A deep-layered gravitational search algorithm for real-world optimization problems

The Gravitational Search Algorithm (GSA) is a physics-inspired optimization method that often struggles with slow convergence and local optima entrapment. This paper introduces a Deep-layered Gravitational Search Algorithm (DLGSA) that adds a new hierarchical layer and an adaptive gravitational constant scheme to the standard GSA. The extra layer (an associate memory of solutions) increases information sharing and preserves diversity, helping the population escape local optima. A log-sigmoid decay rule for the gravitational constant ensures a smooth shift from exploration to exploitation as the search progresses. Tested on 22 real-world optimization problems (CEC2011 benchmarks) against nine advanced GSA variants, DLGSA shows superior performance and maintains higher population diversity to avoid premature convergence. DLGSA achieves these improvements with only minor computational overhead, making it an effective and efficient approach for complex optimization tasks.