Application of the improved sapling development algorithm in the coordination problem of over-current relays and comparison with optimization algorithms

Optimization algorithms are widely used to solve problems that aim to find the minimum or maximum value of a given objective function. These methods employ both mathematical and heuristic approaches to select the best possible alternative. In this study, the Overcurrent Relay Coordination (ORC) problem is addressed, and a nature-inspired metaheuristic algorithm called the Saplings Growing up Algorithm (SGuA), based on the biological growth process, is proposed. The enhanced version of the algorithm, Improved SGuA (ISGuA), is analyzed in detail, with a particular focus on the impact of initial population generation methods on performance. Ten different initialization strategies were evaluated. Among them, the uniform distribution method produced the best result with the lowest total operation time of 6.9002 seconds. It was observed that uniform distribution provided balanced exploration of the solution space by homogeneously sampling the parameter domain, thereby reducing the risk of getting trapped in local minima. Among other distributions, beta distributions allowed early convergence by focusing on specific regions, whereas asymmetric distributions such as log-normal, Rayleigh, Weibull, and exponential led to reduced performance due to insufficient sampling in parts of the search space. Latin hypercube and random initialization also showed weaker performance compared to the uniform approach. The developed ISGuA algorithm was further compared with commonly used metaheuristic methods such as Genetic Algorithm (GA), Whale Optimization Algorithm (WOA), Artificial Bee Colony (ABC), Grey Wolf Optimizer (GWO), Butterfly Optimization Algorithm (BOA), and League Championship Algorithm (LCA). ISGuA outperformed all of these algorithms by achieving the shortest total execution time. The results demonstrate that ISGuA exhibits superior performance both in terms of initialization strategies and overall optimization capability, providing a stable, efficient, and applicable solution for constrained problems such as ORC.