Adaptive Neuro-Fuzzy Inference Systems in Optimization Problems

Adaptive Neuro-Fuzzy Inference Systems (ANFIS) integrate the interpretability of fuzzy logic with the adaptive learning capabilities of neural networks, forming a powerful framework for tackling complex optimisation challenges. In essence, ANFIS constructs a fuzzy inference model whose membership functions and rule consequences are tuned through a supervised learning approach analogous to backpropagation. This hybrid architecture excels in modelling nonlinear systems, managing uncertainty, and accommodating noisy or incomplete data. Over the past decade, researchers have enriched ANFIS with global search techniques—such as particle swarm optimisation, genetic algorithms and quantum‐behaved swarm variants—to accelerate convergence and escape local minima. Applications range from industrial process control and renewable energy management to economic forecasting and biomedical signal processing. The global significance of ANFIS lies in its blend of human-readable rule bases and data-driven adaptation, offering both transparency and performance. Recent advances have explored self-evolving rule structures, adaptive membership functions and hybrid training schemes, yielding more robust and computationally efficient implementations. As optimisation problems grow in scale and complexity, ANFIS continues to evolve, bridging the gap between symbolic reasoning and continuous function approximation in practical engineering and scientific domains.

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In industrial process control, a novel hybrid algorithm combined particle swarm optimisation with multiple ANFIS modules to tune PID controllers for pH regulation in cooling towers. The approach markedly improved dynamic response, reduced overshoot and lowered energy consumption, demonstrating real-time adaptive control in highly nonlinear environments.
 In power system stability, an ANFIS-based controller tuned a wind-turbine-equipped grid to maintain voltage and frequency following faults. The adaptive scheme retained optimal damping over a wide disturbance range, reducing oscillations and enhancing response speed under variable loading.
 On the algorithmic front, an improved quantum-behaved particle swarm technique was developed to train ANFIS parameters without gradient descent. By adapting the contraction-expansion coefficient dynamically, the method achieved faster convergence and higher accuracy across benchmark systems, highlighting the value of metaheuristic-driven ANFIS training for complex optimisation tasks.

Adaptive Neuro-Fuzzy Inference Systems in Optimization Problems publication trend

The graph below shows the total number of articles in adaptive neuro-fuzzy inference systems in optimization problems across all publications each year (not limited to Nature Index journals).

Technical terms

Adaptive Neuro-Fuzzy Inference System (ANFIS): A hybrid model combining fuzzy logic’s rule-based reasoning with neural network learning to approximate nonlinear functions.
 Particle Swarm Optimisation (PSO): A population-based metaheuristic inspired by social behaviour in flocks, used to find optimal parameters by sharing information among candidate solutions.
 Membership Function: A curve defining the degree to which an input belongs to a fuzzy set, adjustable during ANFIS training to capture system behaviour.
 Backpropagation: A gradient-based learning algorithm that updates network or fuzzy model parameters by minimising error through successive layers.
 Metaheuristic: A high-level problem-independent strategy guiding subordinate heuristics to explore and exploit search spaces effectively.

References

1. Optimization of pH Controller Performance for Industrial Cooling Towers via the PSO–MANFIS Hybrid Algorithm. Energies (2025).
2. Training ANFIS Model with an Improved Quantum‐Behaved Particle Swarm Optimization Algorithm. Mathematical Problems in Engineering (2013).
3. A New Adaptive Neuro-Fuzzy Inference System (ANFIS) Controller to Control the Power System equipped by Wind Turbine. ITM Web of Conferences (2022).