Artificial Fish Swarm Algorithm

• Artificial Fish Swarm Algorithm is a bio-inspired optimization method that mimics natural fish behaviors—preying, swarming, and following—to navigate high-dimensional, constraint-rich search spaces.
• It incorporates marine-specific modifications such as hydrodynamic drift, irreversible settlement, and hierarchical communication to enhance performance in underwater environments.
• Recent adaptations demonstrate rapid convergence and scalable sensor network formation, making AFSA a practical tool for autonomous marine robotics and energy-aware collective control.

The Artificial Fish Swarm Algorithm (AFSA) is a bio-inspired population-based optimization method that abstracts core mechanisms from fish swarming behaviors—preying, swarming, and following—and translates these into iterative, distributed solution update rules suitable for high-dimensional, constraint-laden search spaces. AFSA and its underwater adaptations are central in autonomous marine robotics, supporting collective sensing, optimal coverage, formation control, and adaptive response within highly dynamic aquatic environments where communication is limited, environmental variability is severe, and traditional algorithms often fail. Recent surveys position AFSA as a canonical marine swarm control technique, highlighting both its theoretical underpinnings and its pragmatic role in energy-aware, scalable underwater collective autonomy (Ramesh et al., 18 Jan 2026).

1. Biological Inspiration and Core Algorithmic Mechanisms

AFSA draws from ethological models of fish whose local perception, collective response, and distributed action enable robust group behaviors amid noisy, uncertain environments. Each "artificial fish" models fish perception and movement in a D-dimensional search space, with position $X_i\in\mathbb{R}^D$ and an objective function $f(X)$ encoding application-specific reward—such as environment coverage, information gain, or energy minimization.

Three elemental behaviors are encoded:

• Prey: Each agent samples a random candidate within a "visual" neighborhood of radius $v$, moving towards it if this yields better objective value:

$$X_i' = X_i + v\,\text{rand}\,(X_j - X_i), \quad X_j \sim \{\text{neighbors}\},$$

and, if $f(X_i') > f(X_i)$,

$$X_i \leftarrow X_i + s\,\text{rand}\,\frac{X_i' - X_i}{\|X_i' - X_i\|}.$$

• Swarming: The local centroid $X_{\text{cen}}$ of visible neighbors is computed; agents move toward it if the mean fitness improves:

$$X_{\text{cen}} = \frac{1}{N_{\text{vis}}}\sum_{X_j\in \text{visual}} X_j,$$

with analogous movement if $f(X_{\text{cen}})/N_{\text{vis}} > \delta$.

• Following: An agent progresses toward the locally-best neighbor:

$$X_i \leftarrow X_i + s\,\text{rand}\,\frac{X_{\text{best}} - X_i}{\|X_{\text{best}} - X_i\|}.$$

Characteristic parameters include the visual distance $v$, move step size $s$, and an overcrowding-avoidance threshold.

Underwater adaptation is achieved by mapping $f(\cdot)$ to task-relevant criteria, including inter-robot spacing (for formation), energy state (for adaptive role allocation), or local environmental quality (for environmental monitoring) (Ramesh et al., 18 Jan 2026).

2. Marine-Specific Modifications and Hydrodynamic Awareness

In marine settings, hydrodynamic forces, environmental drag, turbulence, and communication constraints necessitate significant modification of AFSA's canonical rules. The NOAH algorithm is exemplary, relocating AFSA's generic mechanisms into a framework explicitly aware of flow fields, agent drag, and environmental cues (Ramesh et al., 17 Oct 2025). Here, the velocity update for each agent includes:

• Inertia ($\omega v_{i,t}$): persistence of prior motion.
• Random Exploration ($\eta \xi_{i,t},\, \xi_{i,t}\sim\mathcal{N}(0,I)$): stochastic search diversity.
• Gradient Exploitation ($\beta(-\hat{\nabla} f(x_{i,t}))$): directed ascent in objective landscape.
• Hydrodynamic Drift ($\gamma U(x_{i,t})$): flow-aligned travel that exploits prevailing currents.
• Colony Field Influence ($\delta\nabla\Phi(x_{i,t})$): long-range attraction to group cues, short-range repellence to mitigate overcrowding.

This compositional update:

$$\tilde{v}_{i,t+1} = \omega v_{i,t} + \eta\,\xi_{i,t} + \beta\,\left(-\hat{\nabla}f(x_{i,t})\right) + \gamma\,U(x_{i,t}) + \delta\,\nabla\Phi(x_{i,t}),$$

can be understood as a generalized AFSA mechanism where biophysical factors and group communication fields modulate agent motion (Ramesh et al., 17 Oct 2025).

3. Settlement, Anchoring, and Irreversible Behaviors

A defining innovation in underwater AFSA adaptations is the introduction of irreversible settlement, motivated by marine larval behaviors (e.g., barnacle nauplii). Each agent is given a binary anchoring flag $a_{i,t}$, and the probability of settlement at each step integrates:

• local fitness advantage ($\Delta f_i$),
• proximity to established colonies ($d_i$),
• hydrodynamic gradient magnitude ($\|\nabla U(x_{i,t})\|$),
• local crowding ($\rho_i$),
• and normalized energy reserve ($E_i$):

$$p_{i,t}^{\mathrm{settle}} = \sigma( \lambda_1\,\mathrm{rank}(\Delta f_i) +\lambda_2\frac{d_i}{d_0} -\lambda_3\frac{\|\nabla U(x_{i,t})\|}{\kappa_0} -\lambda_4\,\rho_i +\lambda_5\,E_i )$$

where $\sigma(\cdot)$ is the logistic function (Ramesh et al., 17 Oct 2025).

Upon settlement ($u < p_{i,t}^{\mathrm{settle}}$), an agent becomes static: $a_{i,t+1} = 1$, velocity is set to zero, and its final position is recorded as a permanent colony, metaphorically echoing the irreversible "cementing" seen in marine invertebrates.

This mechanism creates persistent coverage configurations (e.g., fixed sensor nodes), a critical property for long-term marine monitoring, as opposed to classical AFSA implementations where agents remain mobile and fully adaptive (Ramesh et al., 17 Oct 2025).

4. Communication and Scalability under Acoustic Constraints

Compared to terrestrial and aerial domains, underwater communication is typified by low bandwidth, high latency, and frequent disruptions, especially for large swarms. AFSA-inspired marine algorithms often integrate hierarchical or relay-based message passing rather than the all-to-all interaction typically assumed.

In NOAH, a two-tier protocol is used:

• Free agents occasionally broadcast minimal state information;
• Colonies (settled agents) act as communication cluster-heads, beaconing their location and strength.

Communication success probability is modeled spatially, ensuring that only nearby agents reliably exchange updates:

$$p_k(x) = \begin{cases} 1, & \|x-c_k\| \leq R_k, \ e^{-\alpha(\|x-c_k\| - R_k)}, & \text{otherwise}. \end{cases}$$

This structure reduces per-iteration messaging complexity to $O(N+C)$ instead of $O(N^2)$, and leverages natural colony formation for scalable, multi-hop acoustic relaying (Ramesh et al., 17 Oct 2025).

Such modifications are essential for practical swarm deployments in oceanic settings, and represent a significant evolution from the original AFSA literature.

5. Comparative Performance, Benchmarks, and Limitations

Empirical tests on synthetic benchmark functions (e.g., Rastrigin, Ackley, Rosenbrock, and "Anchoring Bowl") quantify the convergence and accuracy of underwater AFSA variants. The NOAH algorithm exhibits rapid initial convergence (20–30 iterations), consistent anchoring accuracy (86% within 0.5 units; mean distance $0.194\pm0.104$), and outperforms population-based baselines (PSO, CVT, Greedy) in most scenarios (Ramesh et al., 17 Oct 2025).

However, challenges remain:

• Parameter tuning is non-trivial due to the proliferation of behavioral, environmental, and communication weights.
• Irreversible settlement restricts post-anchoring adaptivity.
• Worst-case communication complexity can approach $O(N^2)$ if colony numbers scale with agent count.
• Existing results are primarily validated in 2D, idealized flow fields; real-world, three-dimensional and fully turbulent conditions introduce unaddressed uncertainties.

Standardized, field-validated underwater benchmarks and robust adaptive parameter control mechanisms are cited as immediate open research directions (Ramesh et al., 17 Oct 2025).

6. Trends, Synergies, and Future Directions

AFSA and its underwater adaptations are converging with other marine bio-inspired algorithms (e.g., Whale Optimization Algorithm, Coral Reef Optimization, Marine Predators Algorithm) within comprehensive frameworks that unify coordination, environmental adaptability, and communication robustness (Ramesh et al., 18 Jan 2026).

Key research trajectories include:

• Hybridization with learning-based and adaptive control schemes, including reinforcement learning for dynamic parameter selection.
• Hierarchical, delay-tolerant protocols for large-scale, multi-modal communication networks.
• Empirical performance validation via open-source hardware platforms and shared datasets.
• Integration of energy harvesting, persistent autonomy, and systematic field deployment pipelines.

A significant implication is the consolidation of bio-inspired swarm intelligence principles—drawn from AFSA and kindred models—into modular, cross-layer optimization architectures tailored for the marine domain. This trend is visible in proposals for cross-disciplinary open standards and benchmarks to accelerate reproducibility and system-level innovation (Ramesh et al., 18 Jan 2026).

Table: AFSA in Underwater Swarm Robotics (from (Ramesh et al., 18 Jan 2026, Ramesh et al., 17 Oct 2025))

Core Feature	Canonical AFSA	Underwater Adaptation (e.g., NOAH)
Behavior Update	Prey, swarming, following	Gradient, drift (current), colony field
Movement Constraints	Typically unconstrained	Hydrodynamic drift, drag awareness
Settlement	Always mobile	Irreversible anchoring, colony creation
Communication	Fully connected or local broadcast	Hierarchical, relay via colonies
Scalability	Limited by communication model	O(N+C) per iteration, scalable via hubs
Application Focus	Optimization, coverage, clustering	Persistent sensor networks, marine tasks

Combining the ethological richness of natural fish behaviors with explicit hydrodynamic modeling and scalable communication topologies, AFSA-based algorithms represent a biologically grounded, technically sophisticated foundation for future underwater swarm robotics missions.