Moth-Flame Optimization

Moth-Flame Optimization (MFO) is a nature-inspired, swarm-intelligence metaheuristic modeled on the spiral navigation of nocturnal moths toward light. By combining a logarithmic spiral search pattern with dynamic flame assignment, MFO balances exploration and exploitation effectively, improving the ability to escape local optima and maintain diversity across complex search spaces. Since its introduction, MFO has been widely adopted for solving continuous, discrete, and multi-objective problems, with variants such as binary MFO, hybrid MFO, chaotic MFO, and adaptive MFO expanding its capabilities. These variants address issues of convergence speed, search accuracy, and high-dimensional optimization challenges. MFO’s applications extend across power systems, robotics, medical diagnosis, image processing, software engineering, and cloud computing, where it consistently outperforms many classical techniques. Its integration with modern machine learning frameworks, hybrid metaheuristics, and domain-specific enhancements further underscores its versatility and potential. This chapter presents the fundamentals of MFO, its mathematical formulation, key variants, and a survey of representative applications, highlighting its strengths, limitations, and research opportunities.