 2.2) but provides substantial guidance for the subsequent 20 high-fidelity evaluations, allowing them to focus on refinement in pre-identified promising regions rather than global exploration from random starting points.

Experimental setup and configuration

The experimental evaluation employs the REALM dataset for real-world environment object detection with YOLO11n architecture. Both methods optimize over an identical hyperparameter search space: learning rate in the range [1 × 10⁻⁴, 1 × 10⁻²], batch size as integers in^8,16, momentum in [0.85, 0.95], weight decay in [1 × 10⁻⁵, 1 × 10⁻³], and optimizer type selected from {SGD, Adam}. This five-dimensional mixed continuous-discrete space provides sufficient complexity to meaningfully differentiate optimization performance. Image resolution uses standard 640 × 640 pixels.

Results and performance analysis

Table 10 presents the comprehensive comparison results under equal high-fidelity budgets for both Adam and SGD optimizers, demonstrating consistent superiority of DE-MFO-BO across all performance metrics.

Table 10.

Fair performance comparison (equal HF budget = 20 evaluations).

Method	Best fitness	Precision	Recall	mAP(50–95)	HF Evals	LF Evals	Total time (s)
DE-MFO-BO (Adam)	0.6209	0.8268	0.6998	0.4559	20	44	257,009
Standalone-BO (Adam)	0.6029	0.8111	0.6806	0.4398	20	0	231,001
Improvement (Adam) %	+ 2.99	+ 1.94	+ 2.82	+ 3.66	Equal	-	+ 11.3
DE-MFO-BO (SGD)	0.6226	0.8165	0.7054	0.4596	20	44	254,686
Standalone-BO (SGD)	0.6079	0.8128	0.6931	0.4420	20	0	229,419
Improvement (SGD) %	+ 2.42	+ 0.46	+ 1.77	+ 3.98	Equal	-	+ 11.0

The results demonstrate clear and consistent DE-MFO-BO superiority. For the Adam optimizer, DE-MFO-BO achieves fitness of 0.6209 compared to Standalone-BO’s 0.6029, representing 2.99% improvement in the harmonic mean composite metric. This improvement is balanced across all three-component metrics: precision improves 1.94% from 0.8111 to 0.8268, recall improves 2.82% from 0.6806 to 0.6998, and mean Average Precision improves 3.66% from 0.4398 to 0.4559. The balanced improvement across metrics validates that the harmonic mean fitness function successfully drives optimization toward practical solutions rather than allowing single-metric dominance.

For the SGD optimizer, DE-MFO-BO achieves 0.6226 fitness compared to 0.6079 for Standalone-BO, a 2.42% improvement. The most compelling result is the 3.98% improvement in mAP from 0.4420 to 0.4596, representing the strongest single-metric gain across all experiments and demonstrating particular effectiveness for this critical detection quality metric. Recall shows 1.77% improvement from 0.6931 to 0.7054, while precision shows 0.46% improvement from 0.8128 to 0.8165. Interestingly, SGD achieves slightly higher overall fitness than Adam (0.6226 vs. 0.6209), suggesting that when properly optimized through DE-MFO-BO, traditional stochastic gradient descent can match or exceed adaptive optimizers for YOLO object detection. These performance metrics are also shown in Fig. 33.

Fig. 33.

Performance metrics comparison.

The consistency across two fundamentally different optimizers provides strong evidence for robustness and generalizability. Adam employs adaptive learning rates with momentum and bias correction, while SGD uses fixed momentum-based updates requiring more careful tuning. The fact that DE-MFO-BO outperforms Standalone-BO for both optimizer types indicates that the multi-fidelity strategy effectively navigates different optimization landscapes rather than being tuned for one specific gradient descent variant.

The computational overhead is modest and well-justified as shown in Table 10; Fig. 34. DE-MFO-BO requires 257,009 s (71.4 h) for Adam and 254,686 s (70.7 h) for SGD, compared to Standalone-BO’s 231,001 s (64.2 h) and 229,419 s (63.7 h) respectively, representing approximately 11% additional wall-clock time. This overhead corresponds to the 44 low-fidelity evaluations during the Differential Evolution phase, collectively representing 220 training epochs (44 evaluations × 5 epochs). When normalized by the total high-fidelity cost of 2,000 epochs (20 evaluations × 100 epochs), these 220 exploration epochs represent 11% additional computational investment. The return on investment is substantial: 2.71% average fitness improvement (mean of 2.99% and 2.42%) and 3.82% average mAP improvement (mean of 3.66% and 3.98%), yielding approximately 58 exploration epochs per 1% mAP improvement or equivalently about 3 h per 1% fitness improvement.

Fig. 34.

Computational time and total evaluations comparison.

Analysis and discussion

The superior performance of DE-MFO-BO validates the theoretical advantages of strategic multi-fidelity optimization. The fundamental difference lies in how methods initialize their search and allocate expensive computational resources. Standalone Bayesian Optimization begins with 10 randomly sampled initialization points. Some random samples may land in poor regions, requiring the method to expend precious high-fidelity evaluations discovering these areas are suboptimal. The subsequent 10 GP-based optimization iterations attempt to balance exploration and exploitation, but effectiveness depends critically on initial sample quality. If random initialization misses globally optimal regions, the limited budget of 10 refinement iterations may be insufficient to discover them.

DE-MFO-BO employs a fundamentally different strategy. The 44 low-fidelity evaluations systematically explore the hyperparameter landscape through population-based Differential Evolution before committing any high-fidelity budget. During 5 generations with population size 4, the DE algorithm evaluates diverse configurations at low cost, maintaining population diversity through mutation and crossover operations, handling multi-modal landscapes without local optima entrapment, and operating without gradient information making it suitable for discrete choices like optimizer selection. The adaptive mutation factor decreases from 0.9 to 0.4 across generations, balancing aggressive exploration early with focused exploitation later.

The critical insight enabling multi-fidelity optimization is rank-preservation across fidelity levels. A hyperparameter configuration performing well with 5 training epochs typically also performs well with 100 epochs, even though absolute performance values differ substantially. Poor configurations remain poor and excellent configurations remain excellent regardless of training duration. This property allows low-fidelity evaluations to identify approximate locations of optimal regions without expensive full-fidelity assessment of every candidate. The 44 evaluations at 5 epochs each effectively filter the hyperparameter space, discarding clearly poor regions and concentrating the population around promising areas.

When transitioning to high-fidelity, DE-MFO-BO possesses substantial knowledge that Standalone-BO lacks. The best solution found during DE exploration is validated with 1 high-fidelity evaluation, confirming that low-fidelity ranking correctly identified a genuinely good region. The remaining 19 high-fidelity evaluations are allocated to Bayesian Optimization starting from this validated solution. This warm-start initialization provides multiple advantages. The GP surrogate model begins learning about a region known to contain high-quality solutions rather than attempting to model both good and bad regions simultaneously. The Expected Improvement acquisition function can immediately balance local exploitation around the warm-start point with targeted exploration of nearby regions suggested by uncertainty estimates. The 19-iteration budget can be devoted entirely to refinement rather than wasted discovering that large portions of space are suboptimal.

This complementary combination leverages the respective strengths of Differential Evolution and Bayesian Optimization. DE excels at global exploration through population diversity, handles multi-modality effectively, and works with discrete choices without requiring differentiability or surrogate models. BO excels at local exploitation through probabilistic modelling, predicts performance in unexplored regions, and guides sequential sampling toward expected improvement. The multi-fidelity framework efficiently allocates these mechanisms: cheap DE for global exploration followed by expensive BO for local refinement, rather than attempting both global and local search at expensive high-fidelity throughout.

The practical significance of these improvements extends beyond numerical metrics. In object detection literature, mAP improvements of 2–4% typically require architectural modifications such as novel attention mechanisms, enhanced training procedures such as advanced augmentation strategies, additional training data, or increased model capacity. The proposed method achieves comparable improvements through optimization alone without modifying architecture, data, or model size. For production object detection systems, 3.8% mAP improvement translates to fewer false positives reducing unnecessary alerts or rejections, fewer false negatives improving detection recall for critical objects, and better localization accuracy across varying IoU thresholds. In autonomous vehicles, this could mean earlier pedestrian detection. In manufacturing quality control, fewer defects reaching customers. In medical imaging, improved abnormality detection rates. The 11% computational overhead (approximately 7 h in a 64-hour optimization run) is modest compared to the engineering effort required for alternative approaches to achieving similar performance gains.

This rigorous comparative analysis establishes that DE-MFO-BO significantly outperforms Standalone Bayesian Optimization under fair comparison conditions ensuring both methods receive identical high-fidelity evaluation budgets. With 20 high-fidelity evaluations allocated to each method, DE-MFO-BO achieves 2.71% average fitness improvement and 3.82% average mAP improvement with consistent gains across precision and recall metrics. These improvements are validated across both Adam and SGD optimizers, demonstrating robustness and broad applicability.

The performance advantages are obtained with only 11% additional computational time corresponding to 44 low-fidelity evaluations (220 exploration epochs), representing a highly favourable cost-benefit trade-off. The success validates our core hypothesis that strategic multi-fidelity optimization outperforms uniform high-fidelity search when budgets are properly controlled. By using cheap low-fidelity evaluations to systematically explore the hyperparameter landscape and identify promising regions before committing expensive high-fidelity budget to refinement, rather than relying on random initialization that may miss optimal areas, our method achieves superior configurations without simply benefiting from increased total computational resources. This work demonstrates that multi-fidelity optimization techniques, when properly designed with attention to fair comparison principles and rigorous experimental validation, provide genuine algorithmic value for hyperparameter tuning in object detection systems, offering practitioners a practical and effective approach for optimizing YOLO-based detectors with limited computational budgets.

Conclusions

The problem of hyperparameter optimization for both SGD and Adam optimizers in the context of aerial imagery has been addressed in this work. The standard VisDrone2019 dataset and the Realm dataset (our own aerial dataset) are used to demonstrate the effectiveness of the proposed approach. Differential Evolution (DE) and Bayesian Optimization (BO), guided by a multi-fidelity optimization strategy, are employed to allocate appropriate numbers of epochs for low- and high-fidelity evaluations, thereby structuring how long DE and BO run during the search.

In essence, the proposed method provides a fast and modular framework for hyperparameter tuning in YOLO, using a computationally cost-effective combination of DE and BO. It is well suited for integration into research pipelines where reproducibility and rigorous analysis are essential. The techniques incorporated multi-fidelity evaluation, adaptive search, and rigorous logging offer a practical template for tackling costly optimization problems in deep learning applications.

Empirically, we observe that the performance metrics improve for both Adam and SGD optimizers. Although the gains for SGD are relatively modest, the improvements for Adam are substantial, indicating that the overall mechanism is both efficient and robust. For the VisDrone2019 dataset, the largest improvement for Adam is in recall, with an increase of 18.42%, whereas for SGD the maximum gain is observed in precision, which improves by 5.07%. Similarly, for the Realm dataset, the largest improvement for Adam is in mAP(50–95), which increases by 20.96%, while SGD achieves its highest gain in precision, with an improvement of 2.78%.

Despite these promising results, several limitations should be acknowledged. First, the computational cost of the high-fidelity BO phase remains substantial, with training times ranging from 38,000 to 93,000 s per trial, which may constrain practical deployment in resource-limited environments. Second, although our methodology has been validated on two datasets (VisDrone2019 and Realm), broader evaluation across more diverse aerial imagery conditions and across YOLO architectures beyond YOLO11n would further strengthen claims of generalizability. Third, the relatively marginal improvements observed for SGD on some metrics suggest that the optimization landscape for gradient-based optimizers may be more challenging than for adaptive methods such as Adam. Finally, the fitness function, while effective in this study, relies on a harmonic-mean weighting of metrics that may not align with all application-specific preferences, particularly in scenarios where certain performance metrics are more critical than others.

To sum up, this research introduces several noteworthy contributions. To the best of our knowledge, the combined DE–MFO–BO optimization pipeline has not previously been applied in this manner for YOLO hyperparameter tuning, and systematic hyperparameter optimization for YOLO on the VisDrone2019 dataset has not been extensively documented in the literature. This work therefore lays an initial foundation for understanding the role and significance of hyperparameter optimization in aerial object detection using YOLO-based models.

Author contributions

M.U.G.: Methodology, Validation, Formal analysis, Writing-original draft, Visualization. P.R.: Conceptualization, Methodology, Validation, Resources, Writing-review and editing, Supervision, Project administration, Funding acquisition.

Funding

This research was funded by Universiti Sains Malaysia, Short-Term Grant with Project No: 304/PAERO/6315815.

Data availability

Data will be available on request.

Code availability

The code used in this study is publicly available on GitHub at https://github.com/uzairgill179/YOLO-Hyperparameter-Optimization and permanently archived on Zenodo (DOI: 10.5281/zenodo.19230431). The repository includes all scripts required to reproduce the hyperparameter optimization experiments reported in this manuscript.

Declarations

Competing interests

The authors declare no competing interests.