A Behavior-Centric Taxonomy for Swarm Intelligence: Reclassifying Algorithms Based on Bio-Inspired Mechanisms

Swarm Intelligence (SI) represents a significant paradigm within artificial intelligence, drawing inspiration from the collective behaviors of natural systems to solve complex computational problems. However, the conventional classification of SI algorithms often groups them monolithically or based on superficial characteristics like the inspiring organism, obscuring crucial differences in their underlying operational mechanisms. This article addresses this limitation by proposing a novel taxonomy for SI algorithms grounded primarily in the distinct bio-inspired behavioral mechanisms they emulate. The article defines SI and its core principles, surveys major algorithms and their biological roots, analyzes the distinct behavioral and computational strategies employed, and critically reviews existing classification schemes. Synthesizing these findings, a behavior-centric taxonomy is proposed, featuring categories such as Stigmergic Coordination, Neighbor-Interaction Coordination, Role-Based Coordination, Signal-Based Attraction, and Gradient/Chemotactic Systems. Each category is characterized by its core behavioral inspiration, key computational features, and representative algorithms. This taxonomy aims to provide a more nuanced understanding of SI diversity, facilitate informed algorithm selection, guide principled hybridization, and stimulate future research by highlighting the functional distinctions inherent in different modes of collective intelligence.

1. The Nature and Scope of Swarm Intelligence

1.1. Defining Swarm Intelligence (SI): Core Concepts and Principles

Swarm Intelligence (SI) is formally defined as the collective behavior that emerges from decentralized, self-organized systems, which can be either natural or artificial. Introduced in the context of cellular robotic systems, the concept now permeates significant areas of artificial intelligence (AI) and computational intelligence (CI). SI systems are typically composed of a population of relatively simple agents, often termed 'boids' or particles, which interact locally with one another and with their surrounding environment. A defining characteristic of the field is its deep grounding in biological inspiration; SI explicitly mimics the collective actions observed in natural systems such as ant colonies foraging for food, birds flocking, fish schooling, honeybee colonies coordinating tasks, or even bacterial colonies navigating chemical gradients. This reliance on biological blueprints is not merely illustrative but forms the foundational identity of SI, suggesting that the nuances of these natural strategies are critical to understanding the resulting algorithms. The remarkable capabilities of SI systems arise from a set of fundamental principles governing their operation:

• Decentralization: SI systems operate without a central controller or global knowledge base directing individual agents. Decisions are made autonomously by agents based solely on local information and interactions. This lack of central authority is a key differentiator and confers significant advantages in terms of robustness—the failure of individual agents does not cripple the system—and scalability, as the system can readily accommodate large numbers of agents without a central processing bottleneck.

• Self-Organization: Complex global order and coherent collective patterns emerge spontaneously from simple, local interactions among agents and between agents and their environment. This process is driven by feedback loops (both positive and negative) and does not require external control or pre-programmed global plans. Self-organization allows swarms to adapt dynamically to changing conditions without explicit reprogramming. Examples include the intricate construction of termite mounds or the formation of efficient foraging trails by ants.

• Emergent Behavior: The collective actions of the swarm result in intelligent global behaviors that often surpass the capabilities of any single agent. These emergent patterns, such as the coordinated flight of a flock or the optimal pathfinding of an ant colony, arise non-linearly from the local rules and interactions and may not be easily predictable from individual agent behavior alone. It is this emergence of complex problem-solving ability from simple constituents that embodies the "intelligence" in Swarm Intelligence. This highlights a fascinating aspect of SI: the capacity of groups of simple entities, following basic rules, to collectively address problems of high complexity, such as NP-hard optimization tasks, which often challenge traditional centralized algorithms.

• Interaction and Communication: Coordination within the swarm is achieved through interactions, which can be direct (e.g., based on proximity to neighbors) or indirect. A crucial form of indirect interaction is Stigmergy, where agents communicate by modifying their environment, leaving traces (like pheromones) that influence the subsequent behavior of other agents. This mechanism, exemplified by ant trail formation, enables sophisticated coordination without requiring agents to communicate directly.

These core principles are deeply interconnected and operate synergistically. Decentralization provides the foundation, removing central control and allowing local interactions to dominate. These local interactions, governed by simple rules and feedback, drive the process of self-organization. From this self-organization, complex and adaptive emergent behaviors arise at the swarm level. The specific mode of interaction (e.g., stigmergy versus direct neighbor sensing) critically shapes the nature of self-organization and the resulting emergent intelligence. Consequently, SI systems typically exhibit desirable properties such as scalability (performance often improves with size), robustness (resilience to individual failures due to redundancy), and adaptability or flexibility (ability to respond dynamically to changing environments). These characteristics make SI a powerful approach for tackling complex, dynamic, and large-scale optimization problems across diverse domains including robotics (swarm robotics), data mining, telecommunications network routing, scheduling, bioinformatics, and industrial engineering.

1.2. The Problem: Homogenization and the Need for Nuanced Classification

Despite the richness and diversity of its biological inspirations, the field of Swarm Intelligence often treats its constituent algorithms as a relatively homogeneous group. While the collective, decentralized nature is a unifying theme, classifying algorithms simply as "SI" or grouping them broadly by the source organism (e.g., "ant-based," "bee-based") obscures significant and fundamental differences in the underlying biological strategies being modeled. For instance, algorithms inspired by different insects might rely on entirely distinct mechanisms like indirect environmental cues (ants using pheromones), complex social roles and communication (bees using waggle dances and division of labor), or broadcast signals (fireflies using light flashes). Existing taxonomies frequently rely on these organism-based labels or differentiate SI from other paradigms like Evolutionary Computation, but they generally fail to capture the crucial diversity in the specific behaviors (e.g., path-finding, flocking, hunting, cooperative transport, nest building) and the mechanisms driving these behaviors (e.g., stigmergy, neighbor alignment rules, social hierarchies, signal attraction). This lack of behavioral granularity presents several challenges. It hinders a deeper, functional understanding of why certain algorithms are better suited to particular types of problems than others. It limits the potential for informed algorithm selection, forcing practitioners to rely on empirical trial-and-error or overly broad heuristics. Furthermore, it impedes the principled development of hybrid algorithms that could potentially combine the strengths of different bio-inspired strategies. A classification system that reflects the fundamental differences in behavioral mechanisms is needed to advance the field's theoretical coherence and practical application.

1.3. Objective and Structure

This article aims to address the identified gap by proposing and justifying a novel taxonomy for Swarm Intelligence algorithms. The primary basis for this classification is the set of distinct bio-inspired behavioral mechanisms that the algorithms emulate. The objective is to create a framework that groups algorithms based on how they achieve collective intelligence through interaction and coordination, moving beyond superficial labels towards a more functional and behaviorally grounded understanding. The article follows a systematic structure to develop and present this taxonomy:

1. Introduction: Defines SI, outlines its principles, highlights the problem with existing classifications, and states the article's objective.

2. Survey of Algorithms and Inspirations: Identifies major SI algorithms and details the specific biological species and behaviors that inspired them.

3. Analysis of Behavioral Mechanisms: Examines and compares the distinct natural behavioral mechanisms mimicked by different groups of algorithms (e.g., stigmergy, flocking dynamics, division of labor).

4. Analysis of Computational Strategies: Investigates the computational techniques employed by these algorithms that reflect their differing biological inspirations (e.g., pheromone updates, velocity/position rules, role switching logic).

5. Review of Existing Taxonomies: Critically evaluates previous attempts to classify SI algorithms, focusing on their ability to capture behavioral distinctions.

6. Proposal of Behavior-Centric Taxonomy: Synthesizes the preceding analyses to propose a new set of subcategories based primarily on behavioral mechanisms.

7. Characterization of Subcategories: Describes each proposed subcategory, outlining its core behavioral inspiration, key computational characteristics, and representative algorithms.

8. Conclusion: Summarizes the proposed taxonomy, discusses its implications, benefits, limitations, and potential future directions.

2. A Survey of Major Swarm Intelligence Algorithms and Their Biological Roots

2.1. Inventory of Representative SI Algorithms

The field of Swarm Intelligence encompasses a growing number of algorithms inspired by diverse natural phenomena. To establish a foundation for behavioral analysis, this section identifies a representative set of prominent SI algorithms frequently encountered in the literature. This list, while not exhaustive, covers algorithms that exemplify the breadth of biological inspirations and computational approaches within SI:

• Ant Colony Optimization (ACO): One of the earliest and most well-known SI algorithms. Widely applied to combinatorial optimization problems.Variants include:

  • Elitist Ant System (EAS)

  • Max-Min Ant System (MMAS)

  • Rank-based Ant System (RAS)

  • Continuous Orthogonal Ant Colony (COAC)

  • Recursive Ant Colony (RAC).

• Particle Swarm Optimization (PSO): Another highly popular SI algorithm, known for its simplicity and effectiveness in continuous optimization. Inspired by social behavior like bird flocking or fish schooling.

• Artificial Bee Colony (ABC): Models the foraging behavior of honey bees, incorporating concepts like division of labor and information sharing. Effective for various optimization tasks.

• Firefly Algorithm (FA): Inspired by the flashing behavior of fireflies, using light intensity and attractiveness for optimization.

• Cuckoo Search (CSA): Based on the brood parasitic behavior of cuckoos, often incorporating Lévy flights for search exploration.

• Grey Wolf Optimizer (GWO): Mimics the social hierarchy and hunting strategies of grey wolves. Noted for having few control parameters.

• Bat Algorithm (BA): Inspired by the echolocation or bio-sonar capabilities of microbats. Involves adjusting pulse frequency, rate, and loudness.

• Artificial Fish Swarm (AFS): Simulates various behaviors of fish schools, such as foraging, swarming, and following.

• Bacterial Foraging Optimization (BFO): Models the foraging behavior of E. coli bacteria, including chemotaxis (movement along chemical gradients).

• Glowworm Swarm Optimization (GSO): Inspired by the bioluminescence of glowworms, where individuals attract others based on their light intensity (luciferin level) related to fitness.

It is worth noting that Genetic Algorithms (GA) are sometimes discussed alongside SI algorithms due to their population-based nature. However, GA fundamentally belongs to the distinct field of Evolutionary Computation (EC), relying on mechanisms of selection, crossover, and mutation rather than the agent interaction rules typical of SI. While acknowledging the conceptual overlap in population-based search, this article focuses on algorithms more strictly defined by swarm principles of local interaction and emergent coordination, generally excluding GA from the proposed SI taxonomy.

2.2. Detailed Biological Inspirations

The power and diversity of SI algorithms stem directly from the rich repertoire of collective behaviors observed in nature. Understanding the specific biological context for each major algorithm is crucial for appreciating the mechanisms they employ.

• Ant Colony Optimization (ACO): The primary inspiration is the remarkable ability of ant colonies to find the shortest path between their nest and a food source. This is achieved through stigmergy: ants deposit a volatile chemical substance called pheromone on the ground as they travel. Other ants sense these pheromones and are probabilistically more likely to follow paths with higher concentrations. Shorter paths are traversed more quickly, leading to faster pheromone accumulation and reinforcement, while pheromones on longer or unused paths evaporate over time. This positive feedback loop allows the colony to collectively converge on optimal routes.

• Particle Swarm Optimization (PSO): PSO draws inspiration from the coordinated movement of social animals like flocks of birds or schools of fish. While individual motivations are complex, simplified models like Reynolds' Boids capture key aspects using three rules: separation (avoid crowding neighbors), alignment (steer towards the average heading of neighbors), and cohesion (steer towards the average position of neighbors). PSO abstracts this by having particles adjust their trajectory based on their own best-found position ('cognitive' aspect) and the best position found by the swarm or local neighbors ('social' aspect).

• Artificial Bee Colony (ABC): This algorithm mimics the intelligent foraging strategy of honey bee colonies. Bee colonies exhibit division of labor: 'employed bees' exploit known food sources, 'onlooker bees' wait in the hive and choose food sources based on information shared by employed bees (often via the 'waggle dance'), and 'scout bees' search randomly for new food sources. This system effectively balances exploration (scouting) and exploitation (harvesting known sources).

• Firefly Algorithm (FA): FA is based on the flashing patterns observed in fireflies (Lampyridae). These flashes primarily serve as mating signals. The algorithm assumes that a firefly's brightness is proportional to its attractiveness (representing solution fitness) and that brightness decreases as the distance between fireflies increases (modeling light absorption in the environment). Less bright fireflies are attracted to and move towards brighter ones.

• Cuckoo Search (CSA): The inspiration here is the obligate brood parasitism practiced by certain species of cuckoos. These birds lay their eggs in the nests of other host bird species, often removing a host egg to increase the chances of their own offspring being raised. The algorithm models this by having cuckoos (solutions) lay eggs (new solutions) in nests (potential locations) and includes a probability that the host bird discovers and discards the cuckoo egg (representing abandonment of poor solutions). CSA often incorporates Lévy flights, a type of random walk observed in the foraging patterns of various animals.

• Grey Wolf Optimizer (GWO): GWO is inspired by the social hierarchy and cooperative hunting behavior of grey wolves (Canis lupus). Wolf packs exhibit a strict social structure with dominant leaders (alpha wolves, responsible for decisions), beta wolves (subordinates assisting alphas), delta wolves (submitting to alphas and betas), and omega wolves (lowest rank, often scapegoats). The algorithm models the hunting process (searching, encircling, and attacking prey) guided by the positions of the alpha, beta, and delta wolves, which represent the best solutions found so far.

• Bat Algorithm (BA): This algorithm is based on the echolocation behavior of microbats. Bats emit loud sound pulses and listen for the echoes bouncing off objects to navigate, detect prey, and avoid obstacles in darkness. They can dynamically adjust the frequency, pulse emission rate, and loudness of their calls depending on their proximity to a target or during different phases of hunting. BA models this by associating solutions with bats that adjust these parameters while searching for the optimal solution (prey).

• Artificial Fish Swarm (AFS): AFS simulates collective behaviors observed in fish schools. These behaviors typically include random movement (searching for food), swarming (moving towards the center of the school and avoiding overcrowding), and following (moving towards individuals in better locations, e.g., areas with more food). The algorithm uses these simulated behaviors to explore the search space.

• Bacterial Foraging Optimization (BFO): BFO models the foraging strategy of bacteria like Escherichia coli. A key component is chemotaxis, where bacteria move up concentration gradients of nutrients (attractants) and down concentration gradients of noxious substances (repellents). This involves alternating between 'runs' (swimming in a consistent direction) and 'tumbles' (random reorientations). BFO also models reproduction and elimination-dispersal events.

• Glowworm Swarm Optimization (GSO): GSO is inspired by the behavior of glowworms (larvae or wingless females of certain beetle families, including Lampyridae) that emit light. In GSO, each glowworm carries a quantity of 'luciferin' proportional to its fitness at its current location. Glowworms are attracted to neighbors within a dynamic range that are brighter (have higher luciferin levels) than themselves.

The sheer variety of these biological inspirations—spanning insects, birds, fish, mammals, and microorganisms—underscores the richness of the SI paradigm. It also strongly suggests that algorithms derived from such diverse systems are likely to possess fundamentally different operational characteristics. Modeling ant trails is inherently different from modeling wolf pack hunting or bat echolocation. Even within related groups, like insects, the specific behaviors modeled (path-finding via stigmergy in ACO, role-based foraging in ABC, signal-based attraction in FA) lead to distinct algorithmic approaches. This observation reinforces the inadequacy of classifying algorithms solely based on the organism type (e.g., "insect-based") and motivates a deeper look at the specific behavioral mechanisms being abstracted.

Furthermore, it's important to recognize that all SI algorithms are abstractions of biological reality, simplifying complex natural processes into computational rules. 

The specific aspects chosen for abstraction (e.g., communication method, movement rules, social structure) and the level of abstraction significantly influence the resulting algorithm's behavior and capabilities.

Table 1: Major SI Algorithms and Their Bio-Inspirations

Algorithm Name	Acronym	Primary Biological Inspiration (Species)	Specific Behavior Mimicked
Ant Colony Optimization	ACO	Ants (various species)	Foraging via pheromone trails (Stigmergy)
Particle Swarm Optimization	PSO	Birds (flocking), Fish (schooling)	Coordinated group movement based on individual/social bests
Artificial Bee Colony	ABC	Honey Bees (Apis mellifera)	Foraging with division of labor (employed, onlooker, scout)
Firefly Algorithm	FA	Fireflies (Lampyridae)	Attraction based on flashing light intensity (mating signal)
Cuckoo Search	CSA	Cuckoos (some species)	Brood parasitism, Lévy flight foraging patterns
Grey Wolf Optimizer	GWO	Grey Wolves (Canis lupus)	Social hierarchy and cooperative hunting behavior
Bat Algorithm	BA	Microbats	Echolocation (bio-sonar) for navigation and prey detection
Artificial Fish Swarm	AFS	Fish (schooling)	Collective movement: foraging, swarming, following
Bacterial Foraging Opt.	BFO	Bacteria (e.g., E. coli)	Foraging via chemotaxis (following chemical gradients)
Glowworm Swarm Optimization	GSO	Glowworms (Lampyridae, etc.)	Attraction based on bioluminescence intensity (fitness signal)

3. Analysis of Distinct Bio-Inspired Behavioral Mechanisms

To develop a meaningful classification, it is essential to move beyond the specific algorithms and analyze the underlying types of collective behavior they attempt to capture. Several distinct behavioral mechanisms, inspired by nature, form the core of SI coordination strategies.

3.1. Stigmergy and Indirect Communication

This mechanism involves agents interacting indirectly by modifying their shared environment. Agents deposit persistent traces or cues (like pheromones) that are sensed and influence the behavior of other agents at a later time. This allows for coordination without direct agent-to-agent contact, relying instead on an "environmental memory". The canonical biological example is ant foraging, where pheromone trails guide colony members towards food sources, with stronger trails indicating more efficient paths. Termite mound construction also relies heavily on stigmergic principles. Computationally, this translates to algorithms that maintain and update values associated with environmental states or solution components, guiding the search probabilistically based on these accumulated cues. Key characteristics include asynchronous coordination, robustness to individual agent timing, and suitability for problems involving pathfinding, routing, or optimization on graphs. ACO is the quintessential algorithm based on this mechanism.

3.2. Neighbor-Based Interaction and Coordinated Movement

Here, coordination arises from direct, typically local, interactions between neighboring agents. An agent's behavior, particularly its movement (velocity, direction), is adjusted based on the perceived state (position, velocity, heading) of nearby individuals. Biological examples abound in the synchronized movements of bird flocks, fish schools, and animal herds. Simplified models often capture this using rules for separation (avoid collisions), alignment (match average velocity), and cohesion (move towards the local center of mass). The interaction neighborhood can be defined by metric distance or topological connections (e.g., the k-nearest neighbors). This mechanism leads to real-time coordination, emergent pattern formation (like V-formations or swirling schools), and collective navigation. It relies on agents having some form of direct (though localized) perception of their neighbors. Computationally, this often involves vector-based updates to position and velocity influenced by neighbors or swarm leaders. PSO strongly incorporates elements of this, with particles moving based on personal and neighborhood/global best positions. AFS also explicitly models fish swarming and following behaviors based on neighbors.

3.3. Role-Based Specialization and Division of Labor

This mechanism involves heterogeneity within the swarm, where different agents adopt distinct roles or tasks. This specialization can be based on internal states, responses to local stimuli, predetermined hierarchies, or even fitness levels. Biological examples include the complex caste systems and task allocation in social insect colonies like ants and bees, where individuals specialize in foraging, nursing, defense, etc., often switching tasks based on colony needs. Another example is the social hierarchy in wolf packs, which dictates roles during hunting and other activities. This division of labor allows for parallel processing, efficient resource allocation, and often provides a natural way to balance exploration (e.g., scouts searching new areas) and exploitation (e.g., workers harvesting known resources). Computationally, algorithms implementing this mechanism often maintain distinct subpopulations or agent states corresponding to different roles, with specific logic governing transitions between roles (e.g., based on thresholds, probabilities, or solution improvement). ABC explicitly models employed, onlooker, and scout bees, while GWO utilizes the alpha, beta, and delta wolf hierarchy to guide the search.

3.4. Signal-Based Attraction and Mating Behavior

In this mode of interaction, agents emit signals (e.g., light, sound, chemical) whose properties (intensity, frequency, quality) correlate with their fitness or the quality of their current location. Other agents perceive these signals and are preferentially attracted towards stronger, more desirable signals. Biological inspirations include the light flashes used by fireflies for mate attraction, the bioluminescence of glowworms, and potentially the interpretation of echoes in bat echolocation. Key characteristics include fitness-proportional influence, where better solutions actively broadcast their quality, and often a distance-dependent decay of the signal's influence, modeling physical attenuation. This mechanism is naturally suited for global optimization tasks where the goal is to converge towards the best solutions. FA directly models firefly flashing with brightness linked to fitness and attraction decreasing with distance. GSO uses luciferin levels similarly. BA can be interpreted in this framework, where the quality and timing of returning echoes act as signals guiding the bat's movement.

3.5. Parasitic/Competitive Strategies

Some SI algorithms draw inspiration from antagonistic interactions in nature, such as parasitism or direct competition. In these strategies, some agents may exploit the resources or efforts of others, or directly displace them. The primary biological example informing current algorithms is the brood parasitism of cuckoos, where they lay eggs in host nests, potentially leading to the removal or neglect of host offspring. Computationally, this often translates into mechanisms for replacing existing solutions (especially poor ones) with new ones generated through a potentially disruptive process. This can enhance exploration by preventing premature convergence and introducing novel solutions into the population. CSA models the cuckoo's strategy, incorporating probabilities of nest abandonment (solution replacement) alongside search strategies like Lévy flights.

3.6. Chemotaxis and Gradient Following

This mechanism involves agents navigating their environment by sensing and responding to chemical gradients. Typically, agents move towards higher concentrations of attractants (e.g., nutrients) or away from repellents. The prime biological example is the foraging behavior of bacteria like E. coli, which perform chemotaxis to find food sources. This behavior often involves alternating periods of directed movement ('runs') and random reorientations ('tumbles') to explore the environment and climb gradients effectively. Computationally, this translates to gradient-based search strategies where agents estimate the local gradient of the objective function (or a related environmental cue) and bias their movement accordingly. This mechanism is particularly suited for local optimization and refinement in continuous spaces. BFO is the main algorithm explicitly based on bacterial chemotaxis.

Examining these distinct mechanisms reveals the fundamental ways information is shared and coordination is achieved within different types of swarms. Stigmergy relies on asynchronous, persistent environmental memory. Neighbor interaction depends on synchronous, localized perception. Role-based systems introduce functional heterogeneity. Signal-based systems use broadcast attraction based on quality. Parasitic strategies introduce disruption, while chemotaxis relies on gradient sensing. These differences in information flow and interaction topology are critical drivers of the resulting collective intelligence. Furthermore, these mechanisms represent a spectrum of social complexity being modeled, from relatively simple attraction/repulsion dynamics (FA, GSO) and local averaging (PSO) to intricate social structures with specialized roles (ABC, GWO) and sophisticated indirect coordination (ACO). While distinct, overlaps exist (e.g., foraging is a common goal achieved via different mechanisms in ACO, ABC, BFO), highlighting that the mechanism, not just the high-level goal, is the key differentiator. Recognizing these distinct mechanisms is crucial for understanding algorithm behavior and provides a solid foundation for a behavior-centric classification. It also clarifies the potential for principled hybridization, combining complementary mechanisms (e.g., stigmergic path memory with role-based exploration) in informed ways.

4. Computational Strategies Reflecting Biological Divergence

The distinct behavioral mechanisms identified in the previous section manifest computationally through specific algorithmic operators and strategies. The choice of biological inspiration strongly influences, and often dictates, the core mathematical and procedural structure of the resulting SI algorithm.

4.1. Pheromone Update Mechanisms (Stigmergy)

Algorithms based on stigmergy employ computational analogues of pheromone deposition and evaporation. Typically, this involves maintaining data structures (e.g., matrices or graph edge weights) representing the "pheromone level" associated with solution components or paths. Agents (artificial ants) traversing the solution space probabilistically choose their next move based on these pheromone levels, usually biased towards higher values. After constructing solutions, agents update the pheromone levels along their chosen paths, typically increasing them in proportion to the quality of the solution found. Simultaneously, a pheromone evaporation mechanism is applied, gradually decreasing all pheromone levels over time to prevent premature convergence and allow exploration of new paths. This computational cycle directly mirrors the reinforcement of good paths and the decay of unused trails observed in ant colonies. ACO and its variants are the primary examples utilizing these mechanisms. The specific equations for transition probability (often combining pheromone τ and heuristic information η) and pheromone update rules (Δτ based on solution quality Q/L_k, combined with evaporation ρ) are central to ACO's operation.

4.2. Velocity and Position Updates (Neighbor/Global Influence)

Algorithms inspired by flocking or schooling behavior typically update agent states using vector operations on position and velocity. In PSO, each particle maintains its current position, velocity, personal best position found so far (pbest), and knowledge of the global best position found by the entire swarm (gbest) or within its local neighborhood (lbest). The core update involves adjusting the particle's velocity based on three components: its previous velocity (inertia), the direction towards its pbest (cognitive component), and the direction towards the gbest/lbest (social component). The particle's position is then updated based on this new velocity. This computational structure abstracts the biological tendency of individuals to continue moving, trust their own experience, and follow successful group members. Parameters like the inertia weight (ω), cognitive coefficient (C1), and social coefficient (C2) control the relative influence of these factors, allowing tuning of the exploration-exploitation balance. Various strategies exist for adapting the inertia weight during the search to enhance performance.

4.3. Role Switching and Task Allocation Logic

Algorithms modeling division of labor or social hierarchies incorporate explicit computational logic for managing different agent roles and transitions between them. In ABC, the population is divided into employed bees, onlooker bees, and scout bees. Employed bees exploit specific food sources (solutions) and share information. Onlooker bees probabilistically choose sources based on this information (exploitation). If a source is exhausted (solution not improved), the corresponding employed bee becomes a scout bee, initiating a random search for a new source (exploration). This explicitly balances search phases through role assignment. Similarly, in GWO, the positions of the top three solutions (alpha, beta, delta wolves) guide the movement of the rest of the pack (omega wolves) towards the presumed prey (optimum). The algorithm computationally simulates encircling and hunting based on these leader positions. These strategies reflect the behavioral flexibility and functional specialization seen in their biological counterparts.

4.4. Fitness-Based Attraction and Movement

Algorithms inspired by signal-based attraction directly link an agent's influence or attractiveness to its objective function value (fitness). In FA, a firefly's brightness is calculated from its fitness, and its attractiveness to other fireflies is proportional to this brightness. However, attractiveness decreases with the square of the distance between fireflies, modeling light absorption. A less bright firefly will move towards a brighter one within its perception range. GSO uses a similar principle, where a glowworm's luciferin level is updated based on its fitness. Glowworms probabilistically choose a brighter neighbor within a dynamic range and move towards it. BA can also be viewed through this lens, where bats move towards locations perceived (via echolocation) to be better (e.g., closer to prey or away from obstacles), implicitly driven by the 'quality' of the reflected signal. These computational mechanisms directly model the biological principle of attraction towards fitter individuals or more promising locations indicated by signals.

4.5. Parameter Adaptation Mechanisms

Many SI algorithms incorporate mechanisms to dynamically adjust their control parameters during the search, reflecting the adaptive nature of biological swarms. In BA, the loudness (A) and pulse emission rate (r) of the artificial bats are typically varied as the search progresses. Loudness often decreases, and pulse rate increases as a bat approaches a potential target, mimicking the behavior of real bats refining their search. In PSO, the inertia weight (ω) is often decreased over time or adapted based on search performance to shift the balance from exploration (high ω) to exploitation (low ω). GWO employs a parameter 'a' that decreases linearly from 2 to 0, controlling the range of movement and thus transitioning from exploration to exploitation. These adaptive strategies allow the algorithms to modify their search behavior dynamically, much like biological systems adjust to changing environmental cues or internal states. The complexity and sensitivity of parameterization vary across algorithms, reflecting differences in the modeled behaviors and abstraction choices.

4.6. Probabilistic and Stochastic Elements

Randomness plays a crucial role in almost all SI algorithms, mirroring the inherent variability and unpredictability in biological systems and environments. Stochasticity is introduced in various ways: probabilistic path selection in ACO based on pheromone levels, random numbers scaling cognitive and social components in PSO updates, random initialization of populations, random selection of neighbors or targets, random walks or flights (like Lévy flights in CSA) for exploration, and random parameter initializations or perturbations. This injection of randomness is vital for exploration, preventing premature convergence to local optima, and enabling the swarm to discover novel regions of the search space.

The tight coupling between the biological behavior being modeled and the core computational operators is evident. Stigmergy naturally leads to pheromone update rules, flocking inspires velocity/position updates influenced by neighbors, division of labor necessitates role-switching logic, signaling behavior translates to fitness-based attraction, and biological adaptability motivates parameter adaptation schemes. This strong correspondence reinforces the validity of using the behavioral mechanism as a primary axis for classification, as it directly correlates with the fundamental computational structure and search strategy of the algorithm. Furthermore, the way algorithms balance exploration and exploitation is intrinsically tied to these core computational strategies derived from their biological inspirations – ACO uses pheromone dynamics, PSO adjusts component weights, ABC/GWO employ distinct roles, FA/BA use attraction and parameter tuning. Understanding these computational reflections of biological divergence is key to differentiating SI algorithms meaningfully.

Table 2: Comparative Analysis of Behavioral Mechanisms and Computational Strategies

Behavioral Mechanism Category	Key Computational Strategy/Operators	Representative Algorithm(s)	How Computation Reflects Behavior
Stigmergic Coordination	Pheromone matrix/value updates (deposition, evaporation), probabilistic choice	ACO	Virtual pheromones mimic chemical trails; updates reflect reinforcement/decay; probability models choice.
Neighbor-Interaction Coordination	Velocity/position vector updates based on local/global bests, neighbor averaging	PSO, AFS	Updates simulate attraction/alignment/separation rules based on neighbors or successful leaders.
Role-Based Coordination	Explicit agent roles (e.g., explorer, exploiter), role switching logic	ABC, GWO	Different agent types/states execute distinct search behaviors, mimicking division of labor/hierarchy.
Signal-Based Attraction	Fitness-proportional attractiveness calculation, distance-dependent influence	FA, GSO, BA	Agent influence/attraction calculated from fitness (signal strength), movement towards better signals.
Gradient/Chemotactic Systems	Gradient estimation, movement biased along gradient direction, run/tumble logic	BFO	Agents move based on perceived environmental gradient (e.g., nutrient concentration).
Parasitic/Competitive Strategies	Solution replacement mechanisms, potentially disruptive generation operators	CSA	Simulates parasitic actions like replacing host eggs (solutions) with own.
(Cross-cutting) Parameter Adaptation	Dynamic adjustment of control parameters (e.g., inertia, loudness, step size)	PSO, BA, GWO	Algorithm parameters change over time/based on state, mimicking biological adaptability.
(Cross-cutting) Stochasticity	Use of random numbers in updates, choices, initialization, random walks	Most SI algorithms	Incorporates randomness inherent in biology, aids exploration, prevents stagnation.

5. Review of Existing SI Taxonomies

Before proposing a new classification, it is instructive to review how Swarm Intelligence algorithms have been categorized previously in the literature. Understanding existing approaches and their limitations helps justify the need for a behavior-centric taxonomy.

5.1. Overview of Previous Classification Attempts

Surveys and review papers on SI often implicitly or explicitly group algorithms, creating various forms of taxonomies. Several common approaches can be identified:

• Grouping by Inspiration Source: This is arguably the most frequent method, categorizing algorithms based on the type of biological organism that provided the primary inspiration. Examples include creating categories like "Ant-based Algorithms / Antetic AI," "Bee-based Algorithms," "Bird/Fish-based Algorithms," "Bat-based Algorithms," "Firefly-based Algorithms," and "Wolf-based Algorithms." Some reviews explicitly structure their discussion around such categories; for instance, one study proposed eight major taxonomic categories based on biological inspiration when reviewing SI for feature selection, while another divided algorithms into six categories based on their biological origins. This approach is intuitive due to the field's strong emphasis on bio-inspiration.

• Grouping by Broad Computational Paradigm: A common distinction is made between SI algorithms and other metaheuristic paradigms, particularly Evolutionary Algorithms (EA) like Genetic Algorithms (GA). SI is often considered a subset of nature-inspired computation or computational intelligence. Some reviews focus specifically on population-based metaheuristics, a category that includes SI. This helps position SI within the broader landscape of AI and optimization but offers little differentiation within the SI family itself.

• Chronological Grouping: Some surveys present algorithms primarily in the historical order of their development. This provides a useful perspective on the evolution of the field but does not classify algorithms based on their functional characteristics.

• Application-Based Grouping: Certain reviews focus on the application of SI algorithms to specific problem domains. For example, surveys might concentrate on SI algorithms used for load balancing in cloud computing, feature selection in machine learning, optimization in engineering, or scheduling problems. While valuable for practitioners in those fields, these groupings are based on application context rather than the intrinsic properties of the algorithms.

• Simple Enumeration: Many papers simply list and describe prominent SI algorithms without attempting a strong taxonomic structure, focusing instead on individual algorithm mechanics and performance.

5.2. Evaluation: Assessing Behavioral Granularity

When evaluated against the goal of capturing fundamental behavioral differences, most existing classification approaches fall short.

• Critique of Source-Based Taxonomies: While intuitively appealing and widely used, classifying by the inspiring organism proves to be too coarse and potentially misleading. As demonstrated in Sections 3 and 4, algorithms inspired by organisms within the same biological class (e.g., insects) can employ fundamentally different behavioral mechanisms and computational strategies. Grouping ACO (stigmergy via pheromones), ABC (role-based foraging), and FA (signal-based attraction) under a single "Insect-based" category would obscure their distinct operational dynamics. This approach fails to capture the functional diversity that arises from modeling different behaviors, even if the source organisms are related.

• Critique of Broad Paradigm Taxonomies: Distinguishing SI from EA is a necessary first step in classification, but it provides no insight into the diversity within SI. Lumping algorithms as diverse as ACO, PSO, ABC, GWO, and FA under the single umbrella of "Swarm Intelligence" ignores the rich variety of coordination strategies they represent, rooted in vastly different natural behaviors.

• Critique of Chronological/Application Taxonomies: These classifications serve specific purposes - providing historical context or domain-specific guidance - but they do not offer a fundamental taxonomy based on the intrinsic behavioral or computational mechanisms of the algorithms. An algorithm's development date or its application area does not define its core operational principles.

• Existing Gaps: The review reveals a significant gap in the literature regarding a widely accepted, fine-grained taxonomy of SI algorithms based on their operational mechanisms. While the prevalence of source-based classification highlights the field's connection to biology, it lacks the necessary behavioral granularity. There appears to be no consensus on how to systematically categorize the diverse algorithms within SI beyond these broad or source-based labels. This lack of a standard, mechanism-based classification hinders deeper comparative analysis and theoretical development. The need for better classification is particularly evident in complex application domains like Feature Selection (FS), where understanding the subtle differences in how algorithms search the solution space is crucial for effective application. An appropriate SI algorithm whose behavioral analogy aligns with the problem structure might perform significantly better than one whose mechanism is ill-suited.

Therefore, existing classification schemes do not adequately address the need for a taxonomy that reflects the significant differences in the underlying bio-inspired behaviors and mechanisms.

This confirms the necessity and potential value of developing a new classification framework centered explicitly on these behavioral distinctions.

6. Proposal for a Behavior-Centric Taxonomy of Swarm Intelligence

6.1. Rationale and Synthesis

Based on the detailed analysis of biological inspirations (Section 2), distinct behavioral mechanisms (Section 3), corresponding computational strategies (Section 4), and the identified limitations of existing classifications (Section 5), this article proposes a novel taxonomy for Swarm Intelligence algorithms. The central organizing principle of this taxonomy is the dominant behavioral mechanism employed by the algorithm for information sharing, coordination, and search guidance. This choice is motivated by the observation that the core behavioral strategy being mimicked (e.g., indirect communication via environmental cues, direct coordination based on neighbor interactions, structured coordination via roles or hierarchy, attraction via broadcast signals, navigation via environmental gradients) strongly correlates with the fundamental computational structure and operational dynamics of the algorithm. As demonstrated, stigmergy leads to pheromone-like updates, flocking inspires velocity/position updates based on neighbors, division of labor results in role-switching logic, signaling translates to fitness-based attraction, and chemotaxis yields gradient-following procedures. By prioritizing the mechanism over the organism or the high-level goal (like foraging, which can be achieved through multiple mechanisms), this taxonomy aims to group algorithms that function in fundamentally similar ways. This approach seeks to capture functional similarities and differences more accurately than classifications based on species labels, providing a more insightful framework for understanding the diverse ways collective intelligence emerges in SI systems.

6.2. Proposed Subcategories

Synthesizing the findings, the following subcategories are proposed, primarily reflecting the distinct behavioral mechanisms identified in Section 3:

• Category A: Stigmergic Coordination Systems: Algorithms where coordination primarily occurs indirectly through modifications agents make to a shared environment.

• Category B: Neighbor-Interaction Coordination Systems: Algorithms where coordination primarily arises from direct interactions between agents based on their local neighborhood (spatial or topological proximity).

• Category C: Role-Based Coordination Systems: Algorithms characterized by heterogeneity within the swarm, where agents adopt distinct roles, exhibit specialized behaviors, or operate within a social hierarchy.

• Category D: Signal-Based Attraction Systems: Algorithms where agents are attracted towards other agents or locations based on signals whose strength or quality is proportional to fitness or solution quality.

• Category E: Gradient/Chemotactic Systems: Algorithms where agent movement is primarily guided by sensing and following local gradients in the environment or objective function landscape.

• Category F: Hybrid and Parasitic/Competitive Systems: Algorithms that explicitly combine mechanisms from multiple categories above, or are based on unique interaction paradigms like parasitism or specialized random walk strategies not easily captured elsewhere.

It is acknowledged that some algorithms might exhibit secondary characteristics aligning with other categories. For example, PSO (primarily Neighbor-Interaction) uses a global best component that acts somewhat like a signal. ACO variants might incorporate elitism, amplifying the influence of the best solution (Signal-Based characteristic). Furthermore, explicitly designed hybrid algorithms combining different approaches exist. Therefore, classification should focus on the dominant mechanism driving the algorithm's core search process. The inclusion of Category F provides flexibility to accommodate algorithms that genuinely blend strategies or rely on less common interaction modes like parasitism (as seen in CSA). Clear definitions for each category and explicit reasoning for placing key algorithms are essential for the taxonomy's clarity and utility.

7. Characterization of Proposed SI Subcategories

This section provides detailed descriptions for each proposed subcategory, outlining its defining behavioral inspiration, key computational features, and listing representative algorithms.

7.1. Category A: Stigmergic Coordination Systems

• Core Behavioral Inspiration: This category draws inspiration from natural systems where individuals coordinate indirectly by modifying their shared environment, leaving persistent cues that influence others' actions. The classic example is ant colony foraging, where pheromone trails deposited on the ground guide other ants towards food sources and reinforce efficient paths. Termite construction is another biological analogue.

• Key Computational Characteristics: Algorithms in this category typically employ a form of "environmental memory," often represented as pheromone matrices, potential fields, or values associated with solution components or paths. The core loop involves agents making probabilistic decisions based on the intensity of these environmental cues, followed by updating (reinforcing or decaying) the cues based on the outcomes of their actions or the quality of solutions found. Key features include positive feedback loops for reinforcement, gradual decay (evaporation) to forget poor or outdated information, and asynchronous coordination potential. These algorithms are often particularly well-suited for discrete optimization problems, routing, pathfinding, and scheduling tasks.

• Representative Algorithms: Ant Colony Optimization (ACO) is the archetypal algorithm in this category. Numerous variants exist, such as Elitist Ant System (EAS), Max-Min Ant System (MMAS), Rank-based Ant System (RAS), Ant Colony System (ACS), and Continuous Ant Colony Optimization (e.g., ACOR), all fundamentally relying on the stigmergic principle.

7.2. Category B: Neighbor-Interaction Coordination Systems

• Core Behavioral Inspiration: These algorithms are inspired by the coordinated and synchronized movements observed in groups like bird flocks, fish schools, or animal herds. Coordination emerges from individuals adjusting their movement based on the positions and velocities of their immediate neighbors, often following simple rules like maintaining separation, aligning direction, and moving towards the group center.

• Key Computational Characteristics: The core computational mechanism involves agents (particles, boids, fish) updating their state, primarily position and velocity vectors, based on information gathered from their local neighborhood. This often includes components related to inertia (previous movement), individual experience (personal best), and social influence (neighbors' positions, neighborhood best, or global best). Emphasis is placed on spatial relationships and relative movement. Emergent properties include collective pattern formation, collision avoidance, and synchronized motion. While often incorporating a global best influence (which has signal-like qualities), the fundamental update mechanism relies on relative positions and velocities within the swarm context. These algorithms are frequently applied to continuous optimization problems, robotics (flocking control), and simulations.

• Representative Algorithms: Particle Swarm Optimization (PSO) is the most prominent example, with its core velocity and position update rules reflecting flocking dynamics. Artificial Fish Swarm (AFS), which explicitly models swarming, following, and foraging behaviors based on local fish interactions, also fits well within this category.

7.3. Category C: Role-Based Coordination Systems

• Core Behavioral Inspiration: This category is characterized by mimicking biological systems exhibiting division of labor, task specialization, or social hierarchies. Examples include the distinct roles of queen, drone, worker (further specialized into foragers, nurses, guards) in honey bee colonies, task allocation in ant colonies, or the alpha-beta-delta-omega hierarchy governing wolf pack behavior.

• Key Computational Characteristics: Algorithms in this category feature heterogeneity among agents. Agents may belong to different predefined types, possess distinct behavioral rules, or switch roles dynamically based on performance, environmental stimuli, or probabilistic logic. This explicit differentiation often serves to balance exploration and exploitation phases of the search more deliberately than in homogeneous swarms. Computational frameworks often involve managing separate subpopulations or agent states and defining the rules that govern interactions and transitions between them.

• Representative Algorithms: Artificial Bee Colony (ABC) is a clear example, with its explicit modeling of employed, onlooker, and scout bees performing different search functions. Grey Wolf Optimizer (GWO) also falls into this category due to its reliance on the alpha, beta, and delta wolf positions (representing top solutions) to guide the search behavior of the rest of the pack.

7.4. Category D: Signal-Based Attraction Systems

• Core Behavioral Inspiration: Inspiration comes from organisms that use emitted signals (light, sound, chemical) for purposes like mate attraction or prey location, where the signal's characteristics correlate with the sender's quality or fitness. Fireflies attracting mates with flashes of varying patterns or intensity, glowworms using bioluminescence, and bats using echolocation pulses and interpreting the returning echoes are key examples.

• Key Computational Characteristics: The core mechanism involves calculating an "attractiveness" value for each agent, typically directly proportional to its fitness or objective function value. Agents then move towards other agents that are more attractive (fitter). The strength of this attraction often diminishes with distance, modeling physical signal attenuation. Parameter adaptation may be used to mimic adjustments in signaling behavior (e.g., changing pulse rates or frequencies in BA). These algorithms are generally well-suited for global optimization, as fitter solutions effectively broadcast their quality to guide the swarm.

• Representative Algorithms: Firefly Algorithm (FA) directly implements this concept using brightness as fitness and distance-dependent attraction. Glowworm Swarm Optimization (GSO) uses luciferin levels similarly. Bat Algorithm (BA) fits here as its core involves bats adjusting their flight based on the perceived quality of returning echolocation signals, effectively being attracted towards promising locations indicated by those signals.

7.5. Category E: Gradient/Chemotactic Systems

• Core Behavioral Inspiration: This category is inspired by organisms, particularly microorganisms, that navigate by sensing and responding to gradients in their environment. The primary example is bacterial chemotaxis, where bacteria like E. coli move towards higher concentrations of nutrients or away from toxins by biasing their movement along detected chemical gradients.

• Key Computational Characteristics: Algorithms in this category typically involve agents estimating the local gradient of the objective function or a related environmental property. Agent movement is then biased in the direction of the favorable gradient (e.g., uphill for maximization, downhill for minimization). These algorithms often incorporate mechanisms to handle noisy gradients or flat regions, such as the run-and-tumble strategy (alternating directed movement with random reorientation) seen in bacterial foraging. They are often effective for local search and refinement, particularly in continuous domains.

• Representative Algorithms: Bacterial Foraging Optimization (BFO) is the main algorithm explicitly designed around the principles of chemotaxis.

7.6. Category F: Hybrid and Parasitic/Competitive Systems

• Core Behavioral Inspiration: This category serves as a container for algorithms that either explicitly combine mechanisms from multiple categories above or are based on unique interaction paradigms not well captured by the other categories, such as parasitism or specialized foraging strategies involving non-standard random walks. Cuckoo brood parasitism provides the inspiration for CSA.

• Key Computational Characteristics: Hybrid algorithms intentionally integrate operators or concepts from different SI paradigms (e.g., combining PSO's velocity updates with FA's attraction mechanism). Algorithms based on parasitism, like CSA, feature unique operators such as solution replacement based on a probability of "discovery" by a host. Others might incorporate specific mathematical models of movement, like Lévy flights (a type of random walk with occasional long jumps observed in some animal foraging patterns), which are prominently used in CSA. This category acknowledges the ongoing development in SI, including the creation of tailored hybrids and algorithms based on less common but potentially powerful biological interactions.

• Representative Algorithms: Cuckoo Search (CSA), due to its unique combination of brood parasitism analogy and Lévy flights, fits here. Various explicitly developed hybrid algorithms reported in the literature (e.g., combinations of PSO, ACO, FA, ABC) would also belong in this category.

Table 3: Proposed Behavior-Centric SI Subcategories

Proposed Subcategory Name	Core Behavioral Inspiration (Mechanism)	Key Computational Characteristics	Representative Algorithms
Stigmergic Coordination Systems	Indirect communication via environmental modification (e.g., pheromones)	Environmental memory (pheromone matrix), reinforcement/decay, probabilistic choice based on cues	ACO & variants (MMAS, ACS, etc.)
Neighbor-Interaction Coord. Sys.	Coordinated movement via local neighbor interactions (e.g., flocking)	Velocity/position updates based on neighbors/bests, spatial relationships, emergent patterns	PSO, AFS
Role-Based Coordination Systems	Division of labor / Social hierarchy	Heterogeneous agents/roles, role switching logic, explicit exploration/exploitation balance	ABC, GWO
Signal-Based Attraction Systems	Attraction via fitness-correlated signals (e.g., light, sound)	Fitness-proportional attraction, distance decay, movement towards better signals	FA, GSO, BA
Gradient/Chemotactic Systems	Movement along environmental gradients (e.g., chemotaxis)	Gradient sensing/estimation, biased movement along gradient, run/tumble logic	BFO
Hybrid & Parasitic/Competitive Sys.	Combination of mechanisms / Unique interactions (e.g., parasitism)	Integrated operators from multiple categories, solution replacement, specialized random walks (Lévy)	CSA, Explicit Hybrids

8. Conclusion: Towards a Deeper Understanding of Swarm Intelligence Diversity

8.1. Summary of the Proposed Taxonomy

Swarm Intelligence offers a powerful suite of bio-inspired techniques for tackling complex problems. However, the prevalent tendency to group SI algorithms monolithically or based solely on the inspiring organism has obscured the rich functional diversity within the field. This article has argued for and developed a more nuanced classification system grounded in the fundamental behavioral mechanisms that drive collective intelligence in these algorithms. Synthesizing analyses of biological inspirations, core behavioral strategies (stigmergy, neighbor interaction, roles, signaling, chemotaxis, parasitism), and their computational reflections, a behavior-centric taxonomy is proposed. This taxonomy categorizes SI algorithms into distinct groups:

• Stigmergic Coordination Systems (e.g., ACO)

• Neighbor-Interaction Coordination Systems (e.g., PSO, AFS)

• Role-Based Coordination Systems (e.g., ABC, GWO)

• Signal-Based Attraction Systems (e.g., FA, GSO, BA)

• Gradient/Chemotactic Systems (e.g., BFO)

• And a category for Hybrid and Parasitic/Competitive Systems (e.g., CSA, explicit hybrids).

Each category is defined by the primary way agents interact, share information, and coordinate their search efforts, reflecting deep-seated differences in their operational logic.

8.2. Implications and Benefits

Adopting a behavior-centric perspective on SI classification offers several potential benefits:

• Improved Understanding: The taxonomy provides a clearer framework for comprehending the functional diversity within SI, moving beyond superficial similarities to highlight fundamental differences in coordination and information flow. It helps articulate how different swarms achieve collective intelligence.

• Informed Algorithm Selection: By characterizing algorithms based on their core mechanism, the taxonomy can guide researchers and practitioners in selecting algorithms whose operational logic aligns with the structure and demands of a specific problem. For instance, stigmergic systems might be favored for pathfinding on graphs, neighbor-interaction systems for problems involving spatial coordination or continuous optimization, role-based systems for tasks requiring explicit balancing of exploration/exploitation or handling heterogeneous sub-tasks, and signal-based systems for global optimization where strong solutions should broadly influence the search. This potential for more informed selection can improve application success rates and reduce reliance on extensive trial-and-error.

• Principled Hybridization: Understanding the distinct strengths and weaknesses associated with each behavioral mechanism facilitates the more principled design of hybrid algorithms. Instead of arbitrarily combining algorithms, developers can strategically integrate complementary mechanisms (e.g., using stigmergic memory to augment neighbor-based exploration) to create synergistic effects.

• Guiding Future Research: The taxonomy highlights different paradigms of collective behavior that have been computationally modeled. It can potentially reveal under-explored biological mechanisms that could inspire novel SI algorithms. Furthermore, research can focus on refining algorithms within each category or exploring the boundaries and transitions between categories.

8.3. Limitations and Future Directions

While the proposed taxonomy offers a more functionally relevant classification, certain limitations and areas for future work should be acknowledged.

• Classification Ambiguity: As noted, some algorithms may exhibit characteristics of multiple categories, making definitive placement challenging. The focus on the dominant mechanism helps, but borderline cases may exist, particularly as algorithms become more complex.

• Need for Empirical Validation: The proposed taxonomy is based on conceptual analysis of behavioral and computational mechanisms. Further empirical studies are needed to validate whether algorithms within the same category exhibit demonstrably similar performance characteristics (e.g., convergence speed, robustness, scalability, suitability for specific problem landscapes) compared to algorithms in different categories. Such studies could involve large-scale benchmarking across diverse problem sets.

• Taxonomy Refinement: The proposed categories and their definitions may require refinement as the field evolves. Further theoretical analysis or empirical evidence might suggest merging, splitting, or redefining categories. The classification of newer or less common SI algorithms also needs ongoing consideration.

• Dynamic Nature of SI: Swarm Intelligence is a vibrant and rapidly evolving field, with new algorithms and biological inspirations continually emerging. Any taxonomy must be viewed as a snapshot in time, requiring periodic updates and adaptation to remain comprehensive and relevant. Future work should involve incorporating new algorithms into the framework and assessing whether novel bio-inspirations necessitate adjustments to the taxonomic structure itself.

By shifting the focus from source organisms to the underlying behavioral mechanisms, this article offers a framework for understanding Swarm Intelligence that better reflects its internal diversity and operational principles. This behavior-centric taxonomy holds the potential to enhance theoretical clarity, guide practical application, and stimulate further innovation in this fascinating domain of artificial intelligence.