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

Daniel Molina, Javier Poyatos, Javier Del Ser, Salvador García, Amir Hussain, Francisco Herrera

arXiv:2002.08136v5cs.AI

TL;DR

The paper addresses how the rapid proliferation of nature- and bio-inspired algorithms complicates coherent organization and evaluation. It classifies 518 algorithms through inspiration-based and behavior-based taxonomies, critically examining their similarities and methodological practices. The analysis finds substantial overlap with classical algorithms and motivates stronger standards for comparison, reproducibility, and practical relevance.

  • Problem

    The rapid growth of metaphor-based proposals has created a need to organize algorithms coherently and evaluate their novelty and competitiveness fairly.

  • Method

    The study reviews 518 algorithms, groups them by inspiration source and solution-generation behavior, and compares similarities across proposals.

  • Results

    24% of reviewed proposals were identified as versions of classical algorithms such as PSO, DE, or GA.

  • Takeaways & Limitations

    The findings support emphasizing behavioral differences, verifiable evidence, fair comparisons, and reproducible studies in future bio-inspired optimization research.

  • Takeaways & Limitations

    Published competitiveness claims are often difficult to reproduce because implementations or essential experimental information are unavailable or unreported.

Abstract

from arXiv · show

In recent years, bio-inspired optimization methods, which mimic biological processes to solve complex problems, have gained popularity in recent literature. The proliferation of proposals prove the growing interest in this field. The increase in nature- and bio-inspired algorithms, applications, and guidelines highlights growing interest in this field. However, the exponential rise in the number of bio-inspired algorithms poses a challenge to the future trajectory of this research domain. Along the five versions of this document, the number of approaches grows incessantly, and where having a new biological description takes precedence over real problem-solving. This document presents two comprehensive taxonomies. One based on principles of biological similarity, and the other one based on operational aspects associated with the iteration of population models that initially have a biological inspiration. Therefore, these taxonomies enable researchers to categorize existing algorithmic developments into well-defined classes, considering two criteria: the source of inspiration, and the behavior exhibited by each algorithm. Using these taxonomies, we classify 518 algorithms based on nature-inspired and bio-inspired principles. Each algorithm within these categories is thoroughly examined, allowing for a critical synthesis of design trends and similarities, and identifying the most analogous classical algorithm for each proposal. From our analysis, we conclude that a poor relationship is often found between the natural inspiration of an algorithm and its behavior. Furthermore, similarities in terms of behavior between different algorithms are greater than what is claimed in their public disclosure: specifically, we show that more than one-fourth of the reviewed solvers are versions of classical algorithms. The conclusions from the analysis of the algorithms lead to several learned lessons.

1 Introduction

The introduction motivates organizing the rapidly expanding nature- and bio-inspired optimization literature by both inspiration source and algorithmic behavior. It presents a comprehensive analysis intended to distinguish meaningful behavioral differences, assess similarities, and encourage stronger evaluation practices.

  • Traditional optimization can be unsuitable for complex real-world problems lacking affordable exact solvers or analytical objective and constraint forms.
  • The literature’s rapid growth has made it difficult to organize algorithms and assess whether new biological metaphors produce genuinely distinct solvers.
  • The study classifies 518 works using two taxonomies based on inspiration source and the procedure for generating new solutions.
  • The dual classification places proposals in context by exposing algorithmic similarities and differences alongside their inspirational origins.
  • The report combines taxonomy construction with critical analysis of field strengths, weaknesses, challenges, applications, and methodological practices.
  • Its recommendations call for behavioral novelty, verifiable performance evidence, fair comparisons, reproducibility, and attention to practical optimization problems.

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

Earlier studies organized bio- and nature-inspired algorithms by problem type, inspiration, or selected behavioral principles, but lacked the scope or structure of the present taxonomy. The reviewed literature therefore motivates a dual classification that also examines structural similarities with classical algorithms.

  • Prior surveys covered continuous, combinatorial, multi-objective, and other specific optimization problems, reflecting the field’s broad application diversity.
  • Algorithm-specific reviews analyzed variants of PSO, DE, ABC, BFOA, and Bat Algorithm, while other studies examined individual algorithmic features.
  • Many comparison studies evaluated algorithms mainly to recommend which approach to use for a given problem.
  • Earlier classifications grouped algorithms by biological, physical, chemical, evolutionary, swarm, or human inspiration, but some were not hierarchical taxonomies.
  • The present work combines inspiration-source and behavior-based organization, addressing prior limitations in coherence, thoroughness, and structural comparison with classical meta-heuristics.

3 Taxonomy by Source of Inspiration

The paper introduces a hierarchical taxonomy based on claimed inspirational sources to organize 518 nature- and bio-inspired algorithms. It balances informative distinctions with a manageable structure and reports category distributions.

  • The taxonomy classifies algorithms by the natural or biological inspiration claimed as their design rationale.It is intended to group the growing number and variety of proposals consistently.
  • 518 papers, spanning classical proposals from the late 1980s through techniques published until 2024, were reviewed.The authors describe this as the most exhaustive review in the area to date.
  • Algorithms are organized hierarchically, with categories at the same level treated as disjoint sets.Each proposal is assigned to the category considered most suitable for its algorithmic nuances.
  • The taxonomy seeks a trade-off between information and simplicity by controlling category splits and subcategory counts.Categories should remain useful without producing overly complex hierarchies or incohesive groups.
  • 53% of reviewed algorithms belong to Swarm Intelligence, followed by almost 15% in Physics and Chemistry and 11% in Social Human Behavior.These figures describe the largest reported source-based categories.

3.1 Breeding-based Evolutionary Algorithms

The taxonomy describes breeding-based evolution and Swarm Intelligence as distinct inspiration patterns within population-based optimization. Swarm Intelligence is further organized by animal type, environment, and behavioral pattern.

  • Breeding-based Evolution: Breeding-based Evolution algorithms represent solutions as individuals with fitness values and iteratively apply reproduction and survival.These mechanisms can move populations toward higher-quality regions of the search space.
  • Breeding-based Evolution: Classical Genetic Algorithm, Evolution Strategies, and Differential Evolution appear alongside algorithms inspired by queen bees and weeds.Table 2 compiles reviewed algorithms in the Breeding-based Evolution category.
  • Swarm Intelligence: Swarm Intelligence algorithms model collective behavior emerging from groups of simple agents governed by simple behavioral rules.The category is associated with animal societies such as insect colonies and bird flocks.
  • Swarm Intelligence: The Swarm Intelligence category is divided into flying animals, terrestrial animals, aquatic animals, and microorganisms.This environmental and animal-type grouping is reflected across Tables 3–8.
  • Swarm Intelligence: Examples include PSO and ABC for flying animals, ACO and GWO for terrestrial animals, and WOA and KH for aquatic animals.These examples connect the animal-type categories to established algorithms.
  • Swarm Intelligence: Within Swarm Intelligence, algorithms are also classified by movement or foraging behavior.Movement concerns how animals travel, whereas foraging concerns how they obtain food.

3.3 Physics/Chemistry based Algorithms

Physics- and chemistry-based algorithms imitate physical or chemical phenomena rather than biological organisms. Reviewed examples include classical methods and newer algorithms rooted in established physical approaches.

  • Physics-based algorithms imitate gravitational forces, electromagnetism, electric charges, and water movement.Chemistry-based methods imitate chemical reactions and gas-particle movement.
  • The reviewed category includes Simulated Annealing and Gravitational Search Algorithm among its established examples.The complete lists are provided in Tables 9–11.
  • Several space-based algorithms are described as rooted in Gravitational Search Algorithm.The passage identifies this as an example of lineage within the physics-based category.

3.4 Social Human Behavior based Algorithms

Social Human Behavior algorithms draw inspiration from human social concepts, including decision-making, ideological competition, politics, sports, and brainstorming.

  • Social Human Behavior algorithms emulate decision-making and the expansion or competition of ideologies within society.Examples include Ideology Algorithm and Imperialist Colony Algorithm.
  • The category also includes algorithms inspired by political concepts, sports competitions, and brainstorming processes.Soccer League Competition Algorithm is given as a sports-based example.

3.5 Plants based Algorithms

Plant-based algorithms draw their search process from plants and differ from Swarm Intelligence methods because agents do not communicate.

  • Plant-based algorithms are inspired by plants.
  • Unlike Swarm Intelligence methods, these algorithms involve no communication between agents.
  • Forest Optimization Algorithm is a prominent example, inspired by plant reproduction.

3.6 Algorithms with Miscellaneous Sources of Inspiration

The miscellaneous category collects algorithms whose inspirations do not fit earlier categories, while highlighting the need to organize future proposals into meaningful groups.

  • The miscellaneous category includes algorithms that do not fit any previous inspiration category.Ying-Yang Pair Optimization is given as an example.
  • Its members have diverse characteristics and lack a uniform algorithmic or inspirational structure.
  • The category is intended to support new categories when future algorithms reproduce similar inspirational concepts.
  • Without clearer grouping, accumulating algorithms in the miscellaneous category would prevent the taxonomy from systematically organizing future advances.

4 Taxonomy by Behavior for Population based Nature- and Bio-inspired Optimization

The behavior taxonomy classifies population-based algorithms independently of inspiration by focusing on how new solutions are generated. It distinguishes differential vector movement from solution creation, with differential movement dominating the reviewed proposals.

  • The behavior taxonomy sorts algorithms by operational behavior without regard to their inspirational source.
  • Differential Vector Movement generates new solutions by shifting or mutating a reference solution, which may then compete with existing solutions.
  • Solution creation generates candidates by combining several solutions or using comparable mechanisms rather than mutating one reference solution.Combination or crossover, as in GA, is one example.
  • 69% of the 518 reviewed algorithms use Differential Vector Movement, compared with 31% using Solution Creation.
  • Almost 60% of all reviewed proposals use movement vectors oriented toward the current best or other representative solutions.
  • Stigmergy-based solution creation is a smaller category that includes mostly insect-inspired Swarm Intelligence algorithms and some physics-inspired methods.

5 Taxonomies Analysis: Comparison and More Influential Algorithms

Comparing the taxonomies shows that biological inspiration and algorithmic behavior are weakly related, while many apparently novel proposals resemble classical algorithms. The analysis therefore emphasizes behavior as the more informative basis for comparison.

  • 5.1 Comparison Between both Taxonomies: The two taxonomies show no strong relationship between an algorithm’s inspirational model and its search behavior.Algorithms inspired by different concepts can resemble PSO, while algorithms sharing inspiration can use different procedures.
  • 5.1 Comparison Between both Taxonomies: Almost 60% of the reviewed algorithms fall into representative-solution-guided Differential Vector Movement across diverse inspiration categories.
  • 5.1 Comparison Between both Taxonomies: Algorithmic behavior is more informative than natural or biological inspiration for understanding similarities among proposals.
  • 5.1 Comparison Between both Taxonomies: 23% of reviewed algorithms, 122 out of 518, were identified as incremental variants of classical algorithms.
  • 5.2 Identification of the Most Influential Algorithms: PSO was the most influential classical reference, appearing in 11% of the reviewed literature and almost 47% of clearly derivative proposals.
  • 5.2 Identification of the Most Influential Algorithms: More than half of the reviewed proposals were incremental versions of PSO, DE, or GA.

6 Learned Lessons and Recommendations from the Analysis of the Evolution of Bio-Inspired Optimization

The analysis yields recommendations emphasizing algorithmic behavior, transparent terminology, fair comparisons, broader evaluation, and community-accessible code over merely novel natural inspirations.

  • Algorithmic behavior and properties should matter more than the natural inspiration when designing optimization algorithms.Relevant properties include performance, simplicity, parallelizability, and suitability for specific problem types.
  • Nature-based terminology should be paired with standard optimization language to improve understanding and replication.The correspondence between biological-domain vocabulary and optimization terminology should be explicitly indicated.
  • New proposals need comparisons with competitive or state-of-the-art algorithms rather than only naive classical versions or methods from the same semantic niche.Outperforming basic GA or PSO versions does not establish competitive performance.
  • Algorithms with limited influence should be evaluated across diverse benchmark and real-world problems to assess broader community interest.Some reviewed proposals generated few improved versions or applications after publication.
  • Source-code availability can increase visibility and support implementation beyond what a paper specification alone provides.Published descriptions may omit implementation details needed for clean replication.
  • Competition outcomes suggest that high-performing solvers are often not biologically inspired, while continual proposal growth may divert effort from fewer, better-performing methods.Some successful algorithms retain nature-inspired roots, particularly DE.

7 A Short Reflection on The Good, the Bad and the Ugly

The paper describes a field crowded by metaphor-based proposals, including algorithms criticized as mathematically redundant, physically unsupported, or weakly validated and reproduced.

  • The abundance of bio-inspired alternatives makes algorithm selection difficult and can conceal mathematical similarity to existing methods.Different metaphors may correspond to closely related algorithmic structures.
  • Several named algorithms have been rewritten or analyzed as variants of PSO, evolutionary strategies, ACO, or DE rather than novel methods.Examples include grey wolf, firefly, bat, Intelligent Water Drops, and Cuckoo Search.
  • Some proposed inspirations do not faithfully represent the behavior of their physical or biological analogues.Cat Swarm Optimization is cited as an example because real cats do not appear to cooperate as a swarm.
  • More than 80 researchers called for editorial policies requiring standard optimization descriptions, novelty, and adequate validation for metaphor-based algorithms.The appeal responds to useless metaphors, limited novelty, and poor experimental comparison.
  • Centre-biased operators can favor benchmark optima and make comparisons misleading; in one study, 47 of 90 algorithms exhibited centre-bias.On shifted problems, the worst-performing algorithm barely exceeded random search.
  • Fair evaluation is undermined by weak baselines, benchmark bias, missing statistical significance testing, and unavailable implementations or experimental details.These practices weaken evidence for competitiveness and prevent third-party verification.
  • A novel metaphor alone is insufficient; proposals should demonstrate state-of-the-art performance, mathematical innovation, or practical non-functional benefits.The recommended evidence includes modern techniques, standard benchmarks, and suitable statistical testing.

8 Three Propositional Discussions about Nature- and Bio-Inspired Optimization

The discussion revisits methodological guidance and identifies research directions spanning theoretical analysis, adaptive and scalable optimization, real-world applications, and fair evaluation.

  • The paper combines research challenges, comparison guidelines, and a tutorial covering problem modeling, algorithm design, experimentation, implementation, and validation.This extends beyond guidance focused on only one phase or domain.
  • Research directions: Theoretical work should study fitness landscapes, diversity, local-global search balance, convergence conditions, speed, and stability.These analyses aim to clarify how algorithms perform across problem families.
  • Research directions: Dynamic and stochastic optimization needs reliable real-scenario models, diversity control, and change-detection mechanisms.Detection mechanisms can rely on characteristics of the optimization algorithm.
  • Research directions: Multi- and many-objective optimization requires new solver designs and better scalability with increasing numbers of objectives.Potential approaches include radically new methods and hybridization, but existing solvers often scale poorly.
  • Research directions: Promising directions include multimodal solvers, topology-ensemble combinations, surrogate assistance, distributed EAs, and ensemble or hyper-heuristic methods.These directions target exploration, exploitation, expensive evaluations, parallelism, encoding, and computational complexity.
  • Methodological guidance: Parameter sensitivity analysis and self-adaptation can improve tuning, while fair comparisons require comparable tuning procedures.Parameter adaptation may reduce the number of values that must be tuned.
  • Methodological guidance: Benchmark selection should reflect diverse problem characteristics, and validation should combine appropriate statistical tests with visualization.Raw result tables alone are insufficient for comparative evaluation.
  • Methodological guidance: The abundance of low-impact proposals makes comparative best practices against competitive algorithms and the state of the art especially important.The paper presents fair comparison guidance to clarify the evidence for competitiveness.

9 A Short Recent Literature Analysis: Good Practices, Taxonomies, Overviews, and General Approaches

Recent literature develops taxonomies, novelty tests, algorithm templates, design guidance, bias tests, and benchmark resources to address limited novelty and inconsistent evaluation.

  • Recent studies identify lack of novelty as a continuing problem and propose methods for novelty assessment, metaheuristic design, and statistical comparison.The reviewed approaches span conceptual, mathematical, experimental, and infrastructure-based analyses.
  • Novelty detection has used Markov-chain formulations, Spearman correlations, decomposition templates, and infrastructure for reusable algorithm and problem components.These tools analyze algorithms at conceptual, experimental, or implementation-support levels.
  • Manual and automatic metaheuristic design are presented as alternative approaches, with manual design relying partly on designer intuition and external inspiration.Automatic approaches address the search for effective designs in large spaces.
  • A 2024 discriminant separates root algorithms from homologous algorithms according to the innovation of their reproduction operators.Several named algorithms are classified as homologous to classical algorithms.
  • Guided learning strategies can adjust exploration and exploitation across iterations, while statistical tests can detect origin bias through differing choices between local optima.These methods target performance improvement and undesirable search bias.
  • Other overviews classify algorithms by components, control parameters, trajectory versus population behavior, initialization methods, or benchmark functions and applications.The reviewed resources cover taxonomies, terminology, initialization, more than 200 mathematical functions, and over 50 engineering problems.

10 Conclusions

The field’s rapid growth has made it difficult to assess meaningful algorithmic progress, while the review identifies substantial overlap among supposedly distinct bio-inspired methods. The authors therefore emphasize methodological rigor and redirect attention toward real optimization challenges, while recognizing potential applications in modern AI.

  • The expanding literature has made it difficult to appraise the field’s trajectory and identify scientifically valuable, practically impactful research trends.
  • The review finds that many algorithms claiming different natural inspirations exhibit algorithmic similarities.
  • 24% of the reviewed proposals are versions of classical algorithms such as PSO, DE, or GA.
  • Novel metaphors often fail to produce new solvers, while inadequate comparisons create reproducibility and applicability problems.
  • Bio-inspired algorithms have potential applications in modern AI, including deep-learning evolution, large language models, and GPAIS.
  • The field should address excessive emphasis on biological approaches relative to solving real and complex optimization goals.
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