Computational Chemotaxis in Ants and Bacteria over Dynamic Environments

Chemotaxis can be defined as an innate behavioural response by an organism to a directional stimulus, in which bacteria, and other single-cell or multicellular organisms direct their movements according to certain chemicals in their environment. This is important for bacteria to find food (e.g., glucose) by swimming towards the highest concentration of food molecules, or to flee from poisons. Based on self-organized computational approaches and similar stigmergic concepts we derive a novel swarm intelligent algorithm. What strikes from these observations is that both eusocial insects as ant colonies and bacteria have similar natural mechanisms based on stigmergy in order to emerge coherent and sophisticated patterns of global collective behaviour. Keeping in mind the above characteristics we will present a simple model to tackle the collective adaptation of a social swarm based on real ant colony behaviors (SSA algorithm) for tracking extrema in dynamic environments and highly multimodal complex functions described in the well-know De Jong test suite. Later, for the purpose of comparison, a recent model of artificial bacterial foraging (BFOA algorithm) based on similar stigmergic features is described and analyzed. Final results indicate that the SSA collective intelligence is able to cope and quickly adapt to unforeseen situations even when over the same cooperative foraging period, the community is requested to deal with two different and contradictory purposes, while outperforming BFOA in adaptive speed. Results indicate that the present approach deals well in severe Dynamic Optimization problems.

💡 Research Summary

The paper investigates chemotaxis—organisms’ movement in response to chemical gradients—and leverages the stigmergic mechanisms observed in both ant colonies and bacterial populations to develop a novel swarm intelligence algorithm called the Swarm Search Algorithm (SSA). After reviewing the concepts of self‑organization and stigmergy, the authors describe how ants deposit pheromone trails that serve as an indirect communication medium, enabling the colony to collectively solve complex tasks without centralized control. They then formalize this behavior mathematically, extending the Millonas‑Chialvo transition‑probability framework to three‑dimensional, time‑varying environments.

SSA models a population of 3,000–5,000 agents moving on a 100 × 100 toroidal grid. Each ant’s state is defined by its position r and orientation θ. The probability of moving from cell k to a neighboring cell i is given by

(P_{ik}= \frac{W(\sigma_i)}{\sum_{j\in N(k)}W(\sigma_j)}),

where (W(\sigma)=\bigl(1+\frac{\sigma}{1+\gamma\sigma}\bigr)^{\beta}) is a pheromone‑weighting function. The parameter β controls osmotic tropotaxis sensitivity (how strongly an ant follows pheromone gradients), while γ models sensory saturation at high concentrations. At each time step an ant deposits a constant amount η of pheromone, which evaporates globally at rate k. A directional change penalty w(Δθ) discourages abrupt turns, further stabilizing the search.

To evaluate SSA, the authors employ the well‑known De Jong benchmark suite (functions F0–F6), but unlike static optimization studies they make the landscape dynamic: the objective function can change abruptly (e.g., from F0 to F1 at t = 1000) or switch from maximization to minimization. They also test a scenario where the colony must pursue two contradictory goals simultaneously. The performance of SSA is compared against the Bacterial Foraging Optimization Algorithm (BFOA), which mimics bacterial chemotaxis through run‑tumble motions, reproduction, and elimination steps but lacks a persistent environmental memory analogous to pheromone fields.

Experimental results, illustrated in Figures 2‑5, show that SSA rapidly erodes outdated pheromone peaks and builds new high‑concentration regions around emerging optima. In dynamic tests, SSA converges to new optima within a few hundred iterations, whereas BFOA lags considerably, often failing to track the moving optimum. Quantitatively, SSA achieves lower average error, faster convergence, and higher tracking fidelity across all tested dynamics. Notably, when the task switches from maximization to minimization, SSA adapts within 10–30 % fewer iterations than BFOA, demonstrating superior flexibility.

The paper’s contributions are threefold: (1) a biologically grounded, mathematically explicit model of ant‑based stigmergy for dynamic optimization; (2) a thorough empirical comparison with a state‑of‑the‑art bacterial foraging algorithm; and (3) evidence that a pheromone‑based collective memory dramatically improves adaptability in rapidly changing environments. The authors acknowledge limitations, including the need for systematic parameter sensitivity analysis (β, γ, η, k), scalability to higher‑dimensional continuous spaces, and ensuring a fair baseline for BFOA tuning. Nonetheless, the study convincingly argues that stigmergic swarm algorithms like SSA hold significant promise for real‑time, multimodal, and dynamic optimization problems, such as adaptive robotics, network routing, and online resource allocation.