Comprehensive Taxonomies of Nature- and Bio-inspired Optimization: Inspiration versus Algorithmic Behavior, Critical Analysis and Recommendations (from 2020 to 2024)

1 Introduction

• More than 500 proposals appeared in 2024, while most publications lacked a taxonomy or exhaustive similarity analysis and focused instead on their motivating metaphor.The authors argue that comprehensive classification could help establish criteria for the novelty and contributions of current and future work.Source: §1 · p. 3
• The study classifies 518 metaheuristic works using two taxonomies: one based on natural or biological inspiration and one on how algorithms generate candidate solutions.The paired classifications are intended to group proposals by origin and by algorithmic similarities and differences.Source: §1 · pp. 3–4
• The authors compare classifications across the two taxonomies to test whether shared inspiration corresponds to shared behavior and to identify influential algorithms whose behavior inspired later proposals.They use detected similarities to examine relationships between algorithms placed in the same categories.Source: §1 · p. 4
• The authors recommend investing research effort in behavioral differences and verifiable performance evidence on practical problems, not only producing more proposals.They treat the field’s growth as evidence of activity but argue that its sharp expansion calls for these additional efforts.Source: §1 · p. 4
• The report also considers how population-based optimization may contribute to AI systems and surveys future directions and practices for designing and evaluating bio-inspired methods.Its outlook balances concerns about proposals’ analysis of real problems with the potential role of population-based models in AI.Source: §1 · pp. 4–5
• Their critical analysis addresses promising applications, proposals whose new metaphors do not yield innovative solvers, and methodological weaknesses such as inadequate justification and comparison.The authors call for good practices in designing, describing, and comparing algorithms, including evaluation on established optimization problems.Source: §1 · p. 4

2 Related Literature Studies (before 2020 according to the first version of this report, Feb. 2020)

• Surveys cover optimization problem types and application domains, including continuous, combinatorial, and multi-objective problems as well as fields such as robotics and telecommunications.Some real-world topics, including power systems, clustering, and intrusion detection, received dedicated overviews.Source: §2 · p. 5
• Algorithm-focused surveys examine variants of PSO, DE, ABC, BFOA, and Bat Algorithm, while books describe available methods without deeply classifying or analyzing them.A general account explains how metaphor and biological ideas inform meta-heuristic design.Source: §2 · p. 6
• Comparison studies primarily assess solver performance or suitability, rather than classifying algorithms or identifying shared design patterns.Other studies compare cooperative and noncooperative groups or report PSO outperforming DE, GA, and ABC for Echo State Network training and configuration.Source: §2 · p. 6
• Earlier classifications grouped algorithms by inspiration: lacked hierarchy, while added human-based methods but still used disjoint groups without subcategories.The catalog covered more than 50 proposals.Source: §2 · p. 6
• The survey classified 29 algorithms by learning, cooperation or competition, and population-control behavior, but treated these as independent principles rather than a taxonomy.Learning categories were individual, local, global, or none; population control was converging, diffuse, or without a specific tendency.Source: §2 · p. 6
• The study fills this gap with taxonomies of inspiration source and solution-generation behavior, and specifically examines structural similarities between classical and modern meta-heuristics.The authors state that no prior study had been specifically devoted to unveiling those similarities.Source: §2 · pp. 6–7

• The taxonomy assigns each algorithm to one disjoint category at each level, choosing the category that best distinguishes it from its counterparts.The review covers 518 papers, from classical proposals such as Simulated Annealing and PSO to techniques published through 2024.Source: §3 · p. 7
• Because inspiration sources and classifications vary and can become obsolete, algorithms within categories were selected by relative importance, including citation counts and the number of inspired variants.Source: §3 · p. 7
• To balance simplicity and usefulness, a category is subdivided only when its subcategories are coherent and each contains at least four algorithms.The taxonomy also avoids forcing every algorithm into a subcategory, so that subdivisions remain meaningful rather than forming incoherent catch-all groups.Source: §3 · p. 7
• Swarm Intelligence is the largest category at 53%, followed by Physics and Chemistry at almost 15%, Social Human Behavior at 11%, and Breeding-based Evolution at near 7%.The study also identifies a new Plants Based category, while nearly 10% of proposals are too diverse to group into further categories.Source: §3 · p. 7, Figure 2 · p. 8, Figure 3 · p. 9

3.1 Breeding-based Evolutionary Algorithms

• Breeding-based algorithms evolve populations through generations of reproduction and survival, with offspring introducing variation that can improve search over the solution space.Individuals represent candidate solutions with fitness values; reproduction is the defining feature, while mutation and other operators may also be used.Source: §3.1 · p. 9
• The reviewed breeding-based category includes classical Genetic Algorithms, Evolution Strategies, and Differential Evolution, alongside proposals inspired by organisms such as queen bees and weeds.Source: §3.1 · p. 9

3.2 Swarm Intelligence based Algorithms

• Swarm Intelligence describes collective behavior in decentralized, self-organized systems, with PSO and ACO among the early optimization algorithms and ABC, FA, and GOA among later examples.The term was introduced by Gerardo Beni and Jing Wang in 1989.Source: §3.2 · pp. 9, 11
• SI is the study’s most populated category, grouping algorithms by flying, terrestrial, aquatic, or microorganism inspiration and distinguishing foraging from movement patterns.When an algorithm draws on both movement and foraging, the first taxonomy catalogs it as foraging.Source: §3.2 · p. 11

3.2.1 Subcategories of SI based algorithms by the environment

• The environment-based SI taxonomy groups inspirations by aerial, terrestrial, or aquatic habitat, because environmental conditions shape animals’ movement and hunting modes.The broader animal taxonomy also includes microorganisms.Source: §3.2.1 · p. 11, §3.2 · p. 11

3.2.2 Subcategories of SI based algorithms by the inspirational behavior

• The behavior-based taxonomy separates movement inspiration, such as bird flight in PSO, from foraging inspiration, such as ants’ food-location signaling in ACO.Movement may describe an animal’s own trajectory or population movement; foraging includes food-search mechanisms, even when they also involve movement, and is increasingly explicit in algorithm names.Source: §3.2.2 · p. 18

3.3 Physics/Chemistry based Algorithms

• These algorithms imitate physical phenomena such as gravitational forces, electromagnetism, electric charges, and water movement, or chemical reactions and gas-particle movement.Source: §3.3 · p. 18
• Reviewed methods include Simulated Annealing and Gravitational Search Algorithm (GSA), alongside space-based algorithms such as Black Hole optimization and Galaxy Based Search Algorithm [393].The category’s complete lists are provided in Tables 9 and 10 for physics-based algorithms and Table 11 for chemistry-based methods.Source: §3.3 · p. 18
• Harmony Search is linked to music composition and, through its use of sound waves, is described as closer to physical algorithms than social-human-behavior algorithms.Source: §3.3 · p. 18

3.4 Social Human Behavior based Algorithms

• Examples span ideology expansion and competition (Ideology Algorithm, IA), politics (Imperialist Colony Algorithm, ICA), sports (Soccer League Competition Algorithm, SLC), and brainstorming (BSO.2; GBSO).The complete category list is presented in Tables 12 and 13.Source: §3.4 · p. 18

3.5 Plants based Algorithms

• Forest Optimization Algorithms (FOA.1,) are a well-known example, inspired by plant reproduction.Table 14 details the algorithms classified in this category.Source: §3.5 · p. 18

3.6 Algorithms with Miscellaneous Sources of Inspiration

• The category includes algorithms that do not fit prior categories, such as Ying-Yang Pair Optimization (YYOP).It contains algorithms with diverse characteristics.Source: §3.6 · p. 18
• Although heterogeneous and non-uniform, the category exemplifies the diverse sources of inspiration in the literature and can seed new categories when similar concepts recur.The authors’ goal is to create new categories as more algorithms recreate inspirational concepts already represented in this assorted group.Source: §3.6 · p. 23
• Without grouping assorted algorithms into categories, continued stockpiling would prevent the taxonomy from evolving and undermine its purpose of systematically sorting and easing analysis of future advances.The complete list of algorithms in this category appears in Tables 15 and 16.Source: §3.6 · p. 23

4.1.1 Differential Vector as a Function of the Entire Population

• When the entire population guides movement, each individual influences the others, typically with weights based on fitness differences or distances between solutions.In FA, closer, better solutions exert stronger moving forces on the reference solution.Source: §4 · p. 25, §4.1.1 · p. 27

4.1.2 Differential Vector as a Function of Representative Solutions

• 69% versus 31% of the 518 reviewed algorithms use differential vector movement rather than solution creation; nearly 60% of all proposals move toward representative solutions, chiefly the current best.Representative-solution methods include PSO and most DE variants; the analysis says more than half of all proposals belong to this subcategory.Source: §4 · p. 25, Figure 5 · p. 26, §4.1.2 · p. 27

4.1 Differential Vector Movement

• Differential vector movement generates a candidate by shifting or mutating a reference solution, which may replace it or compete for inclusion in the population.The direction and intensity of movement may use attraction toward better solutions and repulsion from worse or other solutions; its mathematics usually favors numerical, often real-valued, representations.Source: §4.1 · p. 27

4.1.3 Differential Vector as a Function of a Group of Solutions

• Group-based movement uses either a solution’s subpopulation or its local neighborhood, rather than representative solutions from the whole population.Subpopulation-based methods include LA and MBO; BFOA uses neighborhood solutions that can attract or repel according to relative fitness. PSO variants may also fall into this group, while classical PSO is assigned to the representative-solutions group.Source: §4.1.3 · pp. 27–28, §4.1 · p. 27

4.2 Solution Creation

• Solution creation generates candidates without moving a single existing solution, and its adaptable mechanisms can accommodate different solution representations and problem types.This category accounts for almost 31% of proposals and includes classical GA.Source: §4 · p. 25, §4.2 · p. 28

4.2.1 Creation by Combination

• Combination creates new solutions by crossing or otherwise combining multiple existing solutions, a behavior exemplified by GA.The combining method may be problem-specific or designed for a broader family of problems, and can be adapted to different representations; similar behavior appears across algorithms with different inspiration sources.Source: §4.2.1 · pp. 28, 37

4.2.2 Creation by Stigmergy

• Stigmergy creates solutions through indirect coordination mediated by an information-bearing structure, as in ACO, where pheromone trails guide later ants’ choices.The reviewed stigmergy group is smaller than preceding categories, mostly insect-inspired swarm methods, but also includes physics-inspired water-flow and river-formation methods.Source: §4.2.2 · p. 37

5.1 Comparison Between both Taxonomies

• The taxonomies are weakly related: algorithms with different inspirations can behave similarly, while algorithms sharing an inspiration can use different search procedures.GFA and ABO resemble PSO; in contrast, dolphin-inspired DE creates solutions by combination, whereas Dolphin Partner Optimization resembles PSO movement.Source: §5.1 · pp. 37, 42
• More than half of reviewed algorithms (almost 60%) use differential vector movements, a behavior found across every inspiration category.The largest behavioral subcategory includes examples inspired by social human behavior, microorganisms, physics and chemistry, breeding, and plants.Source: §5.1 · pp. 37, 42
• 23% of reviewed algorithms (122 of 518) were incremental variants of classical algorithms, while 396 (about 77%) were considered new proposals.The authors nevertheless note that a significant percentage of the latter lacked originality or justification, including comparison with the state of the art and attention to optimization quality.Source: §5.1 · p. 42, Table 32 · p. 42

5.2 Identification of the Most Influential Algorithms

• PSO appeared in 11% of reviewed literature, nearly 47% of proposals clearly based on a previous algorithm; GA and DE each appeared in around 5%.The analysis attributes PSO's influence to its simplicity and ability to reach an optimum quickly; GA combines solutions, while DE uses linear combinations of population solutions.Source: §5.2 · pp. 42, 44
• About 14% of studied algorithms were variations of Swarm Intelligence methods, while Evolutionary Algorithms and GA were each used in almost 5% of reviewed cases.The authors observe that GA and SA influence appears to be declining relative to DE and PSO.Source: §5.2 · p. 44
• The section concludes that more than half of proposals are minor versions of PSO, DE, or GA, despite the growing number of natural and biological inspirations.It argues that these inspiration sources have not produced significantly disruptive algorithmic behaviors.Source: §5.2 · p. 44

1. The behavior is more relevant than the natural inspiration

• Research should prioritize algorithms’ behavior and properties over novel inspiration sources, since algorithms with different inspirations can behave similarly.Relevant properties include performance, simplicity, parallelizability, and suitability for specific problem types.Source: §6 · p. 44

2. Nature-based terminology can make it more difficult to understand the proposal

• Researchers should describe algorithm components in inspiration-agnostic mathematical terms and explicitly map any nature-based terminology to optimization concepts.Excessive unexplained domain vocabulary can make proposals difficult to understand and replicate.Source: §6 · p. 44

3. Good comparisons are crucial for new proposals

• New proposals need fair comparisons against competitive, state-of-the-art algorithms, not only basic classical methods or algorithms from the same semantic niche.The authors argue that weak comparisons hinder real-world application and community uptake.Source: §6 · p. 44

4. Many proposals have a very limited influence

• Some reviewed proposals have little influence after publication, so researchers should test algorithms on varied problems, including benchmark functions and practical real-world problems.Such evaluation can help gauge community interest in applying a proposal to other problems.Source: §6 · pp. 44–45

5. The interest of making source code available

• Making source code publicly available can improve visibility, enable thorough comparisons, support framework inclusion, and reduce divergent implementations.The authors note that influential implementation details may be absent from algorithm descriptions.Source: §6 · p. 45

6. The role of bio-inspired algorithms in competitions

• Competition leaders are often not biologically inspired, and the authors recommend fewer proposals with better performance rather than continued proliferation.They connect this pattern to weak comparison practices and the limited adoption of these algorithms as reference designs.Source: §6 · p. 45

7.1 The Good: A Present and Future Plenty of Exciting Applications

• Applications span engineering, academic competitions, and machine learning, where evolutionary algorithms support model design, neural architecture search, and other AI systems.Examples include civil engineering and NASA antenna design, DE’s role in competition winners, and applications in deep learning and neural architecture search.Source: §7.1 · pp. 45–46

7.2 The Bad: Novel Metaphors Not Leading to Innovative Solvers

• Despite more than 500 proposals by 2024, metaphor-distinct solvers are often mathematically similar to existing algorithms, and some reiterate PSO.The section notes that the growing number of alternatives makes it harder to choose suitable methods, while mathematical diversity does not match diversity of inspiration.Source: §7.2 · p. 46
• Critiques in question whether some metaphors reflect real phenomena and whether related variants or repeated proposals by the same researchers constitute genuine contributions.Examples include Cat Swarm Optimization, algorithm families inspired by gravitational forces or water, and multiple methods based on the same nature-inspired idea.Source: §7.2 · pp. 46–47
• Simplifying L-SHADE-EpSin and UMOEA-II by removing structurally biasing operators made them more transparent and easier to use, and could improve performance.The study identifies operators that bias sampling toward parts of the decision space and argues other metaheuristics may contain unnecessary or harmful operators.Source: §7.2 · p. 47
• Analyses found Intelligent Water Drops’ main components to be simplifications or special cases of ACO, while Cuckoo Search was characterized as an evolutionary strategy with elements of DE.The latter review concluded that neither the Cuckoo Search metaphor nor algorithm was useful for stochastic optimization.Source: §7.2 · p. 47
• Most algorithms examined in did not produce lifelike features or accurately reflect their analogues, while identified several named methods as variants of PSO and evolutionary strategies.The analyses respectively examined eight nature-inspired algorithms and six algorithms including grey wolf, moth-flame, whale, firefly, bat, and antlion methods.Source: §7.2 · p. 48

7.3 The Ugly: Poor Methodological Practices (Questionable Reproducibility and Comparability)

• 47 of 90 algorithms compared in showed centre bias, and flawed comparisons, biased benchmarks, and overlooked statistical significance undermine claims of competitiveness.The section warns that centre-biased results do not establish suitability for real-world problems and that weak comparison counterparts can make benchmark gains misleading.Source: §7.2 · pp. 47–48, §7.3 · p. 48
• The section flags irreproducible studies and urges state-of-the-art comparisons, standard benchmarks, adequate statistical testing, and evidence of performance, design innovation, or practical benefits.Many studies lack available implementations or information needed for replication; also calls for standard terminology, useful novel concepts, and scientifically justified metaphors.Source: §7.2 · p. 47, §7.3 · p. 48

8.1 Bio-inspired computation: Where we stand and what’s next

• Research priorities include stronger theoretical analysis, reliable modeling and change detection for dynamic or stochastic problems, and scalable, novel approaches for multi- and many-objective optimization.Theoretical work should examine fitness landscapes, diversity, exploration–exploitation balance, and convergence; multiobjective research also needs hybrid approaches and better scalability.Source: §8.1 · p. 49
• Other promising directions span multimodal optimization, topology and surrogate assistance, and distributed evolutionary algorithms for expensive or large-scale problems.Suggested approaches include hybridizing multimodal solvers, combining topologies with ensembles, using deep-learning models in high-dimensional search, and developing asynchronous parallel multiobjective solvers.Source: §8.1 · p. 49
• Further priorities concern large-scale search, ensembles and hyper-heuristics, memetic algorithms, parameter control, and stronger benchmarks and comparisons.Topics include variable grouping, ensemble complexity and low-level component selection, memetic hybridization and self-adaptation, sensitivity analysis and fair parameter tuning, and real-world benchmarks, scalability, and Bayesian tests.Source: §8.1 · pp. 49–50

8.2 Separating the Wheat from the Chaff: Fair and Right Comparisons

• To counter proposals with limited impact, recommends stating hypotheses, analyzing components and search phases, tuning parameters, comparing with state-of-the-art methods, and explaining the proposal’s value.A proposal may merit attention through competitiveness or methodological contributions that enable further research.Source: §8.2 · pp. 50–51
• Fair comparisons require representative benchmarks, analysis of problem characteristics and benchmark bias, and statistical validation with appropriate tests and visualizations.Conclusions depend on the test environment, and raw-result tables alone are insufficient for robust validation.Source: §8.2 · p. 51

8.3 Bridging Theory and Practice in Bio-inspired Optimization: Application to real-world Problems

• The tutorial offers a constructive, comprehensive process for quality research, covering the steps from problem modeling through algorithm validation and implementation.Its recommendations aim to correct misconceptions and poor methodological habits and to promote metaheuristics that are designed and tested for practical real-world use.Source: §8.3 · p. 52
• The proposed workflow covers problem formulation, metaphor-free algorithm design aligned with problem constraints, performance assessment and replicability, and deployment in a real environment.The assessment stage follows the comparison practices summarized in Subsection 8.2.Source: §8.3 · p. 52

9.1 Good Practices for Designing Metaheuristics

• Researchers propose methods to assess novelty, design metaheuristics, and statistically compare them amid concerns about novelty in the evolving field.The section frames these as problems to address to keep the field progressing.Source: §9.1 · p. 53, §9 · p. 53
• Studies use Markov-chain formulations and Spearman correlation to examine conceptual and experimental novelty, pool templates to reveal special-case relationships, and reusable infrastructure to support reproducibility.The pool-template study reviewed 15 metaheuristics; the infrastructure combines reusable algorithm templates, white-box problem descriptions, and remotely accessible components and problems.Source: §9.1 · p. 53
• A mathematical discriminant separates root from homologous algorithms [26]; Harmony Search, Backtracking Search Optimization, Grey Prediction Evolution, Grey Wolf Optimizer, and Gaining-sharing Knowledge-based are classified as homologous to classical algorithms.The proposed orientation is to transform nature metaphors into new structures.Source: §9.1 · pp. 53–54
• A population-dispersion strategy shifts between exploration and exploitation and improved nearly 60 algorithms [30], while a bias test was failed by Grey Wolf, Whale, and Harris Hawk but passed by DE, GA, and PSO.The strategy estimates dispersion from the standard deviation of individuals’ historical locations in recent generations; the test compares behavior across independent runs at two local optima.Source: §9.1 · p. 54

9.2 Latest Metaheuristics based Taxonomies, Overviews, and General Approaches

• A component-based taxonomy groups optimization methods as hill-climbing, trajectory, population-based, surrogate, or hybrid, while an initialization taxonomy covers random, learning, generic, and local-search methods.The first study notes shared components and search strategies across algorithms; the second offers guidance for diverse initial solutions and constrained or discrete optimization.Source: §9.2 · pp. 54–55
• Recent reviews question novelty and minor modifications, distinguish trajectory from population methods, survey advantages and limitations, and trace 50 years while flagging fragmentation, weak theory, tuning, and benchmark gaps.The review of over 100 algorithms finds many new proposals improve established methods; its analysis of Black Widow and Coral Reef Optimization identifies combinations of existing evolutionary operators.Source: §9.2 · pp. 54–55
• A 2024 benchmark overview catalogs over 200 mathematical test functions and more than 50 engineering design problems for evaluating new metaheuristics.It describes each function’s variables and value range.Source: §9.2 · p. 55
• Learn to Optimize approaches train performance-prediction models, single solvers, or solver portfolios to accelerate configuration for unseen instances.These correspond to automated algorithm selection, automatic algorithm configuration, and the more flexible portfolio approach; L2O also applies to general-purpose methods and adversarial attacks.Source: §9.2 · p. 55

10 Conclusions

• 24% of the 518 reviewed proposals were versions of classical algorithms such as PSO, DE, or GA, amid broader algorithmic similarities across different inspirations.The review’s two taxonomies classify algorithms by source of inspiration and behavior in generating candidate solutions.Source: §10 · p. 56
• The review organizes existing and new schemes into two taxonomies: one based on inspiration source and the other on behavior in generating candidate solutions.It provides category descriptions, examples, and an enumeration of the reviewed approaches.Source: §10 · p. 56
• Novel biological metaphors often do not yield innovative solvers, while inadequate comparisons hinder reproducibility and applicability; future studies should follow sound design, description, and comparison practices.The authors also identify weak justification, insufficient comparison with the state of the art, and limited focus on quality for well-known optimization problems.Source: §10 · p. 56
• Bio-inspired algorithms are contributing to DL evolution, LLM design, and GPAIS, with examples including POET, EUREKA, EvoPrompt, and EGANs.The authors frame AI algorithms enhancing other AI systems as an important paradigm for these applications.Source: §10 · p. 56
• The field’s excessive emphasis on biological framing over real problem-solving must be addressed with guidelines for designing metaheuristics suited to emerging, complex optimization challenges.The report notes this evolution in its update, released four years after the original version.Source: §10 · p. 56