Moth-Flame Optimization Algorithms in Engineering Applications

Moth-Flame Optimization (MFO) algorithms constitute a family of nature-inspired metaheuristic techniques that simulate the transverse orientation behaviour of moths navigating by celestial light. In the canonical MFO framework, a population of virtual moths searches a multidimensional solution space by spiralling towards a set of guiding points known as flames. At each iteration, moths update their positions around flames to balance global exploration and local exploitation. This simple yet effective mechanism has been widely adopted for engineering tasks in fields ranging from structural design and mechanical component sizing to control-system tuning, robotics path planning and photovoltaic parameter identification.

Despite its versatility, the original MFO algorithm often suffers from premature convergence, loss of population diversity and entrapment in local optima. To overcome these limitations, numerous enhancements have been proposed. Lévy-flight strategies and hybridisations with simulated annealing or differential evolution have boosted exploration capability, while archive-based migration and stagnation-replacement schemes have preserved diversity. Immune-inspired adaptations incorporating Gaussian mutation and opposition-based learning have further improved convergence speed and solution quality. Collectively, these developments have elevated MFO variants to a prominent role in addressing real-world engineering optimisation challenges under complex and constrained problem settings.

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Recent enhancements have targeted stagnation and diversity maintenance. In 2023, an enhanced MFO-SFR algorithm introduced a stagnation finding and replacing strategy to identify and rejuvenate trapped solutions. By maintaining an archive of high-quality candidates and replacing stagnant moths with archived solutions, the algorithm achieved superior robustness and global search performance when solving benchmark functions and mechanical design problems.

In 2022, an immune-inspired MFO variant was developed for automatic parking path optimisation in intelligent vehicles. This approach embedded an adaptive inertia weight, Gaussian mutation and opposition-based learning to balance global and local search efforts. The resulting model delivered smoother, more accurate parking trajectories and outperformed traditional optimisation routines in both simulation and semi-physical experiments.

Moth-Flame Optimization Algorithms in Engineering Applications publication trend

The graph below shows the total number of articles in moth-flame optimization algorithms in engineering applications across all publications each year (not limited to Nature Index journals).

Technical terms

Moth-Flame Optimization algorithm: A swarm intelligence method in which agents (moths) update their trajectories around reference points (flames) to explore and exploit a search space.

Metaheuristic algorithm: A high-level, general optimisation strategy that guides subordinate heuristics to find near-optimal solutions for complex problems.

Exploration–exploitation balance: The trade-off between searching new regions of the solution space (exploration) and refining known good solutions (exploitation).

Population diversity: The degree of variability among candidate solutions, crucial for preventing premature convergence to suboptimal regions.

Opposition-based learning: A technique that simultaneously considers current and opposite candidate positions to accelerate convergence and enhance global search capability.

References

1. Lévy‐Flight Moth‐Flame Algorithm for Function Optimization and Engineering Design Problems. Mathematical Problems in Engineering (2016).
2. A hybrid SA-MFO algorithm for function optimization and engineering design problems. Complex & Intelligent Systems (2018).
3. Hybrid Symbiotic Differential Evolution Moth-Flame Optimization Algorithm for Estimating Parameters of Photovoltaic Models. IEEE Access (2020).
4. Migration-Based Moth-Flame Optimization Algorithm. Processes (2021).
5. MFO-SFR: An Enhanced Moth-Flame Optimization Algorithm Using an Effective Stagnation Finding and Replacing Strategy. Mathematics (2023).
6. Automatic Parking Path Optimization Based on Immune Moth Flame Algorithm for Intelligent Vehicles. Symmetry (2022).
7. Application of Improved Moth-Flame Optimization Algorithm for Robot Path Planning. IEEE Access (2021).