Metaheuristic algorithms can be broadly classified into four principal categories based on their source of inspiration: evolutionary-based, swarm-based, physics-based, and human-based algorithms [38], [39]. Each category encompasses multiple algorithms with distinct search mechanisms, parameter requirements, and computational characteristics that determine their suitability for specific AI optimization tasks. Table 1 presents a comprehensive taxonomic classification of the sixteen most widely applied metaheuristic algorithms in AI optimization contexts, along with their key parameters and typical application domains. continuous hyperparameter spaces [42].

tasks [43].

ineffective for global search [47].

Typical AI Application Weight initialization, HPO Feature selection, CNN optimization HPO, clustering optimization Feature selection, weight optimization HPO, ensemble learning

Evolutionary algorithms constitute the oldest and most extensively studied family of metaheuristic methods in AI optimization. The GA, proposed by Holland [20] and popularized by Goldberg [40], operates on a population of candidate solutions represented as chromosomes, applying biologically inspired operators— selection, crossover, and mutation—to evolve superior configurations over successive generations. In the context of NAS, each chromosome may encode an entire network architecture, with genes representing layer types, widths, kernel sizes, and connectivity patterns [41]. DE, introduced by Storn and Price [21], extends this paradigm with a distinctive mutation strategy that generates trial vectors by adding weighted differences between randomly selected population members to a third member, offering superior performance in

Swarm intelligence algorithms represent the largest and most rapidly growing family of metaheuristics applied to AI optimization. PSO, introduced by Kennedy and Eberhart [23], models a flock of particles navigating a search space, each adjusting its trajectory based on its personal best position and the global best position discovered by the swarm. The GWO, proposed by Mirjalili et al. [26], simulates the hierarchical leadership and hunting behavior of grey wolves, with alpha, beta, delta, and omega wolves guiding the search through encircling, hunting, and attacking phases. The WOA, also by Mirjalili and Lewis [27], mimics the bubble-net hunting strategy of humpback whales, combining shrinking encircling, spiral updating, and random search mechanisms. HHO, proposed by Heidari et al. [28], models the cooperative hunting behavior of Harris's hawks using surprise pounce and rapid dive strategies, demonstrating strong performance in feature selection

From a formal optimization perspective, AI model design and configuration can be cast as a general optimization problem: given a search space S defining the set of all possible configurations (architectures, hyperparameters, feature subsets), find the configuration x ∗ ∈ S that minimizes (or maximizes) an objective function f(x) measuring model performance on a validation dataset [44]. This formulation, while conceptually straightforward, is complicated by several characteristics that distinguish AI optimization from classical optimization problems. First, the search space is typically vast, combinatorial, and mixed-type—containing continuous variables (learning rate, weight decay), discrete variables (number of layers, neurons per layer), categorical variables (activation function type, optimizer choice), and conditional variables (parameters that exist only when certain architectural choices are made) [45]. Second, the objective function is stochastic, expensive to evaluate (each evaluation may require training a neural network for hours or days), and non-differentiable with respect to architectural and categorical decisions [46]. Third, the fitness landscape is highly multimodal, with numerous local optima separated by rugged terrain, making gradient-based optimization

The dimensionality of the search space varies dramatically across optimization tasks. HPO for a simple Support Vector Machine (SVM) may involve 3–5 continuous parameters, whereas NAS for a modern Convolutional Neural Network (CNN) can encompass 10² or more possible architectures when considering all layer-wise decisions [48]. Feature selection over a dataset with n features defines a binary search space of n 00

2 possible subsets, which exceeds 10³ for high-dimensional genomic datasets with 1,000 features [49]. These exponential search spaces render exhaustive enumeration infeasible and demand intelligent search strategies capable of efficiently identifying high-quality solutions without exploring more than a minuscule fraction of the total space [50].

The exploration–exploitation dilemma is a central challenge in applying metaheuristic algorithms to AI optimization [51]. Exploration refers to the broad sampling of diverse, potentially distant regions of the search space to discover promising basins of attraction, while exploitation focuses on intensifying the search around known good solutions to refine them toward local optima [52]. In the context of AI optimization, excessive exploration wastes valuable computational resources by evaluating many poor architectures or hyperparameter configurations, while premature exploitation can trap the search in suboptimal local minima, missing superior architectures or feature subsets that lie in unexplored regions [53].

The high dimensionality and rugged topology of AI search spaces exacerbate this trade-off. NAS landscapes, for example, exhibit complex interactions between layers—modifying a single layer's width can alter the optimal configuration of every subsequent layer—creating epistatic dependencies that frustrate local search strategies [54]. Metaheuristic algorithms address this challenge through diverse mechanisms: GA uses mutation rate adaptation to modulate exploration intensity, PSO employs inertia weight decay to transition from exploration to exploitation over iterations, and GWO uses a linearly decreasing control parameter a that governs the balance between encircling (exploitation) and random search (exploration) [26]. Recent advances include adaptive and self-adaptive parameter control strategies, where algorithm parameters are co-evolved alongside candidate solutions, enabling automatic adjustment of the exploration–exploitation balance based on search progress [55].

A critical practical consideration in metaheuristic-driven AI optimization is the computational cost of fitness evaluation. Unlike classical benchmark functions that can be evaluated in microseconds, evaluating a candidate AI model configuration typically requires training the model from scratch on a dataset, a process that may consume minutes (simple ML models on tabular data), hours (CNNs on Canadian Institute For Advanced Research-10 (CIFAR-10), or days (large models on ImageNet) [56]. A population-based metaheuristic with 50 individuals running for 100 generations requires 5,000 fitness evaluations; at 1 GPU-hour per evaluation, this amounts to approximately 208 GPU-days—a computational budget that exceeds the resources available to most research groups [57]. This constraint has motivated several computational cost-reduction strategies, including early stopping of unpromising candidates, weight sharing across architectures, surrogate-assisted optimization using cheap approximation models, and transfer learning from smaller proxy tasks [58], [59]. These strategies have reduced the computational cost of metaheuristic-based NAS from thousands of GPU-days (as in early work by Zoph and Le [10]) to single-digit Graphics Processing Unit (GPU)-days in recent approaches, making the methodology accessible to a broader research community [60], [61].

NAS represents perhaps the most ambitious and computationally demanding application of metaheuristic algorithms in AI, aiming to automate the discovery of optimal network topologies that match or exceed human-designed architectures [10], [11]. The pioneering work of Zoph and Le [10] demonstrated that RL could discover competitive architectures on CIFAR-10, but required 800 GPU-days of computation—a cost that motivated researchers to explore population-based metaheuristic alternatives capable of achieving comparable quality at significantly reduced computational expense [60].

Evolutionary NAS: GAs have been extensively applied to CNN architecture search, with each chromosome encoding a complete architecture specification. Real et al. [63] proposed AmoebaNet, an evolutionary NAS approach that discovered architectures achieving 96.66% accuracy on CIFAR-10 with 3.2 million parameters, demonstrating that evolutionary methods could match RL-based NAS while providing greater diversity in discovered architectures. Sun et al. [64] developed an Evolutionary Convolutional Neural Network (EvoCNN) framework using a variable-length genetic encoding scheme that simultaneously optimized network depth, layer widths, kernel sizes, and skip connections, achieving 96.37% on CIFAR-10 with only 2.0 GPU-days of search cost. Liu et al. [65] introduced hierarchical evolution for architecture search, discovering cells that could be stacked to form networks of varying depth, achieving 97.14% accuracy on CIFAR-10.

Swarm-based NAS: PSO has been adapted for NAS by encoding network architectures as particle positions in a mixed continuous–discrete search space. Junior and Yen [66] proposed PSO-NAS, achieving 96.98% on CIFAR-10 with a search cost of 1.5 GPU-days by employing a discrete velocity update mechanism for categorical architectural parameters. The WOA has been applied to transformer architecture search by Brodzicki et al. [67], optimizing attention head count, embedding dimensions, feed-forward widths, and depth simultaneously, achieving competitive performance on language modeling tasks. Singh et al. [68] employed GWO for Recurrent Neural Network (RNN)/Long Short-Term Memory (LSTM) architecture optimization, discovering structures that reduced training time by 35% while maintaining comparable sequence modeling accuracy.

Hybrid and surrogate-assisted NAS: to address the prohibitive computational cost of evaluating candidate architectures, several studies have combined metaheuristic search with surrogate models that predict architecture performance without full training [59], [69]. Lu et al. [70] combined GA with a Graph Neural Network (GNN) surrogate, reducing the required number of full training evaluations by 80% while maintaining search quality. DE with surrogate assistance has been shown to discover competitive CNN architectures on CIFAR-100 in less than 0.5 GPU-days [71]. Table 3 presents a comparative summary of metaheuristic NAS approaches.

The results in Table 3 reveal several key findings. First, surrogate-assisted methods (GA + GNN Surrogate, DE-NAS) achieve the greatest computational cost reductions while maintaining competitive accuracy, reducing search cost by over 99.9% compared to the original NASNet approach. Second, swarm-based methods (PSO-NAS, HHO-CNN, MPA-NAS) generally achieve lower search costs than pure evolutionary methods due to their more directed search behavior. Third, the performance gap between metaheuristic-discovered architectures and human-designed networks has narrowed substantially, with the best metaheuristic approaches achieving accuracy within 0.5% of state-of-the-art manually designed architectures.

HPO addresses the challenge of selecting optimal values for the configuration parameters that govern the training process and structural decisions of ML models [12], [13]. Unlike model weights, which are learned through gradient-based training, hyperparameters must be set before training and profoundly influence model performance, convergence speed, and generalization capability. The hyperparameter space for a modern DL model may include continuous variables (learning rate: 10⁻⁶ to 1; weight decay: 10⁻⁶ to 10⁻¹), discrete variables (number of layers: 1 to 100; batch size: 8, 16, 32, 64, 128, 256), and categorical variables (optimizer: Stochastic Gradient Descent (SGD), Adaptive Moment Estimation (Adam), Adaptive Gradient Algorithm )AdaGrad), Root Mean Square Propagation (RMSProp); activation: Rectified Linear Unit (ReLU), Exponential Linear Unit (ELU), Gaussian Error Linear Unit (GELU), Swish) [74].

Metaheuristic algorithms have been applied to HPO across the full spectrum of ML models, from classical algorithms (SVM, Random Forests (RFs), gradient boosting) to DNNs (CNNs, RNNs, transformers). PSO-based HPO is particularly popular due to its natural handling of continuous search spaces and rapid convergence properties. Lorenzo et al. [75] applied PSO to simultaneously optimize SVM kernel parameters (C, γ) and feature subsets, achieving classification accuracy improvements of 3.2–5.8% over grid search on multiple UCI datasets. GA-based HPO has been applied to RF optimization, tuning the number of trees, maximum depth, minimum samples per split, and feature sampling ratio, with improvements of 2.1–4.3% over default configurations [76]. Table 4 presents a comprehensive comparison of metaheuristic HPO results across algorithms and datasets.

Several important observations emerge from the HPO results. First, the magnitude of improvement from metaheuristic HPO is inversely related to model complexity and dataset difficulty; simple models on small datasets (SVM on UCI datasets) show improvements of 3–5%, while complex DL models on larger datasets (ResNet on CIFAR-100) show more modest but still significant improvements of 2–3%. This pattern reflects the fact that DL models have more hyperparameters and more complex interactions between them, requiring more evaluations to achieve substantial gains [85]. Second, computational cost scales dramatically with model training time—HPO for SVM requires less than 1 hour, while HPO for deep CNNs on CIFAR-100 requires over 50 hours even with modest population sizes [86]. Third, among the algorithms tested, DE and PSO consistently demonstrate the best trade-off between solution quality and computational efficiency for continuous hyperparameter spaces, while GA excels when the search space includes many categorical variables [87].

Feature selection—the process of identifying the most informative subset of input variables from a potentially large set of candidates—is a fundamental preprocessing step that directly impacts model accuracy, training efficiency, and interpretability [14], [15]. From an optimization perspective, feature selection is a combinatorial problem; given n features, the goal is to find the subset of size k ≤ n that maximizes classification or regression performance while minimizing subset size [88]. Metaheuristic algorithms are naturally suited to this problem because they can efficiently explore the 2 possible subsets without exhaustive enumeration, and they can simultaneously optimize the classifier parameters alongside the feature subset in a wrapper-based framework [89], [90].

The wrapper-based approach, in which a metaheuristic algorithm guides feature subset selection while a classifier serves as the fitness evaluator, has become the dominant paradigm for metaheuristic feature selection [91]. In this framework, each candidate solution (individual, particle, wolf) represents a binary vector of length n, where 1 indicates feature inclusion and 0 indicates exclusion. The fitness function typically combines classification accuracy with a penalty for the number of selected features: f(x) = α · Accuracy(x) + (1 − α) · (1 − |S|/n), where S is the selected feature subset and α controls the trade-off between accuracy and dimensionality reduction [92]. GWO, WOA, and HHO have proven particularly effective for binary feature selection due to their strong exploration capabilities and ability to escape local optima in high-dimensional binary spaces [78], [92]. Table 5 summarizes representative feature selection results.

The results in Table 5 demonstrate several consistent findings across the reviewed studies. First, metaheuristic feature selection consistently improves classification accuracy compared to using all features, with improvements ranging from 5.8% (Sonar) to 15.5% (Madelon). This counterintuitive result—that using fewer features yields higher accuracy—reflects the removal of noisy, redundant, and irrelevant features that introduce variance and degrade generalization [101]. Second, the feature reduction ratios are remarkably high, particularly for high-dimensional datasets; genomic datasets (Lung Cancer, Leukemia, Colon Cancer) with thousands of features are reduced to fewer than 130 selected features (>97% reduction) while simultaneously improving accuracy by 8–13 percentage points. Third, recent algorithms (HHO, MPA) tend to outperform classical methods (GA, PSO) on high-dimensional datasets, likely due to their superior balance of exploration and exploitation mechanisms [102].

Beyond binary feature selection, metaheuristic algorithms have been applied to feature construction—the automated creation of new features through mathematical transformations of existing ones. GP-based feature construction generates composite features using arithmetic, trigonometric, and logical operators, discovering discriminative feature combinations that are not present in the original feature space [103]. Recent work by Tran et al. [104] demonstrated that PSO-based feature construction improved CNN classification accuracy by 2.4% on texture recognition tasks by generating informative hand-crafted features that complemented learned representations.

While gradient-based optimizers (SGD, Adam, AdaGrad) dominate neural network training, metaheuristic algorithms offer complementary capabilities for specific training challenges, including weight initialization, learning rate scheduling, and loss function optimization [105]. The weight initialization problem—setting initial values for millions of network parameters before gradient-based training begins—significantly influences convergence speed and the quality of the final solution [16]. Poor initialization can lead to vanishing or exploding gradients, convergence to suboptimal local minima, or failure to converge entirely. Metaheuristic algorithms can search for initialization points that lead to faster convergence and better final accuracy by evaluating the training trajectory from different starting points [106].

Several studies have applied metaheuristic algorithms to optimize learning rate schedules—the function governing how the learning rate changes over the course of training. Rather than using fixed schedules (step decay, cosine annealing), metaheuristic approaches search over the space of possible schedules, discovering novel patterns tailored to specific dataset–architecture combinations [107]. DE-based learning rate schedule optimization has been shown to reduce training loss by 8–15% compared to standard cosine annealing across multiple architectures [108]. Table 6 presents comparative results for metaheuristic training optimization.

The training optimization results indicate that metaheuristic approaches provide meaningful but modest improvements over well-tuned gradient-based optimizers. The primary benefits are observed in convergence speed (15%–28% faster convergence to target accuracy) and training loss reduction (8%–15%), rather than dramatic accuracy improvements. This is expected, as gradient-based methods are highly effective for the smooth, differentiable portions of the training optimization landscape, and metaheuristics primarily contribute by finding better initialization points or learning rate trajectories that guide the gradient-based optimizer toward superior basins of attraction [113].

Ensemble learning—the combination of multiple base models to produce a single, more accurate prediction—presents several optimization challenges naturally suited to metaheuristic solution: 1) selecting which base models to include in the ensemble, 2) determining the optimal weighting of each model's contribution, and 3) designing the ensemble architecture (bagging, boosting, stacking configurations) [19], [114]. Metaheuristic algorithms can simultaneously optimize all three aspects, searching for ensembles that maximize diversity among base models while minimizing prediction error on validation data [115].

GA-based ensemble optimization has been applied to select optimal subsets of base classifiers from large pools of candidates. Rather than including all trained models, GA searches for the subset whose combined predictions achieve the highest accuracy, exploiting complementary error patterns across models [116]. PSO has been used to optimize the continuous weights assigned to each base model in weighted voting ensembles, discovering non-uniform weight distributions that outperform simple averaging by 1.5%–3.2% across multiple benchmark datasets [117]. DE has been applied to optimize stacking architectures, simultaneously selecting base learners, their hyperparameters, and the meta-learner configuration [118]. Table 7 summarizes ensemble optimization results.

The ensemble optimization results consistently demonstrate that metaheuristic-optimized ensembles outperform both individual models and heuristically constructed ensembles. The improvements range from 1.65% (on the already high-performing Segment dataset) to 5.22% (on the more challenging Liver dataset), with larger gains observed on datasets where individual models exhibit greater diversity in error patterns. The selective ensemble approach, where GA identifies the optimal subset of models to include, is particularly effective at eliminating weak or redundant models that would otherwise degrade ensemble performance through negative transfer [116].

The intersection of metaheuristic optimization and RL has produced a growing body of work addressing policy optimization, reward shaping, and environment design through population-based ES [37], [122]. Neuroevolution—the application of evolutionary algorithms to optimize neural network architectures and weights for RL agents—has demonstrated competitive performance with gradient-based RL methods, particularly in environments with sparse rewards, deceptive gradients, or large action spaces where policy gradient methods struggle [123].

Salimans et al. [124] demonstrated that ES could achieve performance competitive with state-of-the-art RL algorithms on Atari games and MuJoCo locomotion tasks, with the advantage of linear scalability across hundreds of CPUs and no need for backpropagation through time. Such et al. [109] further showed that simple GAs applied to evolve neural network weights could match the performance of deep RL methods on several Atari games, challenging the assumption that gradient information is necessary for effective policy optimization. More recently, Covariance Matrix Adaptation Evolution Strategy (CMA-ES) has been applied to optimize reward shaping functions, automatically discovering auxiliary reward signals that accelerate RL training by 40%–60% in sparse-reward environments [125]. Population-Based Training (PBT), introduced by Jaderberg et al. [126], combines evolutionary selection with gradient-based training by maintaining a population of agents whose hyperparameters (learning rate, entropy regularization, discount factor) are mutated and selected based on performance, effectively performing online HPO for RL agents.

To systematically assess the relative effectiveness of different metaheuristic algorithms across AI optimization tasks, we synthesized results from the reviewed studies using standardized comparison metrics. For each AI task–dataset combination, we identified the best-performing and second-best-performing metaheuristic algorithm, computed the performance gap, and assessed statistical significance using reported p-values from Wilcoxon signed-rank tests or Friedman tests [127]. Table 8 presents the cross-domain benchmarking results. The cross-domain analysis reveals several algorithm-specific strengths. GA and DE dominate NAS tasks, likely due to their effective handling of discrete, variable-length representations and their ability to maintain population diversity across complex architectural search spaces. PSO and DE excel in continuous HPO tasks, benefiting from their efficient traversal of smooth, continuous hyperparameter landscapes. For feature selection, GWO dominates low-dimensional problems while HHO shows superior performance on high-dimensional datasets—a finding consistent with HHO's progressive transition from exploration to exploitation that is well-suited for navigating vast binary search spaces [28]. Notably, the performance gaps between the best and second-best algorithms are generally modest (0.28–1.24%), and statistical significance is not always achieved (p > 0.05 for transformer NAS and weight initialization), suggesting that algorithm selection is less critical than careful implementation and parameter tuning [128].

A central question in the AI optimization literature is whether metaheuristic algorithms offer genuine advantages over simpler alternatives, particularly random search [34] and BO [35]. Bergstra and Bengio [34] demonstrated that random search is surprisingly competitive for HPO due to the low effective dimensionality of many hyperparameter spaces, while BO, leveraging GP surrogates, achieves superior sample efficiency on low-dimensional problems [129]. We synthesized comparative results from 42 studies that included both metaheuristic and non-metaheuristic baselines. Table 9 presents the aggregated comparison.

The aggregated comparison reveals a performance hierarchy that varies by task complexity. For NAS—the most complex and high-dimensional task—metaheuristic algorithms achieve the highest accuracy (97.08%), outperforming BO by approximately 0.8–0.9 percentage points. This advantage is attributed to the population-based nature of metaheuristics, which enables parallel exploration of diverse architectural regions, and their ability to handle the mixed-type, conditional search spaces characteristic of NAS without requiring differentiability or surrogate approximations [45]. For HPO, the advantage of metaheuristics over BO narrows to 0.4–0.7 percentage points, reflecting the effectiveness of GP surrogates for the lower-dimensional, predominantly continuous hyperparameter spaces [130]. For feature selection, metaheuristics demonstrate the largest advantage (4.6–5.4 percentage points over BO), as the binary, combinatorial nature of feature selection is poorly suited to the continuous surrogate models underlying BO [131].

Hybrid approaches combining metaheuristic search with surrogate models achieve the best overall performance across all tasks while simultaneously reducing the number of required evaluations by approximately 49% compared to standalone metaheuristics. This finding suggests that the most effective strategy is not to choose between metaheuristics and BO, but to integrate them in complementary roles— using the surrogate model to cheaply pre-screen candidate solutions and the metaheuristic to guide the global search strategy [132].

The combination of metaheuristic algorithms with specific AI models has produced a class of hybrid approaches that leverage the strengths of both components synergistically. These hybrids typically use the metaheuristic to optimize the AI model's architecture or hyperparameters while the AI model serves as the fitness evaluator or, in some cases, as a surrogate for fitness estimation. Table 10 summarizes representative hybrid approaches and their reported performance improvements.

The hybrid approaches consistently demonstrate both accuracy improvements (1.64–4.56%) and computation reductions (38–61%) compared to default configurations or manual tuning. The largest accuracy improvements are observed for classical ML models (GWO-SVM: +4.56%) where the hyperparameter space is relatively small but the sensitivity to parameter settings is high. Computation reductions are most pronounced for hybrid approaches that incorporate early stopping and surrogate-assisted evaluation, preventing the waste of resources on unpromising configurations [138].

To rigorously assess the statistical significance of performance differences among metaheuristic algorithms across AI tasks, we employed the Friedman test followed by Nemenyi post-hoc analysis, following the methodology recommended by Demšar [127] for comparing multiple classifiers over multiple datasets. The Friedman test rejected the null hypothesis of equal algorithm performance across all tasks (χ² = 47.83, p < 0.001, df = 9), confirming significant differences among the tested algorithms.

The Nemenyi post-hoc analysis with a Critical Difference (CD) of 2.14 at α = 0.05 revealed that: 1) DE and GA are statistically tied for overall best performance (average ranks of 2.31 and 2.48, respectively) and both significantly outperform random search (rank 8.67), 2) PSO (rank 3.12) and GWO (rank 3.45) form a second tier that is not significantly different from the top tier but significantly outperforms SA (rank 6.83) and BA (rank 7.14), and 3) recently proposed algorithms (HHO, MPA, SSA) achieve intermediate ranks (4.21–5.38) that are not significantly different from either the top or bottom tiers, suggesting that their advantages are task-specific rather than universal. These findings caution against claims of universal superiority for any single metaheuristic algorithm and support the recommendation that algorithm selection should be guided by task characteristics—problem dimensionality, variable types, evaluation cost, and time budget [128], [139].