Quasi-random Fractal Search (QRFS): A dynamic metaheuristic with sigmoid population decrement for global optimization

Global optimization of complex and high-dimensional functions remains a central challenge with broad applications in science and engineering. This study introduces a new optimization approach called quasi-random metaheuristic based on fractal search (QRFS), which harnesses the power of fractal geometry, low discrepancy sequences, and intelligent search space partitioning techniques. The QRFS uses fractals' inherent self-similarity and intricate structure to guide the solution space exploration. For the proposal, a deterministic but quasi-random element is used in the search process using low discrepancy sequences, such as Sobol, Halton, Hammersley, and Latin Hypercube. This integration allows the algorithm to systematically cover the search space while maintaining the level of diversity necessary for efficient exploration. The QRFS employs a dynamic strategy of partitioning the search space and reducing the population of solutions to optimize the use of function accesses, which causes it to adapt well to the characteristics of the problem. The algorithm intelligently identifies and prioritizes promising regions within the fractal-based representation, allocating computational resources where they are most likely to yield optimal solutions. Experimental evaluations on several benchmark problems demonstrate that QRFS consistently outperforms modern, canonical metaheuristics and variants of algorithms such as differential evolution (DE), particle swarm optimization (PSO), covariance matrix adaptive evolution strategy (CMA-ES), regarding solution quality. Besides, the algorithm shows remarkable scalability, which makes it suitable for high-dimensional optimization tasks. Overall, QRFS offers a robust and efficient approach to solving complex optimization problems in various domains, paving the way for improved decision-making in real-world applications.