The computing literature first entertained solving technical optimization problems by simulating evolution and recombination [1], [2], and the six decades since that beginning carry a record this survey reads as a chronicle. Metaheuristics, iterative search procedures that exchange guarantees of global optimality for broad applicability and modest modeling assumptions, matured into a default instrument of engineering design, operations research, and machine learning. The trajectory records three inflections of identity. The No Free Lunch theorems delimited what any single optimizer can achieve on average [3]. The novel metaphor debate then cast doubt on whether hundreds of nature-inspired algorithm names amount to cumulative science [4]. Most recently, Large Language Models (LLMs) entered the record as both optimizers and designers of optimization algorithms [5]. Each inflection redrew what the community accepts as a contribution, so a sixty-year retrospective is an audit of how a discipline reorganizes itself, first under criticism and then under new technology. The publication record of these six decades is the object this survey measures, decade by decade and cluster by cluster.

Influential syntheses already cover parts of this record, and their coverage delimits the gap this survey fills. Blum and Roli [6] supplied the canonical conceptual comparison of metaheuristic paradigms. Boussaïd et al. [7] charted the algorithmic landscape of the early 2010s. Talbi [8] codified design and implementation methodology, and the textbook of Eiben and Smith [9] has distilled the field's foundations for two decades of students. Those works predate the LLM-era turn, and none quantifies the field's internal structure across the full six-decade span with transparent, reproducible bibliometric evidence. No existing study simultaneously establishes how the intellectual core evolved, which families dominate publication activity, what co-citation structure reveals about the schools of thought, which methodological factors recur in reported performance gains, and how foundation models reshape optimizer design.

The instrument assembled for this purpose has two parts: A Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA)-style systematic screening protocol adapted from the systematic-review literature [10], and the analytic apparatus of bibliometrics, namely descriptive publication statistics, keyword co-occurrence and drift analysis, and co-citation network analysis in the tradition of Small [11], with community detection by Louvain modularity maximization [12] and science-mapping tooling [13]. Interrogation of five databases, the Web of Science Core Collection, Scopus, Institute of Electrical and Electronics Engineers (IEEE) Xplore, the Association for Computing Machinery (ACM) Digital Library, and arXiv, yielded 12,904 screened records and a core corpus of 2,847 documents published between 1962 and 2025. Four axes organize the material: Chronological, through five thematic decade arcs; taxonomical, through a working taxonomy of algorithm families; structural, through six co-citation clusters; and meta-analytical, through a narrative synthesis of 120 focal empirical studies. The scope embraces metaheuristic methods for optimization and tuning; exact algorithms of mathematical programming and the training procedures internal to machine learning enter only where they intersect that scope. Five Research Question (RQ) discipline the analysis:

RQ1. Through what stages did the intellectual core of metaheuristics evolve across the decades from 1962 to 2025?

RQ2. Which algorithmic families command the publication record, and how measurably did the novel metaphor debate reshape the field?

RQ3. What does the co-citation structure of the core corpus reveal about the field's schools of thought and their interdependencies?

RQ4. Which methodological factors recur across study after study in association with reported performance gains in controlled empirical comparisons?

RQ5. Through what routes are foundation models and LLMs reshaping the design and tuning of optimizers? Audited against the prior survey record, the present study occupies a defined position. The conceptual comparison of Blum and Roli [6], the algorithmic landscape of Boussaïd et al. [7], and the design methodology codified by Talbi [8] map the paradigms but stop before the LLM-era turn; the textbook of Eiben and Smith [9] instructs practitioners without measuring the field's corpus-level structure. Single-strand surveys narrow the window further: The constraint-handling survey of Coello Coello [14], the fitness-approximation survey of Jin [15], the parameter-control survey of Karafotias et al. [16], the Bayesian optimization review of Shahriari et al. [17] and co-workers, the hyperparameter-tuning chapter of Feurer and Hutter [18], and the nonparametric-testing tutorial of Derrac et al. [19] each track one thread of a six-decade record. The metaphor critique of Sörensen [4] evaluates the field's sociology of novelty yet reports no corpus. None of these works screens multiple databases under a PRISMA-style protocol, none resolves the full 1962–2025 span into co-citation clusters, and none measures venue concentration or geographic diffusion. The present survey supplies that layer: A reproducible 2,847-document corpus, six quantified schools of thought, a meta-analysis of 120 focal studies, and the scientometric trajectory of Section 5.4.

Questions of this kind demand evidence rather than recollection, and the contribution of this article is precisely an evidence base and a chronicle of it. Seven deliverables carry the weight. First, corpus construction in reproducible form: 12,904 records screened, all 10,057 exclusions documented stage by stage, and 2,847 core documents retained with decade-level statistics and growth modeling. The remaining deliverables are the analyses that such a corpus makes possible.

I. A PRISMA-style screening flow with fully documented arithmetic (Table 1), together with a decade-level corpus profile and growth modeling (Table 2, Figs. 1 and 3).

II. A chronological-thematic synthesis in five decade arcs (Section 3), binding each period's bibliometric profile to its primary intellectual developments.

III. A working taxonomy of metaheuristic families, with crisp definitions, per-family corpus counts, metaphor classes, and eras of emergence (Section 4, Table 3).

IV. A co-citation network analysis (41,203 links; modularity 0.68) isolating six schools of thought, C1–C6, with representative works, bridge works, and turnover patterns (Section 5, Tables 4 and 5, Fig. 3), plus a scientometric layer measuring venue concentration and geographic diffusion (Table 6, Fig. 4).

V. A narrative meta-analysis of 120 focal empirical studies quantifying how often five performance drivers are invoked and what ranges they claim, under explicit bias caveats (Section 6, Table 7).

VI. A comparative computational vignette racing four era markers on a shared testbed, with a random-effects meta-analysis of standardized effect sizes (Section 7, Tables 8 and 9, Fig. 5).

VII. An assessment of the foundation-model and LLM frontier, with its open problems of evaluation integrity, replication, and cost accounting (Section 8).

The remainder of the article proceeds as follows. Section 2 sets out the survey methodology, from data sources to analytical methods; Section 3 traverses the six-decade arc; Section 4 presents the taxonomy; Section 5 reports the co-citation analysis and the scientometric layer built upon it; Section 6 synthesizes the performance-driver evidence; and Section 7 races four era markers, Simulated Annealing (SA), UMDA, the Cross-Entropy Method (CEM), and JADE, on a shared testbed and synthesizes them meta-analytically. Section 8 maps the emerging frontiers, Section 9 confronts the survey's own validity threats, and Section 10 closes with explicit answers to the five RQ.

The methodology of this survey was engineered for traceability: Every count in later sections reduces to a documented screening or analytical decision, in the spirit of the PRISMA statement for systematic reviews [10]. The protocol adapts PRISMA's staged screening to a bibliometric setting, in which the unit of analysis is the publication rather than the trial. Sections 2.1 through 2.4 cover the data sources and search strategy, the inclusion and exclusion criteria with the screening flow, the resulting corpus statistics, and the analytical methods applied to the corpus. The four subsections that follow keep that order, and each reports its own counts.

RQ1 and RQ2 receive a chronological answer, a traversal of the corpus in five thematic arcs. Each arc binds the decade's bibliometric profile (Tables 1 and 2; Figs. 1 and 3) to the intellectual developments that the primary literature itself records, and citations to primary works anchor every historical claim. The five arcs run from the evolutionary roots (1960s–1970s) through consolidation and simulated physics (1980s–1990s) and the swarm wave and hybridization (2000s) into critique and rigor (2010s), ending in the data-driven foundation-model era (2020s).

3.1|1960s–1970s: Evolutionary Roots

The corpus begins in 1962, yet the ambition of evolving solutions by machine reaches back further. As early as 1957, Fraser simulated genetic systems on a digital computer, studying evolutionary dynamics rather than optimizing anything [20]. Friedberg's [21] 1958 learning machine attempted to improve computer programs through random mutation and selection, and its honestly reported failure, in which undirected mutation proved hopelessly inefficient, prefigured the field's later insistence on informed variation. The 1960s then witnessed evolution implemented in software and in dedicated hardware alike: An 'evolutionary machine' reported in 1963 automated mutation and selection on physical apparatus, one of several pre-software evolution devices preserved in the field's historical record [22]. For this survey's narrative, such precursors matter, because they fix the field's intellectual core, variation plus selection implemented and measured, before any of its canonical algorithms existed.

Across the corpus's first two decades, three research traditions consolidated, each with its own vocabulary and, at first, barely any mutual citation. Fogel et al. [23] in evolutionary programming treated populations of candidate finite-state machines as artificially intelligent agents subject to simulated evolution. Rechenberg's evolution strategies, grown around hardware experiments at the Technical University of Berlin, introduced mutation with strategy parameters adapted online and culminated in his 1973 monograph [24]; Schwefel's [25] 1977 German monograph and its 1981 English extension fixed the notation, the self-adaptation of mutation strengths, and the recombination operators that later crossed into other families. Holland's [2] GA, outlined as early as 1962 and synthesized in his 1975 monograph on adaptation in natural and artificial systems, supplied the schema-theoretic vocabulary and a population-level theory of adaptation [26]. The corpus registers 41 documents for the 1960s and 96 for the 1970s; their venue and keyword traces, papers dispersed across cybernetics, simulation, and artificial intelligence outlets under the self-description 'adaptive systems', show a shared identity yet to form, a fact the co-citation structure of Section 5 confirms directly.

3.2|1980s–1990s: Consolidation and Simulated Physics

Together, the 1980s and 1990s turned scattered research programs into an internationally recognized field, and two imports from outside population genetics reshaped the canon. SA carried statistical mechanics into stochastic search. Kirkpatrick et al.'s [27] 1983 paper recast combinatorial optimization as controlled cooling under an explicit temperature schedule trading exploration for exploitation; appearing in a general-science venue, it carried metaheuristic ideas to physics, chemistry, and engineering audiences and produced the corpus's first large citation crossover beyond computing. Tabu search supplied the opposite pole of the later taxonomy, a trajectory-based method built on adaptive memory rather than population sampling; Glover's [28] 1986 programmatic essay introduced the concept, and his journal treatise consolidated it [29]. The evolutionary traditions theorized in the same decades: Goldberg's [30] 1989 textbook carried GA into engineering practice and spawned a generation of applications, while Bäck's [31] comparative synthesis at last aligned the three evolutionary traditions under one formalism.

The 1990s in turn delivered their most durable innovations within a four-year span. Dorigo's [32] 1992 dissertation proposed ant colony optimization, with the ant-system formulation following in 1996, a genuinely different search principle built on stigmergic communication rather than selection [33]. Kennedy and Eberhart's [34] 1995 Particle Swarm Optimization (PSO) likewise issued from simulations of social behavior rather than biology and became the fastest-spreading algorithm of its decade. Storn and Price's [35] 1997 DE demonstrated that recombining scaled differences of population vectors suffices for competitive continuous optimization; in the same year Wolpert and Macready's [3] No Free Lunch theorems proved that, averaged over all possible problems, no search algorithm outperforms any other, a negative result that steered the field toward problem-dependent design and honest benchmarking. Theoretical self-examination matured alongside: Fitness–distance correlation yielded empirically workable measures of problem difficulty [36], and constraint handling, long the weak point of population methods, received from Michalewicz and Schoenauer [37] its first systematic treatment. The consolidation is legible in the corpus: 214 documents in the 1980s, 389 in the 1990s, core output roughly doubling every five years between 1990 and 2005, and 'genetic algorithm' dominant as a keyword throughout 1990–2005.

3.3|2000s: The Swarm Wave and Hybridization

The 2000s stand as the expansion decade: 611 core documents, raw growth near its peak (Section 2.3), and a thematic profile ruled by swarms, hybrids, and scale. Four developments define the arc. Covariance matrix adaptation matured evolution strategies into the strongest available baseline for continuous search: Hansen and Ostermeier's [38] fully derandomized self-adaptation learns a complete covariance model of successful steps, and its descendants still anchor continuous benchmarking (Section 5.3). The multi-objective wave followed: Non-dominated Sorting Genetic Algorithm II (NSGA-II) married fast non-dominated sorting to crowding-based diversity preservation and became, by in-corpus citation count, the most cited algorithmic contribution of the decade [39], while constraint handling consolidated into a deployment methodology for real-world engineering, surveyed contemporaneously by Coello Coello [14]. Hybridization itself graduated into a design pattern rather than a single algorithm; the memetic idea of Moscato's [40] 1989 report, population search punctuated by individual local learning, stood as the default in applications by decade's end. The swarm wave proper ran in parallel. Dorigo and Stützle's [41] monograph gave ant colony optimization a theoretical and experimental backbone; Karaboga's [42] artificial bee colony extended swarm modeling to foraging economies; and harmony search, whose musical metaphor would later make it a focal point of the metaphor debate, likewise dates from the wave's opening years [43]. The expansion wore a second face: As evaluation budgets grew and applications moved toward expensive engineering simulations, fitness approximation, surveyed comprehensively by Jin [15], initiated the surrogate-assisted line that would in time converge with Bayesian optimization [44]. Application breadth erupted across engineering design, scheduling, bioinformatics, and finance, and around mid-decade keyword control passed from 'genetic algorithm' to 'swarm intelligence'. Section 2.3 quantifies the bibliometric cost of this expansion: During 2005–2015 the pass-through rate of the methodological screens fell, leaving a growing share of published records with too little verifiable methodology to enter the core corpus [4].

3.4|2010s: Critique, Novelty Debate, and Rigor

The 2010s hold the corpus's largest decade share, 913 documents and 32.1%, yet their defining event was internal: the decade watching the field turn a critical lens on itself. The trigger assembled over years rather than arriving at once: Hundreds of algorithms proposed under natural metaphors, the grey wolf optimizer [44] prominent among the wave's later representatives, with novelty claims resting on narrative inspiration rather than identifiable mechanism. Weyland's [45] rigorous analysis of harmony search demonstrated that the algorithm could be restated, term by term, as an existing evolution strategy in different dress, challenging the community to distinguish reformulation from invention. Sörensen's [4] essay generalized the charge: Research disguised in ever-fresh metaphors, he argued, crowds out cumulative science and burdens practitioners with unsearchable pseudo-methods. Tracked here as the metaphor debate, the exchange reshaped editorial and reviewing norms, and its bibliometric footprint is measurable: Raw screened-record growth slowed from 14.2% per year in 2005–2015 to 6.1% per year in 2016–2023 as low-substance submissions receded. Novelty as such escaped condemnation, for teaching–learning-based optimization, introduced with minimal metaphorical apparatus and few control parameters, shows that the target was framing rather than invention [46].

Evaluation science supplied the decade's second theme. Benchmarking standardized around the Congress on Evolutionary Computation (CEC) competition suites, whose 2017 problem definitions remain the de facto reference for bound-constrained comparison [47]; García et al. [48] established nonparametric statistical testing as the expected reporting standard, and Derrac et al. [49] tutorial carried it into practice. The CEC 2014 winner, Linear Population Size Reduction Success-History Based Adaptive DE (L-SHADE), combining success-history parameter adaptation with linear population-size reduction on the Success-History Based Adaptive Differential Evolution (SHADE) line [50], [51], fixed the performance reference point of the era and anchored the empirical-methodology cluster of the co-citation network (Section 5.2). Adaptivity rose to first-class standing: The parameter-control framework of Eiben et al. [51] was extended by Karafotias et al. Each document is assigned the single family of its central algorithm; counts sum to 2,847. The trajectory versus population dichotomy is orthogonal to the five families [6].

Operationally, the families are defined as follows. Evolution-based methods manipulate encoded candidate solutions through variation operators and selection pressure drawn from population genetics: GA, evolution strategies, evolutionary programming, DE, covariance matrix adaptation, and the SHADE line. Swarm-based methods derive their movement rules from local interactions among simple agents: PSO, ant colony optimization, artificial bee colony, and later social-predator metaphors such as the grey wolf optimizer. Physics-based methods transcribe physical dynamics, among them annealing, gravitation, and electromagnetism, into acceptance or movement rules. Human/social-based methods borrow from cultural, pedagogical, or organizational processes, as in tabu search's memory of forbidden moves, harmony search's ensemble improvisation [43], and teaching–learning-based optimization's classroom metaphor [46]. Finally, hybrid and data-driven methods superimpose a learning- or model-based component on any of the foregoing: Memetic hybrids [40], surrogate-assisted evolution [15], Bayesian hyperparameter optimization [17], and LLM-in-the-loop optimizers [5].

Three observations follow from Table 3. Evolution-based methods remain the field's center of gravity at 1,104 documents and 38.8% of the corpus, with swarm-based methods second at 841 documents (29.5%); biological metaphors thereby account for over two-thirds of all core documents, a concentration that explains why the metaphor debate struck so near the field's identity [4]. Family shares are not static either: After 2005, the hybrid and data-driven family's share of each decade's output climbs steadily, peaking in 2020–2025 in step with the surrogate, Bayesian, and LLM arcs of Section 3.5, and every family to emerge after 1995 is population-based or explicitly hybrid. Two limitations are acknowledged, namely that single-family assignment understates hybrid designs, which are counted under their dominant component, and that the boundary between physics-based and human/social-based metaphors is occasionally arbitrary; the taxonomy is a working instrument of corpus accounting, not a claim about algorithmic essence.

RQ3 is answered through the co-citation structure of the core corpus. Section 5.1 reports network construction and statistics; Section 5.2 interprets the six clusters; Section 5.3 identifies the bridge works and turnover patterns that connect and renew them; and Section 5.4 widens the lens to the venues and geographies across which the literature has diffused. Clusters are labeled C1 through C6 as fixed in Section 5.2 and used consistently thereafter.

RQ4 falls to the 120 focal studies, the most-cited core documents whose central contribution is a controlled performance comparison, analyzed for the mechanisms they invoke as drivers of improvement. For each study, the extraction recorded the driver category (adaptive parameter control, hybrid local search, diversity management, surrogate modeling, restart mechanism, or other), the claimed effect range, the benchmark suite, and the statistical protocol. Primary studies rarely report the variance information that inverse-variance pooling demands, so the synthesis is narrative rather than statistical: Frequencies and claimed ranges, not pooled effect sizes. That limitation is itself a finding, for the reporting practices recommended by the statistical-methodology literature [48], [19] remain, for much of this literature, aspirational. The narrative form keeps every claim traceable to its primary study.

Adaptive parameter control is the most recurrent driver, present in 71% of top-quartile improvement reports with median claimed gains of 10–30%. Its lineage runs from the formal control framework of Eiben et al. [51] through the success-history adaptation of SHADE and L-SHADE [49], [50] to full covariance adaptation in CMA-ES [38], with Karafotias et al. [16] survey consolidating the underlying evidence. The claim's plausibility is high, since parameter sensitivity is repeatedly demonstrated to be first-order, yet the reported gains are usually measured under tuning effort that the baselines never receive, so the effect conflates the mechanism itself with the experimenter's effort budget.

Frequency then orders the remaining drivers. Hybrid local search, the memetic pattern [40], surfaces in 58% of focal studies with claimed gains of 5–25%; diversity management in 44% (claimed 8–22%), implemented as explicit diversity metrics, stagnation-triggered renewal of subpopulations, or multi-population structures. Surrogate models appear in 37% (claimed 15–40% in expensive-evaluation settings, where the figure often counts evaluations saved along with quality gained) [15], [17]. Restart mechanisms close the register at 29% (claimed 5–15%), the restart-CMA-ES line standing as the most-cited exemplar [66], and Table 7 gathers the synthesis.

Effect ranges are as claimed by the primary studies and were not independently re-measured here; see the bias

Drivers co-occur, and the frequencies of Table 7 must accordingly be read as other than independent effects: The strongest recent systems combine several at once, L-SHADE being at once a parameter-adaptation, a population-size-control, and a restart-adjacent mechanism [50]. Three biases fence every inference: 1) all effect ranges are self-reported and exposed to benchmark-selection bias: Algorithms are developed, tuned, and evaluated on the same public suites, a practice that invites overfitting to the benchmark rather than to the problem class [47], 2) publication bias suppresses negative comparisons, since a method that fails to beat its baselines is rarely published, and so inflates the apparent success rate of every driver, and 3) citation-visibility selection of focal studies favors established methods and groups. Table 7 therefore reports the field's collective self-assessment: A meaningful signal, though one that independent replication has only partially corroborated [4], [48].

Sections 2 through 6 measured the field's literature; this section measures four of its algorithms. The six-decade chronicle carries an implicit, testable claim that successive design eras left distinguishable signatures in search behavior, and a comparative computational vignette was appended to examine it. Four era-marking algorithms, one from each design generation of the Section 4 taxonomy, were raced on a shared testbed under identical evaluation accounting, and their outcomes were synthesized meta-analytically. The vignette is compact and secondary to the bibliometric core: Its role is calibration, not leaderboard ranking.

SA 1983, simulated- Physics-based (trajectory Initial acceptance 0.8, Kirkpatrick et physics era method) geometric cooling factor 0.95 al. [27] UMDA 1996, 1990s model- Evolution-based (model- Population 100, truncation Mühlenbein based era based population selection ratio 0.5, univariate and Paaß [67] method) Bernoulli margins CEM 1999, rare-event and Hybrid and data-driven Elite quantile 0.10, dynamic Rubinstein [68] model-based era (explicit density model) smoothing 0.70 JADE 2009, 2000s Evolution-based (DE Population 100, p = 0.05, c = Zhang and adaptive era line) 0.1, external archive sized to Sanderson [69] the population

Settings follow the schedules and defaults of the source publications [27], [67–69]; no per-problem retuning was applied. Family placements follow the taxonomy of Table 3.

Because the three families live on different error scales, the primary measure is a standardized effect size. For each unit, the comparison of an era marker against the SA anchor was reduced to the Hedges' g of Eq. (4), the small-sample-corrected standardized mean difference of the two arms' final log-transformed errors, with s_AB the pooled within-arm standard deviation and the leading factor the bias correction. SA anchors the comparison as the oldest of the four and the field's classical baseline [27]. The primary synthesis pools the twenty g values per method under the DerSimonian-Laird random-effects estimator, justified by genuine variation of true effects across families; secondary outcomes are the success rate at the fixed target of 1 × 10⁻ , median evaluations to target, and the budget-share quartiles of the next subsection.

3 ̅ X − ̅ X

g = (1 − ) . (4)

4(nA + nB) − 9 SAB

The corpus analysis leaves the field at a hinge: The evaluation culture consolidated in the 2010s now confronts optimization methods whose core components are statistical learners at unprecedented scale. The frontier of RQ5 reaches well beyond the current LLM applications, and six open problems emerge directly from the survey's findings. Each is stated alongside the evidence that motivates it.

I. Foundation-model tuning at scale: Scaling laws tie capability to compute, so each evaluation of a foundation-model configuration is expensive enough to invalidate conventions built around millions of cheap function evaluations [58]. The binding constraint is now the evaluation budget, which returns hyperparameter optimization [54], multi-fidelity search, and population-based training to the center of optimizer design. II. LLM-in-the-loop optimizers: Feasibility is established by OPRO [5], FunSearch [60], and LLaMEA [61], but the open questions are the grammar of operator design, prompt and model-version sensitivity, and comparison against classical baselines under equal evaluation budgets rather than equal wall-clock time. III. Benchmark contamination: Pretrained models may already have memorized classical test functions and their optima, and contamination-resistant, dynamically generated problem distributions are the precondition for taking LLM-era performance claims at face value.

IV. Explainability of search dynamics: Landscape-aware method selection would extend the theoretical tradition [36], [63] from static difficulty measures to online diagnosis of search behavior, yet the field still lacks a shared vocabulary for explaining why a run failed.

V. Rigorous evaluation culture: The methodological agenda of pre-registered comparisons, overfitting-resistant suites, and search-effort reporting [4], [47], [48] now has to be extended to learners in the loop, where the object under evaluation changes with every model release.

VI. Replication and cost accounting: Code and prompt release, model-version pinning, and token and energy accounting for LLM-based search [61] would elevate cost per improvement into a first-class metric, as fungible as the function-evaluation counts that ruled the 2010s.

None of these problems is technical alone; each binds an algorithmic question to an institutional one, much as the metaphor debate bound method design to reviewing norms. The survey's cluster structure suggests where the work will appear: C6 supplies the methods, but C4's evaluation apparatus, with its historical capacity for self-correction, will decide whether the new methods are absorbed into the canon or dissolved into it.

The corpus stands conditional upon its databases, and there the threats begin. Web of Science and Scopus coverage thins markedly before 1990, and the foundational monographs [24–26] entered the corpus by snowballing rather than by search; the decade counts of the 1960s through 1980s are accordingly lower bounds. IEEE Xplore and the ACM Digital Library overweight engineering and computing venues, so metaheuristic work published in general-science or domain-specific journals is undercounted, precisely the venues through which SA originally reached the field [27].

Two further selection threats compound the coverage bias. Because full-text assessment required English or an available English translation, Schwefel's original German monograph, the Japanese and Chinese metaheuristic literatures, and Soviet-era work on random search are undercounted, and the corpus overstates the field's Anglophone share. Citation lag presses on the most recent period: References to 2024–2025 works accumulate for years, so C6's 12.2% share and the LLM subset's 2025 count understate the niche, and cluster boundaries involving C6 are best treated as provisional estimates, re-computed as citations mature.

Methodological threats close the register. Keyword drift means that post-2020 metaphor coinages may slip past even the extended algorithm-name list of Section 2.1; screening rested on a single researcher with no second independent coder; and the co-citation apparatus carries known limits of its own, for threshold choices shape cluster structure and the Louvain algorithm's resolution limit can merge small communities into large ones [70]. None of these threats plausibly overturns the six-cluster macro-structure, which held robust under threshold and seed variation (Section 5.1), yet each should temper fine-grained readings of cluster shares, growth rates, and driver frequencies. The threats are listed in decreasing order of structural consequence. The computational vignette of Section 7 carries threats of its own, distinct from the corpus threats. Its testbed is narrow by construction: Ten continuous, unconstrained problems at two dimensions say nothing about combinatorial, constrained, dynamic, or expensive evaluation settings. Parameter provenance is a second exposure, for settings were taken from the source publications rather than retuned per problem, which favors eras whose defaults were normalized on testbeds of this shape. The SA anchor is a third, since every effect size is measured against the 1983 baseline rather than each challenger's contemporaries, so the design answers questions about eras, not pairwise superiority among the challengers. The heterogeneity statistics of Section 7.3 bound the claim: Pooled orderings are averages over families, not properties of any single problem.

What this survey set out to draw was a quantitative self-portrait of metaheuristic optimization across its six decades, from the recombination studies of 1962 to LLM-based optimizers of 2025, and the five research questions of Section 1 can now be answered directly. The answers condense the evidence of Sections 2 through 9 and together describe a field that has grown by absorbing its critiques and is now absorbing its newest external shock.

RQ1. Through five arcs, the intellectual core evolved, from paradigm formation in the 1960s–1970s and imported physics and canon formation in the 1980s–1990s through expansion and hybridization in the 2000s and self-critique and evaluation science in the 2010s to data-driven foundation-model search in the 2020s, while the co-citation canon stayed anchored in a small set of classical works Table 5.

RQ2. Evolution-based methods command publication activity with 38.8% of the core corpus and swarm-based methods with 29.5%; the metaphor debate reshaped the field measurably, coinciding with a slowdown of raw growth from 14.2% per year in 2005–2015 to 6.1% per year in 2016–2023 and a migration of novelty claims from narrative inspiration toward adaptive and data-driven mechanisms.

RQ3. The co-citation network decomposes into six stable schools, C1 through C6, at modularity 0.68, joined by bridge works, among which the No Free Lunch theorems, CMA-ES, and NSGA-II are the most consequential, connecting theory, methodology, and application.

RQ4. The most frequently invoked performance driver is adaptive parameter control, appearing in 71% of top-quartile improvement reports with claimed gains of 10–30%, ahead of hybrid local search (58%; 5–25%), diversity management (44%; 8–22%), surrogate modeling (37%; 15–40% in expensive settings), and restart mechanisms (29%; 5–15%), all under the strong caveat that every range is self-reported and benchmark-selection-biased.

RQ5. Foundation models have turned evaluation cost into the binding constraint of modern search and have entered the loop as both optimizers and algorithm designers, and the open problems are contamination-resistant evaluation, prompt and version reproducibility, and cost accounting.

Sixty years of metaheuristics exhibit a field that institutionalized its own critique: The evaluation science of the 2010s was a direct institutional response to the metaphor flood, and it is precisely that apparatus which the LLM era must now inherit. The scientometric layer of Section 5.4 adds a coda, for across the same decades the literature decentralized, the top-five venue share dispersing from 38.2% to 14.7% while Global South participation widened from 4.1% to 22.6%, leaving the community to face the foundation-model transition broader and more geographically distributed than any the field has known. The computational vignette of Section 7 adds an empirical coda: The four era markers finished in the order JADE, CEM, UMDA, SA, mirroring the six-decade drift the co-citation record documents under a standing No Free Lunch caution. The survey's instrument, a reproducible corpus, a stable cluster structure, and the diffusion measures built upon it, is offered for reuse: Re-running the protocol in 2030, when the LLM-related niche has consolidated or receded, would make a revealing experiment in the field's capacity for self-knowledge. The corpus, the screening arithmetic, and the cluster definitions are reported in enough detail to make that re-run straightforward.

All aspects of the research and manuscript preparation were carried out by the author. The author has read and approved the final version of the manuscript.

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