Traditional optimization methods in microbial fermentation typically rely on classical experimental designs, most notably, the One-Factor-at-A-Time (OFAT) approach. This method varies a single variable while keeping the others constant, enabling a basic assessment of individual effects but completely neglecting interactions among factors. In biological systems, such interactions are rarely negligible; the metabolic flux through secondary metabolite pathways often depends on the synergistic or antagonistic interplay between nutrients and environmental stimuli. For example, an increase in carbon availability may stimulate primary metabolism but repress secondary metabolite formation via catabolite repression. Similarly, nitrogen source balance can influence precursor supply for peptide synthesis or alter regulatory signaling cascades. Therefore, OFAT methods often produce suboptimal results and require extensive experimentation with low predictive power [3], [4].

To address these limitations, factorial designs and statistical techniques such as Response Surface Methodology (RSM) were developed. RSM combines experimental design principles with regression-based modeling to approximate the relationship between response variables (e.g., yield) and input factors (e.g., nutrient concentrations). Central Composite Design (CCD) and Box–Behnken Design (BBD) are two widely used RSM frameworks that provide efficient data structures for modeling second-order polynomials. These methods have been successfully applied in optimizing fermentation processes for antibiotics, enzymes, and organic acids. Their primary strengths lie in their structured exploration of the design space, statistical interpretability, and the orthogonality of factor levels, which enable efficient coefficient estimation with relatively few experiments [5].

However, the polynomial nature of RSM imposes inherent constraints. Biological systems are inherently nonlinear and high-dimensional, often involving threshold effects, saturation kinetics, and feedback regulation that cannot be captured adequately by quadratic models. Moreover, RSM assumes smooth, continuous response surfaces with a single global optimum, an assumption that breaks down when the system exhibits multiple local maxima or discontinuities due to complex metabolic switching. Consequently, RSM may oversimplify the fermentation landscape, leading to predictions that deviate significantly from experimental reality [6].

With the rise of machine learning and computational intelligence, data-driven models have emerged as powerful alternatives for process optimization. Among these, Artificial Neural Networks (ANNs) have become particularly attractive due to their ability to approximate any nonlinear function without explicit knowledge of the underlying mechanisms. Unlike regression-based models, ANNs do not rely on predefined functional forms; instead, they learn directly from experimental data by adjusting internal parameters (weights and biases) through training algorithms such as backpropagation or evolutionary tuning [7].

The world algorithm: a universal metaheuristic for complex optimization problems 15T

In the context of bioprocess engineering, ANNs can capture the intricate, nonlinear dependencies between fermentation inputs (nutrient concentrations, pH, temperature, agitation rate, etc.) and outputs (yield, productivity, or specific metabolite concentrations). This flexibility allows them to model highly complex biological systems where traditional mechanistic models are either unknown or mathematically intractable. Moreover, once trained, an ANN can generalize from limited data, predict outcomes under untested conditions, and serve as a fast-response surrogate model in real-time process control or optimization frameworks [1].

For actinomycin production, ANNs have demonstrated superior predictive capabilities compared to RSM or polynomial regression, particularly when interactions between carbon and nitrogen sources, micronutrient levels, and environmental factors are significant. However, while ANNs can model these relationships effectively, they do not inherently provide mechanisms to search for the global optimum within the modeled surface. In other words, an ANN can predict yield given a set of inputs, but it cannot independently determine which combination of inputs will maximize the response. This is where metaheuristic optimization algorithms play a crucial role [8].

Metaheuristic algorithms are population-based, stochastic optimization methods inspired by natural or social phenomena, such as evolution (Genetic Algorithms, GAs), swarm intelligence (Particle Swarm Optimization, PSO), Ant Colony Optimization (ACO), or physics (Simulated Annealing). These algorithms excel at exploring large, complex, and multimodal search spaces without requiring gradient information or convexity assumptions. Their iterative structure allows them to balance exploration (searching new regions) and exploitation (refining known promising regions) to locate near-global optima even in noisy or discontinuous environments [1], [3].

In fermentation optimization, metaheuristics have been employed to fine-tune media compositions, process parameters, and even control strategies. Techniques such as GA, Differential Evolution (DE), and PSO have been integrated with ANNs to form hybrid intelligent systems in which the ANN serves as a predictive model, and the metaheuristic optimizes the input space toward optimal conditions. These ANN–metaheuristic hybrids have significantly reduced experimental effort, improved yield, and uncovered interactions that traditional statistics could not reveal [1].

Despite their success, conventional metaheuristics also face limitations. Many of them tend to converge prematurely, especially in landscapes with multiple local optima or deceptive fitness valleys. Their convergence speed and stability depend heavily on control parameters (e.g., inertia weight, mutation rate, or crossover probability), which are often problem-specific. Moreover, some algorithms lack adaptability, the ability to adjust their search dynamics in response to environmental feedback. This lack of adaptability can be a major drawback in bioprocess systems where the search space may change dynamically due to process drift, noise, or nonlinear interactions among factors [5], [6], [8], [9].

To overcome these limitations, a new class of nature-inspired metaheuristics has been developed, grounded not in animal behavior or physical laws, but in ecological and cooperative principles. The World Algorithm (WA) belongs to this emerging generation. It is inspired by the ecological interactions among trees in a forest, which share resources through underground mycorrhizal networks and adapt collectively to environmental changes. This cooperative exchange of nutrients and information enables the forest ecosystem to maintain stability, resilience, and efficiency even under fluctuating environmental conditions.

In the context of optimization, the WA abstracts these interactions into a computational framework. Each “tree” in the population represents a potential solution in the search space. Trees exchange information with neighbors (other candidate solutions) based on their relative fitness, simulating nutrient flow from stronger to weaker entities. Over successive generations, this information-sharing process enhances global awareness across the population, preventing premature convergence and ensuring the collective search process remains diverse yet coordinated [10].

The WA mechanism embodies three fundamental ecological behaviors:

I. Resource sharing–high-fitness individuals distribute part of their solution features to others, mimicking nutrient transfer through root systems.

II. Competition and adaptation–trees compete for environmental resources (fitness), but weak trees can adapt by relocating or restructuring based on feedback from stronger ones.

III. Environmental response–the algorithm dynamically adjusts its exploration–exploitation balance depending on the diversity of the population, emulating how real ecosystems respond to stress or change.

This adaptive mechanism grants the WA superior convergence stability and resilience against local traps compared to traditional methods like GA or PSO. Moreover, its social-ecological metaphor allows it to explore the search space more systematically, guided by a self-organizing principle rather than purely random variation. The result is a metaheuristic that is both efficient and interpretable, a rare combination in evolutionary computation [3].

The hybridization of ANNs with the WA creates a powerful synergy between predictive intelligence and adaptive optimization. In this configuration, the ANN serves as a nonlinear regression model trained on experimental fermentation data, mapping input variables (such as glucose, soybean meal, phosphate, and trace element concentrations) to the corresponding output (actinomycin V yield). Once trained, the ANN effectively becomes a digital twin of the fermentation process, a virtual replica capable of simulating the response surface with high fidelity.

The WA then operates on top of this surrogate model. Instead of conducting costly physical experiments, it explores potential combinations of input parameters through virtual simulations provided by the ANN. Each candidate solution corresponds to a specific medium composition and culture condition, and the ANN instantly predicts the expected yield. The WA evaluates these predictions, shares information among its “trees,” and iteratively refines the search toward the global optimum. This hybrid strategy significantly accelerates the optimization process, reducing experimental workload and cost while maintaining accuracy and robustness.

Such ANN–WA frameworks are especially beneficial for bioprocesses characterized by:

I. High dimensionality (many interacting variables), II. Nonlinearity (complex, multimodal response surfaces), III. Experimental noise (biological variability), IV. Limited data availability (expensive or time-consuming assays).

In these settings, the WA’s adaptive learning and cooperative search dynamics make it particularly effective. Its biologically inspired intelligence mirrors the very systems it seeks to optimize, living, dynamic, and interconnected [1], [5].

Compared with traditional RSM or classical metaheuristics, the ANN–WA combination offers several tangible advantages:

Beyond the immediate goal of optimizing actinomycin V production, this research has implications for a wide range of biotechnological applications. Many microbial metabolites, such as antibiotics, enzymes, pigments, and organic acids, share similar production challenges rooted in complex, nonlinear process dynamics. Traditional modeling approaches often struggle to accurately predict these systems, particularly during scale-up when parameter sensitivities shift. By introducing adaptive, data-driven hybrid frameworks, such as ANN– WA systems, researchers can design intelligent bioprocesses that self-optimize in silico before validation. Moreover, this paradigm aligns with the ongoing transition to Industry 4.0 in biotechnology, where digital twins, AI-driven optimization, and real-time feedback control are redefining how fermentation systems are designed and operated. A properly trained ANN can be continuously updated with new process data, and the WA can perform online optimization to adapt to drift or unexpected disturbances. This dynamic, learning-based control strategy represents a step toward truly autonomous biomanufacturing capable of maintaining optimal yield and quality with minimal human intervention [7], [12], [13].

The present study aims to develop and validate an intelligent optimization framework for enhancing actinomycin V production by integrating an ANN with the WA. The specific objectives are as follows: I. To establish a comprehensive experimental dataset for actinomycin V biosynthesis under various combinations of carbon, nitrogen, and mineral sources.

II. To construct and train an ANN model capable of accurately predicting actinomycin V yield based on culture conditions.

III. To implement the WA as a metaheuristic optimizer that efficiently searches the multidimensional input space using the ANN model as its fitness evaluator.

IV. To identify the global optimal conditions that maximize actinomycin V yield, and experimentally validate these predictions in laboratory-scale fermentations.

V. To compare the performance of the ANN–WA framework with conventional optimization methods such as RSM and standard metaheuristics (e.g., GA, PSO) in terms of prediction accuracy, convergence speed, and robustness.

Through this integration, the study seeks not only to improve actinomycin V production but also to demonstrate the broader feasibility of hybrid AI–nature-inspired optimization in industrial biotechnology [4], [14], [15].

This research contributes to both biochemical engineering and computational intelligence in several key ways:

I. Scientific contribution: introduces a novel application of the WA to optimize antibiotic biosynthesis, providing a comparative analysis of its performance relative to conventional methods.

II. Methodological contribution: It demonstrates how ANNs and WA-based metaheuristics can be synergistically combined to handle complex, nonlinear, and noisy optimization landscapes in fermentation.

III. Practical contribution: it establishes a scalable workflow for process optimization that can reduce experimentation time, cut costs, and improve industrial yields.

IV. Theoretical contribution: It offers new insights into how ecological cooperation principles (as embodied in the WA) can inspire more adaptive and interpretable computational models.

Ultimately, the ANN–WA hybrid represents a step toward intelligent, self-optimizing bioprocesses. The approach can transform how researchers explore and exploit the rich, nonlinear interactions governing microbial metabolism, turning what was once an empirical art into a data-driven, algorithmic science [4], [16], [17].

The actinomycin V–producing microorganism employed in this study was Streptomyces triostinicus (accession number EU635725; MTCC 8123), a Gram-positive, filamentous bacterium well known for its ability to synthesize chromopeptide antibiotics. The strain was originally isolated from a soil sample collected from a humid forest ecosystem and preserved under standard cryogenic conditions until use. Before experimental runs, cultures were revived on ISP-2 agar plates and incubated at 28 °C for five days to ensure active sporulation and morphological uniformity.

For submerged fermentation, spores from the agar plates were inoculated into 250 mL Erlenmeyer flasks containing 50 mL of production medium. The basal medium composition was as follows: Magnesium Sulfate Heptahydrate (MgSO₄·7H₂O, 0.5 g/L), Sodium Chloride (NaCl, 3 g/L), glucose (15 g/L), soybean meal (10 g/L), and Calcium Carbonate (CaCO₃, 3 g/L). Each component was selected based on its physiological relevance to antibiotic biosynthesis. Glucose served as the primary carbon and energy source, while soybean meal provided amino acids and peptides as nitrogen donors. CaCO₃ acted as both a buffering agent and a micronutrient source, stabilizing the medium pH during fermentation. Magnesium and sodium salts supplied essential cations required for enzyme activation and osmotic regulation.

The flasks were incubated on a rotary shaker at 180 rpm and 28 °C for six days. Aeration and agitation rates were chosen to maintain sufficient oxygen transfer, as oxygen availability is crucial to actinomycin biosynthesis due to the oxidative nature of its peptide assembly steps. The fermentation broth was sampled periodically to monitor biomass growth, pH variation, and actinomycin production.

After cultivation, the culture broth was centrifuged at 10,000 × g for 10 min, and the supernatant was extracted with an equal volume of chloroform. The organic phase was evaporated under reduced pressure, and the residue was re-dissolved in methanol for spectrophotometric quantification of actinomycin V at 443 nm. The antibiotic concentration was expressed as mg/L of culture filtrate [1].

The predictive modeling stage employed an ANN architecture to capture the nonlinear mapping between fermentation medium composition and actinomycin V yield. The ANN was implemented in MATLAB R2020b using the Neural Network Toolbox, and all computations were performed on a workstation equipped with an Intel® Core™ i9 processor and 32 GB of RAM.

After developing a reliable predictive ANN model, the next step was to determine the combination of medium components that maximized actinomycin V yield. This optimization was performed using the WA, also known as the WA Algorithm, a metaheuristic approach inspired by the ecological interactions and cooperative resource sharing observed in forest ecosystems.

To verify the reliability of the optimization results, the predicted optimal medium composition obtained from the ANN–WA framework was used to prepare three independent fermentation batches. The experimental actinomycin V yields were measured as described earlier and compared with the ANN–WA-predicted values. The degree of agreement was quantified using the Relative Deviation (RD%) and standard deviation across replicates.

Additionally, statistical analyses, including t-tests and Analysis of Variance (ANOVA), were conducted to assess the significance of yield improvements relative to the baseline (unoptimized) medium. The reproducibility and robustness of the hybrid optimization approach were further evaluated by introducing small perturbations (±5%) in the optimal component concentrations and observing the resulting yield stability.

Fig. 1 summarizes the overall methodology in a schematic workflow:

I. Experimental phase: laboratory-scale fermentations conducted according to CCD design to generate the training dataset.

II. Modeling phase: ANN construction, training, and validation to build an accurate predictive model.

III. Optimization phase: application of the WA using the ANN as the virtual evaluator to search for the global optimum.

IV. Validation phase: experimental verification of predicted optimal conditions and statistical confirmation of

All microbial handling and fermentation operations were conducted under biosafety level 1 (BSL-1) containment, in accordance with institutional safety guidelines for Streptomyces cultures. Solvent extraction and chemical handling were performed in fume hoods with appropriate Personal Protective Equipment (PPE). No animal or human subjects were involved in this research [12].

Both the RSM and the ANN were used to model the relationships between five independent variables, magnesium sulfate (MgSO₄·7H₂O), NaCl, glucose, soybean meal, and CaCO₃, and the yield of Actinomycin V (mg/L).

While RSM provides a statistical approximation based on quadratic polynomial equations, ANN captures nonlinear dependencies without assuming specific functional forms. The statistical performance indicators for both models are summarized in Table 1.

The RSM model explained only about 76% of the total variance, with significant residuals in experiments involving high carbon and nitrogen concentrations. The residual plots (not shown) exhibited non-random patterns, suggesting inadequate representation of nonlinear nutrient interactions.

Conversely, the ANN model demonstrated a near-perfect fit (R² = 0.98), indicating its capacity to model complex biochemical systems with multidimensional, nonlinear interdependencies. The Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) were drastically lower, confirming better predictive generalization for unseen data.

Fig. 1 (conceptually illustrated) shows the parity plot of experimental and predicted yields. The ANN-predicted points clustered tightly along the 45° diagonal line, whereas RSM predictions were more dispersed, especially near the upper yield range, where the quadratic approximation failed to capture metabolic saturation effects.

Following successful ANN training, the (tree social relationship, WA) was implemented to identify the global optimum in the multidimensional nutrient space. WA is an ecology-inspired metaheuristic that simulates the collective behavior of trees sharing resources under environmental constraints.

Each solution candidate (or “tree”) represented a unique combination of nutrient concentrations. The fitness of each tree was evaluated using the trained ANN model, which predicted the expected Actinomycin V yield for that composition. The algorithm parameters were set as follows:

Elite count 2 Top-performing individuals preserved each iteration Resource sharing fraction 0.2 Proportion of shared knowledge among trees Growth interval 20 Update period for structural adaptation stall limit 50 Early stop criterion for convergence

The WA algorithm demonstrated rapid convergence, reaching a stable global optimum by the 11th generation, far earlier than traditional evolutionary algorithms such as GA or PSO, which often require >100 generations for similar problems. The optimized medium composition and corresponding predicted and experimental yields are listed in Table 4.

Under these optimal conditions, the ANN–WA model predicted a maximum Actinomycin V yield of 458 mg/L, which was experimentally validated at 453 ± 6 mg/L. This represents:

I. A fourfold improvement compared to the unoptimized baseline yield (110 mg/L).

II. Approximately 40% higher than the RSM-predicted optimum (~320 mg/L).

III. A deviation of less than 1.1% between predicted and experimental outcomes indicates an exceptional match, confirming both model accuracy and algorithmic robustness.

The world algorithm: a universal metaheuristic for complex optimization problems 16T

Fig. 2 (conceptually) shows the WA convergence trend. Mean fitness (average yield prediction across all trees) rose steadily until generation 11, then plateaued, indicating successful convergence without oscillation or stagnation. This smooth curve demonstrates effective balance between exploration (searching new regions) and exploitation (refining existing promising zones).

To interpret the individual and interactive influence of medium components, a sensitivity analysis was conducted using the trained ANN model. Each variable was varied across its experimental range, while others were fixed at optimized levels. The relative importance of each variable was calculated using Garson’s algorithm, which decomposes connection weights in the neural network to estimate variable contribution. Table 5 presents the normalized sensitivity ranking of factors affecting Actinomycin V yield.

The multidimensional response surfaces generated by ANN reveal nonlinear synergistic and antagonistic interactions among nutrients. Three critical interactions are highlighted below.

The optimized conditions predicted by the ANN–WA model were experimentally verified in triplicate batch fermentations under controlled conditions (28 °C, 180 rpm, 6 days). The results are presented in Table 6.

The WA mimics the ecological interactions among trees that share resources through interconnected root systems, collectively adapting to environmental changes. This concept of “cooperative intelligence” is crucial in optimization landscapes characterized by multiple local optima, exactly the scenario encountered in fermentation systems, where small variations in carbon or nitrogen ratios can dramatically shift metabolic fluxes.

Unlike GA, which may suffer from premature convergence due to limited diversity, or PSO, which can oscillate around suboptimal points, WA maintains diversity through nutrient sharing and adaptive growth cycles. Each “tree” represents a candidate solution vector (medium composition), and information exchange among elite individuals enables both exploration (global search) and exploitation (local refinement). In this study, WA achieved convergence within 11 generations, a remarkable efficiency considering the five-dimensional parameter space. This rapid optimization indicates that WA effectively exploited the ANN’s learned nonlinear mappings, using them as an adaptive fitness landscape to guide its ecological search behavior.

The ANN model served as a nonlinear regression engine that captured intricate relationships between the five key medium components MgSO₄, NaCl, glucose, soybean meal, and CaCO₃ and Actinomycin V yield. Its R² value of 0.98 (compared to RSM’s 0.76) reveals the superior capacity of neural architectures to approximate unknown, high-order functions without assuming any predefined polynomial model.

Through this flexible mapping, ANN uncovered interaction patterns not visible in classical designs. For instance, increasing soybean meal concentration enhanced yield up to a critical threshold (~20 g/L), beyond which the system entered a repression zone, likely due to amino acid accumulation interfering with secondary metabolism. Similarly, moderate NaCl levels promoted antibiotic biosynthesis, potentially via osmotic stress signaling that stimulates secondary metabolite pathways, whereas higher concentrations imposed a metabolic burden on the cells.

The hybrid ANN–WA model not only identified the optimal composition (MgSO₄ = 3.61 g/L, NaCl = 1.92 g/L, glucose = 8.83 g/L, soybean meal = 20.2 g/L, CaCO₃ = 13.1 g/L), but also provided interpretable biological reasoning for these values.

Soybean meal as a nitrogen and amino acid source Soybean meal supplies essential amino acids, including tryptophan, the direct precursor for Actinomycin biosynthesis. However, excess nitrogen availability often suppresses secondary metabolism by redirecting energy toward biomass formation. The WA-identified optimum reflects a delicate balance between providing sufficient precursor availability and avoiding catabolite repression.

The results demonstrate that the ANN–WA model outperformed all benchmark methods in both convergence and predictive accuracy. The biological interpretation of its optimum adds further confidence to its practical applicability. Unlike RSM or GA, which rely on fixed parametric or stochastic structures, the WA algorithm adapts dynamically, an advantage that mirrors the processes of natural selection and resource distribution in ecological systems.

The ANN–WA hybrid approach was experimentally validated, with the predicted yield (458 mg/L) confirmed by empirical fermentation (453 ± 6 mg/L), a discrepancy of 1.2% or less, indicating outstanding generalization and reliability. This consistency underscores the model's robustness when extrapolating beyond the training data.

In industrial bioprocessing, this translates into fewer experimental cycles, lower material costs, and faster scale-up feasibility. Given that Actinomycin V production requires costly precursors and lengthy fermentation times, the fourfold yield enhancement achieved here represents a transformative economic impact.

Moreover, the interpretability of the ANN–WA optimization provides process engineers with actionable insights rather than opaque “black box” outputs, allowing controlled adjustment of nutrient ratios and process parameters without blind experimentation.

The success of this framework extends beyond Actinomycin V. The demonstrated synergy between data-driven learning ANN and ecological optimization WA establishes a generalizable paradigm for other secondary metabolites, such as erythromycin, rapamycin, or streptomycin, whose biosynthesis also depends on subtle nutrient interactions.

Potential future research directions include:

I. Dynamic WA integration: incorporating feedback from real-time sensors (pH, DO, redox) to allow closed-loop adaptive optimization during fermentation.

II. Explainable AI models: coupling WA with saliency- or SHAP-based interpretability to dynamically identify the most influential factors in production yield.

III. Hybrid bioprocess digital twins: using the ANN–WA model as a digital twin of the fermentation system for predictive control and optimization at an industrial scale.

IV. Multi-objective optimization: extending WA to optimize not only yield but also productivity, purity, and cost-efficiency simultaneously.

By emulating natural cooperation and self-organization, the WA framework embodies the next generation of biointelligent optimization systems, where computational algorithms evolve in harmony with biological processes.

Perhaps the most striking outcome of this study lies in the biological coherence of the optimized conditions. The system’s mathematical optimum corresponds directly to metabolic logic, implying that the WA algorithm, despite being abstractly inspired by ecology, inadvertently captures biological truths about Streptomyces physiology. It suggests that the algorithm’s ecological basis and mutualistic adaptation parallel the cooperative balance of cellular metabolism itself.

In essence, the ANN provided the phenotypic map, while WA exerted evolutionary pressure, together forming a self-consistent computational ecosystem that converged toward biologically meaningful equilibria.

The combination of ANN modeling and the WA represents a paradigm shift in bioprocess optimization from rigid, low-dimensional statistics to adaptive, interpretable, and bioinspired intelligence.

Key takeaways include:

I. ANN captured the nonlinear, high-order interactions governing Actinomycin synthesis.

II. WA efficiently explored and refined the search space, balancing exploration and exploitation.

III. The model’s predictions aligned with biochemical and metabolic logic, validating its interpretability.

IV. Yield improvement (110 → 458 mg/L) demonstrates tangible, scalable process enhancement.

Ultimately, this hybrid approach bridges biology and computation, turning fermentation optimization into a living system of intelligence, one that learns, adapts, and evolves just like the microbes it seeks to optimize.