A useful classification records both the update mechanism and the biological representation. Table 1 provides a descriptive taxonomy of familiar algorithm names and potential application contexts. Its listed examples are schematic associations, not a measured prevalence distribution or evidence that every listed application has been demonstrated by the originating algorithm paper.

Swarm flocking and fish schooling estimation, neural network Optimization training Ant Colony ACO Swarm Intelligence 1996 Pheromone trail-following in MSA, DNA motif finding, Optimization ant colonies pathway analysis Differential DE Evolutionary 1997 Differential mutation of ODE parameter estimation, Evolution vector populations energy minimization, systems biology Artificial Bee ABC Swarm Intelligence 2005 Foraging behavior of honey Protein structure prediction, Colony bee colonies gene clustering Firefly FA Swarm Intelligence 2009 Bioluminescent signaling in Feature selection, classification, Algorithm fireflies clustering Cuckoo CS Swarm Intelligence 2009 Brood parasitism in cuckoo Gene regulatory network Search birds; Lévy flights inference, biomarker discovery Bat BA Swarm Intelligence 2010 Echolocation behavior of Molecular docking, drug design Algorithm microbats Grey Wolf GWO Swarm Intelligence 2014 Leadership hierarchy and Species distribution modeling, Optimizer hunting strategy of grey feature selection, ecological wolves optimization Whale WOA Swarm Intelligence 2016 Bubble-net hunting strategy Medical image segmentation, Optimization of humpback whales EEG signal classification Algorithm

Note: Introduction-year labels follow the named canonical formulations; application labels are illustrative rather than quantitative evidence of usage or effectiveness.

Evolutionary search uses variation and selection on an encoded candidate. Binary strings can represent selected features or planning units; real-valued vectors can represent kinetic parameters; structured objects can represent alignments or trees. Differential evolution combines difference-based mutation with recombination rather than replacing recombination altogether [4]. Its continuous representation explains a modeling fit, not general superiority in systems biology.

Particle swarm optimization requires a specified position, velocity and boundary rule [5]. Ant-system construction requires a graph, feasible moves and pheromone updates [6]. Discrete transfer functions or domain-specific construction rules change these mechanisms and must be described. The biological setting does not automatically make a swarm method more appropriate than local search, mathematical programming or a specialized inferential procedure.

Simulated annealing provides a trajectory-based search mechanism [7]. Asymptotic convergence statements depend on explicit assumptions about cooling and reachability and do not certify the quality of a practical finite run. Its documented use in Marxan conservation planning illustrates a link between spatial decisions and a defined score [9].

Representation determines which candidates and moves are admissible. Four recurring forms are binary selection, continuous parameters, permutations and hierarchical structures. These are modeling choices rather than guarantees of effectiveness.

Binary encoding assigns a selection indicator to each feature or planning unit. With p candidate features there are 2 raised to p possible subsets. A search procedure still needs a feasible-subset rule, an evaluation design and constraints on subset size. Feature selection must occur inside the training procedure to avoid using held-out biological outcomes during model selection [10].

Real-valued encoding is appropriate for continuous kinetic or model parameters. Differential evolution and particle swarm optimization operate in this space [4], [5]. Bounds, identifiability, observation error and numerical integration tolerance remain properties of the biological calibration problem and cannot be delegated to the optimizer.

Permutation encoding is useful when the decision is an ordering, such as a schedule or scaffold sequence. Variation should preserve a valid permutation or use an explicit repair. A permutation is not a general substitute for a phylogenetic tree or a gapped alignment; those objects require representations that preserve their own structure.

A tree representation can encode topology and branch information separately. Rearrangement operators define admissible topological moves, and continuous branch parameters can be optimized conditionally. The likelihood model and the uncertainty attached to phylogenetic inference are separate from the choice of search operator [11].

Multi-objective biological decisions can balance predictive performance with parsimony or biodiversity representation with cost. The objectives should remain interpretable, and hard requirements should not be relaxed silently through arbitrary penalties. NSGA-II is one documented non-dominated search architecture [8]; it is not a universal biological standard or evidence that every reported front is globally Pareto-optimal. A non-dominated candidate cannot be improved in one stated objective without worsening another within the compared candidate set. This finite-set property does not imply that no better feasible solution exists elsewhere. A reported frontier should therefore be described as an approximation and evaluated for feasibility, diversity and sensitivity to objective scaling.

The scope includes sequence analysis, protein modeling, feature selection, phylogenetics, conservation planning and systems biology. Foundational algorithm papers and selected domain examples provide conceptual connections. The numerical search compilation in Table 2 lacks the database exports, exact full queries, screening decisions and included-study identifiers needed to establish a reproducible systematic search. Its counts are not used to define the evidence population.

Note: The reported database and screening counts have not been linked to identifiable records and are excluded from quantitative synthesis.

A relevant source must identify a biological decision or explain a search or validation principle used in that decision. Methodological reviews are useful for context but do not substitute for primary performance data. Synthetic-function benchmarks cannot establish superiority on biological applications. A complete domain evidence extraction would need task identities, objective definitions, datasets, algorithms, budgets and source locations for every reported quantity.

The quality criteria concern problem formulation, representation, feasibility, matched comparisons, independent validation and reproducibility. No measured inter-rater agreement or independently completed quality-scoring exercise is asserted. Such claims require reviewer identities, a defined rubric and the underlying study-level assessments.

The synthesis is qualitative. Tables 3-10 preserve a numerical compilation whose source mappings, common evaluation conditions and generating records remain unverified. Their numbers are not treated as pooled effects, reproducible benchmark results or statistical evidence of an optimizer advantage. Table 11 likewise lacks a traceable bibliometric corpus. These limits apply to every comparative interpretation in the article.

Multiple sequence alignment optimizes a stated scoring rule over gapped biological sequences. Complexity depends on the formulation; the sum-of-pairs problem is analyzed by Wang and Jiang [3]. A higher score is not automatically a more accurate reconstruction of evolutionary homology, so biological benchmark accuracy and objective value should be reported separately.

SAGA is a documented genetic-algorithm approach to sequence alignment [12]. Its relevance is the use of domain-specific variation on alignments. This establishes an algorithmic connection, not the numerical values attributed to it in Table 3. Later methods require their own verified representations and benchmark protocols. BAliBASE 3.0 provides reference alignments for evaluation [13]. Sum-of-pairs and total-column accuracy measures assess different aspects of agreement with a reference. Version identity, sequence subsets and scoring conventions must be held fixed in a comparison. Source dates in Table 3 precede the benchmark version for some rows; without a documented later reimplementation those rows cannot be read as results from the original cited studies.

Note: Numerical entries and attribution strings are retained as reported and do not establish a common BAliBASE 3.0 comparison.

The trade-off between alignment quality and computational cost is meaningful only under a matched protocol. An algorithm published before a benchmark can be reimplemented on it later, but the reimplementation, code, settings and measurements must be identified. Chronological inconsistency cannot be resolved by assigning an unsourced score to the originating paper.

Other sequence tasks, such as motif discovery or primer selection, require their own objectives and validation. Alignment, motif enrichment and primer specificity are not interchangeable outcomes. A credible comparison should state which biological property is measured and avoid transferring accuracy figures between distinct tasks.

Protein structure modeling involves structural representations and objectives whose relationship to biological conformation must be justified. Energy minimization and agreement with an experimental reference are distinct measures. A lower value from one energy function is not directly comparable with a value from another, and cannot alone certify a more accurate structure.

Simplified search models can test conformational operators, while realistic structure prediction introduces richer physical and learned constraints. Modern learned structure prediction, exemplified by AlphaFold [14], answers a different modeling question from a generic optimizer benchmark. Search may support refinement or sampling, but the contribution requires controlled evaluation rather than a universal energy-minimization claim.

A structural benchmark comparison must identify targets, versions, templates, training information and scoring procedures. Table 4 attributes later CASP targets to papers with earlier dates and mixes different targets. It therefore cannot support a common comparative ranking without a documented reimplementation and target-level extraction.

Note: Target identities, source attribution and common evaluation conditions require validation; entries are excluded from comparative conclusions.

The structure literature cannot be summarized by treating energy, RMSD and GDT-TS as interchangeable or by ranking values from different targets. A hybrid method should identify the source of learned constraints and isolate the contribution of search under a common starting model and budget. The numerical compilation does not currently establish that differential evolution or any hybrid is consistently superior.

AutoDock4 documents a docking architecture with a Lamarckian genetic search and local optimization [15]. Molecular docking predicts binding poses under a scoring model and is distinct from de novo protein folding. A source on GPU acceleration or gradient-based local search should not be relabeled as evidence for differential evolution.

Gene-expression feature selection faces a large number of candidate variables relative to biological samples. The statistical task is to identify predictive and stable features while evaluating generalization outside model selection. Feature-selection frameworks and their biological roles are reviewed by Saeys et al. [10]. Compactness, prediction and functional interpretation are separate objectives.

A binary feature selector explores 2 raised to p subsets for p candidate genes. This count motivates restricted search but does not prove that a particular optimizer is necessary or dominant. Preprocessing, feature selection, hyperparameter tuning and classifier fitting must be performed within the training folds, with independent data reserved for final assessment.

The dataset names and dimensions in Table 5 do not, by themselves, define a comparable experiment. Different preprocessing, train–test splits and selected sample subsets can yield different results under the same dataset label. Each row requires an identifiable primary source or a released common reimplementation before its accuracy, AUC or feature-reduction value can be compared.

Note: Dataset versions, source rows, feature selection and validation protocols are unresolved; numerical entries are not pooled or ranked.

The displayed feature-reduction percentages describe the retained subset relative to the stated feature count. They do not establish preserved out-of-sample performance or biological relevance. Classifier choice and nested selection can affect the result as much as the optimizer. External cohorts, stability analyses and biological validation address questions that a high internal classification score cannot answer.

Claims that selected genes identify disease pathways require traceable gene identifiers, an enrichment background and a documented analysis. A predictive signature can be useful without constituting a causal mechanism. The review does not infer clinical efficacy or pathway confirmation from unverified optimization tables.

Maximum-likelihood phylogenetic inference optimizes the likelihood of aligned observations under a substitution model [11]. The topology count (2n − 5)!! is approximately 2.84 × 10⁷⁴ for 50 labeled taxa. Search avoids exhaustive enumeration, while inference still depends on the alignment, substitution model, branch treatment and uncertainty analysis.

Topology search may use stochastic variation, local rearrangements or their combination. Algorithm families should be compared through the moves they implement and their stopping rules. A genetic label does not confer a statistical interpretation on a tree, and a high likelihood does not establish that the inferred topology is the biological truth.

Table 6 lacks row-level source mappings, sequence alignments, substitution models and matched runtime measurements. Its log-likelihoods, tree lengths and distances cannot establish an algorithm order. A Robinson–Foulds comparison also requires a defined reference tree and compatible taxa.

Note: Source datasets, models, reference trees and runtime protocols must be established before interpretation.

Comparative phylogenetic evaluation should state the optimization target, starting trees, branch optimization and total likelihood evaluations. The same likelihood scale is needed for a numerical comparison. A topological distance is descriptive relative to a chosen reference, not a certificate of causal evolutionary accuracy. Numerical entries in Table 6 remain outside the validated synthesis.

Ecological optimization includes model calibration and spatial planning, with uncertainty in observations, future environments and management priorities. The search layer evaluates a stated model; biological validity and policy consequences require separate evidence. The conservation-planning example below illustrates that distinction.

The official Marxan manual describes selection of planning units using a score containing planning cost, a spatial boundary term and penalties for unmet representation targets [9]. Penalty weights and the boundary modifier encode priorities. A low combined score should be accompanied by explicit target attainment and spatial interpretation; it cannot be compared across incompatible penalties or study regions.

Species-distribution modeling requires independent spatial evaluation and attention to sampling bias. Tuning a predictive model through a metaheuristic may improve a selected score, but it does not by itself establish habitat realism or conservation benefit. Table 7 lacks the extraction and validation records needed to verify its ecological performance claims.

Note: Study areas, source results and metric definitions are not reconciled; entries do not support cross-region optimizer rankings.

Multi-objective planning can expose feasible alternatives balancing representation, cost and connectivity [8]. The returned set is an approximation, and final decisions depend on priorities and model uncertainty. A Pareto presentation is useful when these trade-offs are explicit, but does not remove the need for ecological constraints or establish complete global optimality.

Systems biology combines mechanistic models and observations to examine biological dynamics. Parameter calibration and network-topology inference are related but distinct inverse problems. A favorable fitted score must be assessed together with identifiability, observation assumptions and predictive behavior.

For n genes, a directed signed graph without self-edges has n(n − 1) potential edges and 3 raised to n(n − 1) signed configurations when activation, repression and absence are separate states. GRN inference requires more than choosing among these configurations. Model assumptions, perturbation data, noise and identifiability affect which interactions can be supported [16]. DREAM-related benchmark work illustrates the need for explicitly defined inference and evaluation tasks [17].

Table 8 does not identify the particular network, simulations, train–test information or generating implementation for each result. Precision, recall and their derived F1 measure must refer to the same edge set and averaging convention. Numerical agreement within a row cannot establish biological or computational provenance.

Note: Network identities, source mappings and evaluation conventions require validation before comparative interpretation.

Different network and parameter representations produce different search problems. Kimura and colleagues describe cooperative coevolution for S-system network inference [18]; this should not be relabeled as generic DE superiority. The present numerical compilation does not establish that a DE–PSO hybrid has the best performance across identifiable DREAM networks.

Dynamic-model calibration can contain weakly identified parameter combinations, as illustrated by work on sloppy sensitivities in systems biology [19]. Search may find several parameter vectors with similar fit, but optimizer diversity is not a confidence interval. Independent predictions, sensitivity analysis and an appropriate inferential framework are needed to interpret those solutions.

Metabolic optimization includes problems that can be expressed through mathematical programming and problems involving discrete interventions. These cases require their own formulations. A metaheuristic should be justified by the resulting decision structure, rather than assumed necessary for every biological model or every flux analysis.

Table 9 retains cross-domain labels, gaps and p-values whose study-level evidence has not been established. No complete common algorithm-by-instance score matrix or effect-size extraction is available. These entries cannot identify the best algorithm in a domain or support a pooled cross-domain conclusion.

Note: Best-algorithm labels, gaps and p-values are unvalidated reporting and are excluded from the review conclusions.

Cross-domain transfer should concern representations and mechanisms, not a pooled league table of incompatible scores. Alignment accuracy, protein-structure error, classification performance and conservation cost have different meanings and evaluation units. Any quantitative synthesis must specify which comparable effects are combined and how uncertainty, dependence and study quality are treated.

Hybridization combines components that perform different mathematical roles. A classifier can evaluate a feature subset, a local search can refine a candidate, and a surrogate can approximate an expensive objective. These are distinct forms of combination. Their benefit must be measured with matched evaluation budgets and suitable ablations.

A feature-selector–classifier pipeline searches for subsets whose prediction performance is assessed by a classifier. The classifier is an evaluator, not necessarily a second optimizer. A valid nested evaluation must isolate final assessment data from every selection or tuning step [10].

Combining two search rules creates a hybrid whose order, state exchange, control parameters and acceptance mechanism must be specified. Merely assigning labels such as GA–SA or DE–PSO does not determine an executable algorithm. Local and global evaluation costs should be counted together.

A learned surrogate or initialization model can guide search, but the final candidate should be checked through the stated underlying evaluator. Table 10 does not provide traceable primary comparisons or matched budgets for its reported gains and speedups. It is not evidence that deep-learning hybrids dominate biological optimization.

Note: Reported gains, speedups and attribution labels require primary source extraction and are not accepted as comparative evidence.

A claim that a transformer-guided alignment optimizer improves accuracy and convergence requires an identifiable paper, an explicit sequence representation and evaluation records. Biological contact prediction, alignment scoring and conformational sampling should not be conflated. No gain is inferred from the unsupported values in Table 10.

Scalability must be evaluated on a stated implementation and biological task. Population size and representation dimension account for only part of the cost; objective evaluation, constraints, synchronization and data access can dominate.

For a basic vector-population implementation, updating candidates may take cost proportional to population size times dimension. This excludes the cost of evaluating biological objectives and does not establish how many iterations are needed for a target solution quality.

Swarm and evolutionary methods require comparable accounting of update, evaluation and memory costs. No dimension threshold establishes a universal speed advantage of one family over another. Scaling claims should be measured with task identities, hardware and achieved solution quality.

Trajectory-based search can use inexpensive local changes when the objective admits incremental updates. Parallel candidate evaluation or multiple trajectories may help, but the attainable gain depends on synchronization and the model. A generic search label is insufficient to assert scalability to a specific number of planning units.

Friedman testing ranks the same algorithms within each independent problem instance; it requires a complete matched design. Table 9 supplies only best and second-best labels, not such a score matrix. The previously reported omnibus statistic cannot be reproduced from that table and is not asserted as a validated result. The five reported average ranks, 1.85, 2.15, 2.60, 3.25 and 3.80, sum to 13.65, whereas valid complete ranks for five algorithms must sum to 15, including averaged ties. They therefore cannot establish the stated Friedman or Nemenyi inference. For illustration of the method only, the usual Nemenyi convention with five algorithms, ten independent instances and q = 2.728 gives a critical difference of about 1.93; this is not a reconstructed test result for the unverified compilation.