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There is no published, controlled four-way test showing that Harris Hawks Optimization (HHO) beats grid search, random search, or Bayesian optimization for the exact CNN–random-forest tuning problem. HHO is a population-based metaheuristic with promising applications in machine-learning tuning, but available studies use different models, datasets, objectives, and validation schemes. Their scores cannot be converted into a universal ranking.
The defensible way to choose among the four methods is to run a matched experiment: identical data partitions, preprocessing, model pipeline, search space, completed-trial budget, and validation objective. Report both predictive quality and the cost and variability required to obtain it.
What can be concluded about the four-way comparison
Harris Hawks Optimization models cooperative pursuit and surprise-pounce behavior among hawks. Ali Asghar Heidari and coauthors introduced it in 2019 and evaluated it on mathematical benchmark functions and engineering problems. That work establishes the algorithm’s design and its original test scope, not a victory over conventional hyperparameter search for a CNN followed by a random forest.
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Grid, random, Bayesian, and HHO searches make different assumptions about how to spend evaluations. A method that wins on one objective and budget can lose when the dataset, metric, parameter types, or evaluation time changes. The available publications therefore support a comparison framework, not a winner’s table for this exact title.
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- A 2026 Scientific Reports study used a hybrid Aquila Optimizer–HHO method to tune a CNN for brain-MRI tumor classification. Its reported 77.85-second computation time and 87.34% accuracy, precision, recall, and F1-score belong to that hybrid, dataset, and protocol.
- A 2025 PeerJ Computer Science paper applied a modified HHO to XGBoost and a hybrid CnnSVM cybersecurity workflow. It used a 70% training, 10% validation, and 20% test split and reported five-fold cross-validation in its protocol.
- A 2022 HHO survey covers CNN tuning and random-forest optimization as separate application areas, rather than a combined CNN–random-forest benchmark.
- Bergstra and Bengio’s 2012 analysis explains why random search can use a finite budget efficiently when only a subset of hyperparameters strongly affects performance.
- Turner and colleagues’ 2021 analysis of the NeurIPS 2020 Black-Box Optimization Challenge compares Bayesian optimization and random search on benchmark tasks. Its results are not a universal ranking and do not include the exact HHO/CNN–random-forest setup.
No directly matching controlled comparison was located. Treat that absence as an evidence boundary: do not substitute scores from unrelated medical-imaging or cybersecurity tasks.
What each search strategy actually does
Harris Hawks Optimization
HHO maintains a population of candidate solutions and updates them through exploration and exploitation behaviors inspired by hawks surrounding, chasing, and surprise-pouncing on prey. Each candidate is a complete assignment of the parameters you expose, and its fitness is the score returned by your CNN–random-forest evaluation pipeline.
The original paper’s often-quoted description is that HHO is inspired by “the cooperative behavior and chasing style of Harris’ hawks in nature called surprise pounce.” The same paper notes that metaheuristics can be sensitive to user-defined parameters. In practice, you must specify population size, stopping conditions, random seed, constraint handling, and how categorical, integer, and continuous values are represented. Those choices are part of the method’s reproducibility burden.
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HHO is attractive when the objective is noisy, discontinuous, mixed-type, or difficult to model with a smooth surrogate. It is still a stochastic optimizer: one run can find a different region from another, and a larger population or more iterations increases model-training cost.
Grid search
Grid search enumerates every combination in a predefined Cartesian product. It is deterministic once the grid and evaluation order are fixed, easy to audit, and useful when only a few parameters have a small number of scientifically justified values.
Its cost grows multiplicatively. A grid with five values for each of six parameters requires 15,625 combinations before cross-validation or repeated seeds. If most parameters have little influence, many of those evaluations contribute little information. A grid also misses values between the chosen points unless you refine it with another grid.
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Random search
Random search samples configurations from specified distributions until the evaluation budget is exhausted. Continuous ranges can be explored without manually listing every value, and each new trial is independent of earlier scores.
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Bayesian optimization
Bayesian optimization builds a surrogate model of the objective from completed trials, chooses the next configuration with an acquisition rule, evaluates it, and updates the surrogate. This sequential feedback can reduce wasted evaluations when each CNN training run is expensive.
It also introduces modeling decisions: surrogate type, acquisition function, initialization trials, treatment of categorical variables, noise assumptions, and handling of failed runs. Turner and colleagues’ 2021 Black-Box Optimization Challenge analysis found benchmark-specific differences between Bayesian optimization and random search; those findings motivate including both methods, but they do not establish a result for HHO or for a CNN–random-forest pipeline.
| Method | How the next configuration is selected | Strengths | Costs and failure modes |
|---|---|---|---|
| Grid | All combinations in a fixed Cartesian set | Transparent, repeatable, simple to parallelize | Combinatorial growth; wastes trials on unimportant dimensions; resolution is limited to the grid |
| Random | Independent samples from declared distributions | Strong finite-budget baseline; handles mixed spaces with straightforward sampling | Does not learn from earlier trials; results depend on bounds, distributions, and seed |
| Bayesian | Surrogate and acquisition function select promising or informative trials | Can exploit feedback when evaluations are costly; supports adaptive allocation | Surrogate and acquisition choices add complexity; poor modeling of noisy or categorical spaces can mislead selection |
| HHO | Population updates based on exploration and exploitation rules | Derivative-free search for irregular, noisy, and mixed objectives; naturally explores multiple candidates | Stochastic variation, population and control parameters, constraint handling, and no universal guarantee of superiority |
Clarify what “CNN–random-forest tuning” means
The phrase can describe two different experiments, and the distinction changes the search space.
CNN feature extractor followed by a random forest
In a two-stage pipeline, the CNN produces embeddings or class probabilities and the random forest consumes those features. CNN parameters may include architecture choices, learning rate, batch size, augmentation, optimizer, training epochs, and layer-freezing decisions. Random-forest parameters may include tree count, maximum depth, feature-sampling strategy, minimum samples for a split or leaf, and class-weight policy.
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You must state whether the CNN is pretrained or trained from scratch, whether its weights are frozen while the forest is tuned, and whether the optimizer proposes both stages jointly. Joint tuning gives one candidate control over the entire pipeline but makes each evaluation expensive and can create interactions between embedding quality and forest capacity. Staged tuning is cheaper but can lock in a suboptimal representation.
CNN and random forest as competing model families
In a model-selection study, a CNN and a random forest are alternative predictors rather than sequential components. The optimizer then needs a conditional search space: CNN-specific parameters are active only for CNN trials, and forest-specific parameters only for forest trials. Reporting an average score without identifying the active branch obscures how the budget was spent.
Before comparing HHO with the other methods, publish a diagram or precise pipeline description. Otherwise, a result for a CNN classifier, a forest on tabular features, and a CNN-plus-forest stack can be mistaken for the same task.
What the adjacent publications show
Hybrid AO–HHO CNN study in 2026
Manoj Kumar and colleagues reported a hybrid Aquila Optimizer–Harris Hawks Optimization framework for CNN hyperparameter tuning in brain-MRI tumor classification in Scientific Reports, published 9 March 2026. In that experiment, the paper reports 77.85 seconds of computation time and 87.34% for accuracy, precision, recall, and F1-score.
Those figures are bounded by the study’s medical-imaging dataset, CNN design, metric definitions, hardware and implementation, and hybrid algorithm. They are not standalone-HHO measurements, random-forest results, or evidence from a four-way comparison with grid, random, and Bayesian search. A fair article can cite this as an example of HHO-related CNN tuning, but must not present 87.34% as a general HHO accuracy.
Modified HHO for cybersecurity models in 2025
A 2025 PeerJ Computer Science article used a modified HHO to tune XGBoost and a hybrid CnnSVM system for cyber-threat detection. Its reported protocol describes 70% of data for training, 10% for validation, and 20% for testing, together with five-fold cross-validation.
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This is useful as a reporting model: identify the model family, data split, validation procedure, and objective instead of publishing an unexplained score. It does not transfer a performance number to a CNN–random-forest task, and it does not compare HHO with all three conventional search strategies.
Survey coverage in 2022
The 2022 “Harris Hawk Optimization: A Survey on Variants and Applications” reviews variants and applications that include CNN hyperparameter tuning and random-forest optimization in separate contexts. Its breadth supports the claim that HHO has been tried across machine-learning workflows. It does not supply a controlled experiment in which one HHO implementation tunes a CNN–random-forest pipeline against grid, random, and Bayesian methods on the same data.
General evidence for random and Bayesian baselines
The 2012 JMLR paper by Bergstra and Bengio is the appropriate foundation for the finite-budget random-search baseline. The 2021 analysis by Turner and colleagues is a reason to include Bayesian optimization and to report benchmark conditions carefully. Neither source resolves the title’s specific comparison because neither evaluates the same pipeline, search space, and validation design.
How to run a defensible four-way experiment
The following protocol makes the methods comparable without assuming that one will win.
- Freeze the task definition. State whether the system is a CNN feature extractor plus random forest or a competition between the two model families. Define the prediction target, allowable preprocessing, class-weight policy, and primary metric before any tuning run.
- Lock data partitions. Create train, validation, and test partitions once, using stratification or grouped splitting when the data require it. Fit normalization, feature selection, and augmentation statistics only on the training portion. Do not let the test set influence search decisions.
- Write one evaluator. Every method must call the same function, which receives a configuration, builds the pipeline, trains it, calculates the validation objective, records elapsed wall-clock time, and returns a clearly defined failure value for invalid configurations. The evaluator should log software versions, hardware, seed, memory use, and early-stopping behavior.
- Declare the search space in advance. Mark each variable as categorical, integer, or continuous and publish its bounds or probability distribution. For example, a CNN learning rate might be sampled on a logarithmic scale, while tree count is an integer and activation is categorical. These are illustrative design choices; the important requirement is that all four methods receive the identical domain.
- Encode conditional parameters consistently. If a forest is used only after a CNN, expose both stages in every joint trial. If models are alternatives, define inactive parameters explicitly so that HHO, Bayesian optimization, and random search do not receive an unfair representation advantage.
- Equalize completed evaluations. Give every strategy the same number of completed model evaluations, not merely the same nominal number of iterations. A grid may exhaust its combinations, while HHO may use a population multiplied by iterations and Bayesian optimization may include startup trials. Report the exact accounting.
- Separate search validation from final testing. Use the validation score to select configurations. After selection, retrain the chosen configuration according to a predeclared rule and evaluate it once on the untouched test set. Repeatedly checking the test score turns it into another tuning set.
- Repeat stochastic methods. Run HHO, random search, Bayesian optimization, and any stochastic training procedure with multiple independent seeds. Keep the data partitions fixed while varying seeds, and report the median, mean, spread, and best result. A single lucky run is not a method comparison.
- Measure quality and resource use together. Record validation and test metrics, wall-clock time, accelerator or CPU time, peak memory where relevant, number of failed trials, and total training runs. A one-point gain that requires several times the compute is a different engineering choice from a similarly accurate method.
- Publish the complete trial history. Include configuration, objective, seed, duration, status, and failure reason for every trial. Curves of best-so-far score against evaluations and elapsed time reveal whether a method finds good settings early or only wins after a long search.
How to interpret the results
Compare at equal evaluation counts
Plot each method’s best validation score after 1, 2, and subsequent completed evaluations. This answers a practical question: which strategy gives useful models early? Also plot score against wall-clock time because CNN training durations can vary with architecture, input resolution, and hardware.
Report typical performance, not only the champion
For each method, give the distribution across independent seeds. Include a central estimate and a spread, such as median and interquartile range, alongside the single best run. If differences overlap substantially, describe them as inconclusive rather than declaring a winner.
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Account for failed and invalid trials
Out-of-memory errors, illegal parameter combinations, and unstable training are part of operational cost. List their counts and causes. Silently dropping failures can make a method appear more efficient, while assigning an arbitrary excellent score can distort the ranking.
Use a predeclared decision rule
Decide in advance whether the preferred method maximizes a metric subject to a time limit, minimizes time subject to a quality threshold, or uses a multi-objective trade-off. This prevents selecting the rule after seeing which method benefits from it.
When each method is a sensible choice
Choose grid search for a small, trusted space
Grid search is appropriate when domain knowledge limits the space to a few high-value settings, reproducibility and auditability matter, and the total combination count fits the compute budget. It is a poor default for many continuous CNN parameters or a large joint CNN–forest space.
Choose random search as the baseline you should not skip
Random search is easy to implement, parallelize, and reproduce from a seed. Use distributions that reflect the parameter scale instead of sampling a learning rate uniformly in its raw value. Its performance is informative only when the same bounds and evaluation budget are offered to the other methods.
Choose Bayesian optimization when evaluations are expensive
Bayesian optimization is appealing when each completed pipeline run is costly and observations are informative enough for a surrogate to learn. Validate that the chosen implementation supports your categorical and conditional variables, handles noisy validation scores, and does not spend most of the budget on surrogate overhead or failed proposals.
Choose HHO for an explicit metaheuristic experiment
HHO is worth testing when you need derivative-free population search over an irregular or noisy objective and can afford repeated stochastic runs. Document its population, control parameters, stopping rule, constraint repair, and encoding. A hybrid AO–HHO result cannot be used to claim that standalone HHO will outperform the baselines.
Common comparison mistakes and their fixes
- Unequal budgets: Counting one HHO iteration as one trial while counting each grid combination hides the true cost. Compare completed evaluations and report total compute.
- Validation leakage: Selecting settings on the test set produces an optimistic estimate. Keep the test partition untouched until the final locked evaluation.
- Confusing hybrid and standalone algorithms: Label AO–HHO, modified HHO, and plain HHO separately. Their operators and tuning burdens differ.
- Transferring scores across datasets: The 87.34% result belongs to a 2026 brain-MRI hybrid CNN experiment; cybersecurity XGBoost/CnnSVM scores belong to a different 2025 protocol. Neither predicts a forest or a combined pipeline’s score.
- Ignoring training randomness: CNN initialization, minibatch order, augmentation, and forest bootstrap sampling can change the objective. Use repeated seeds and disclose them.
- Reporting only the best run: A champion configuration without its typical result and cost is not enough to choose an optimizer.
- Changing the evaluator between methods: Different preprocessing, early stopping, folds, or hardware allocation invalidates the comparison. Keep the pipeline identical.
- Overlooking conditional spaces: Treating inactive CNN and forest parameters as if they applied to every trial can unfairly help or hurt a search strategy. Encode the branches explicitly.
Minimum reproducibility checklist
| Item | What to record |
|---|---|
| Data | Dataset identity, geographic or institutional scope where relevant, partition method, class balance, and preprocessing fit rules |
| Pipeline | CNN architecture or feature source, forest configuration, training schedule, frozen or trainable stages, and conditional branches |
| Search space | Parameter names, types, bounds or distributions, categorical encoding, invalid-combination rules, and constraint repair |
| Optimizer settings | Grid resolution, random seed and distributions, Bayesian surrogate/acquisition and startup trials, HHO population and stopping settings |
| Budget | Completed evaluations, parallel workers, retries, failed trials, wall-clock duration, and hardware |
| Validation | Primary and secondary metrics, folds or fixed split, early stopping, and test-set lock |
| Uncertainty | Independent seeds, central estimates, spread, confidence intervals or paired tests where appropriate |
| Artifacts | Trial-level log, selected configurations, source-code version, environment, and final test predictions |
Bottom line for a CNN–random-forest project
Use random search as a transparent baseline, add Bayesian optimization when model evaluations are expensive, retain grid search when the space is genuinely small, and evaluate HHO as a stochastic metaheuristic rather than assuming it is superior. The available publications demonstrate that HHO and HHO hybrids are used in machine-learning tuning, but they do not establish a winner for this exact CNN–random-forest comparison. Only a matched, repeated, budget-controlled experiment can answer which method is best for your data and objective.
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