Advances in Production Engineering & Management
Volume 20 | Number 3 | September 2025 | pp 309–324
https://doi.org/10.14743/apem2025.3.542
Golden Drop Algorithm: A Water Wave and Golden Ratio inspired novel metaheuristic for global optimization
Karaçizmeli, İ.H.
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A B S T R A C T
Metaheuristic methods are approximate solution techniques that are widely used to solve complex optimization problems. Drawing inspiration from nature, physics, or human behavior, researchers have developed a diverse range of metaheuristic algorithms, either population-based or single-solution-based, with varying neighborhood structures and memory usage. Due to the diversity and complexity of optimization problems in different domains, no single algorithm can be universally effective for all types of problems. This study proposes a novel metaheuristic algorithm, the Golden Drop Algorithm (GDA), which is simple, efficient, and easy to implement. GDA is a physics-inspired method that simulates the propagation of circular waves formed by raindrops falling into water, with wave expansion governed by the golden ratio. The algorithm was evaluated using the Congress on Evolutionary Computation (CEC) 2017 benchmark functions and was compared with three well-known metaheuristics: Genetic Algorithm (GA), Grey Wolf Optimizer (GWO), and Particle Swarm Optimization (PSO). The results demonstrate that GDA is not only straightforward and computationally efficient, but also capable of producing competitive and feasible solutions. In 50 % of the CEC 2017 benchmark functions, GDA ranked first, while in 32 % of the functions, it secured second place. In addition, its performance was validated through three benchmark engineering design problems: welded beam design, pressure vessel design, and compression spring design, highlighting its robustness and effectiveness in solving constrained nonlinear optimization tasks.
A R T I C L E I N F O
Keywords • Metaheuristic optimization; Physics-inspired metaheuristics; Water wave; Golden ratio; CEC 2017 benchmark functions; Engineering design problems
Corresponding author • Karaçizmeli, İ.H.
Article history • Received 6 August 2025, Revised 8 September 2025, Accepted 15 September 2025
Published on-line • 31 October 2025
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