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PKO demonstrates superior exploration and exploitation tendencies while effectively avoiding local optima.Official website: Javier Gutierrez Chamorro The overall results highlight PKO’s exceptional ability to tackle intricate optimization problems characterized by challenging search spaces. The comparative analysis employs various performance metrics, including the Friedman mean rank and the Wilcoxon rank-sum test, to reveal PKO’s effectiveness and efficiency. The 3rd category includes advanced algorithms, such as Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and Ensemble Sinusoidal Differential Covariance Matrix Adaptation with Euclidean Neighborhood (LSHADEcnEpSin). The 2nd category encompasses recently published algorithms, including Harris Hawks Optimization (HHO), Whale Optimization Algorithm (WOA), Sine Cosine Algorithm (SCA), Grey Wolf Optimizer (GWO), Gravitational Search Algorithm (GSA), and Moth-Flame Optimization (MFO). The 1st category comprises well-established and widely-cited optimizers such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). To gauge PKO’s efficacy, it is subjected to a comparative analysis against 3 categories of rival optimizers. Additionally, eight real-world engineering optimization problems, including both constrained and unconstrained scenarios, are considered in the assessment.

The algorithm’s performance is rigorously evaluated across thirty-nine test functions, which encompass various unimodal, multimodal, composite, and hybrid ones. These behavioral aspects are translated into mathematical models capable of effectively addressing a wide array of optimization challenges across diverse search spaces. The PKO algorithm is structured around three distinct phases: perching/hovering for prey (exploration/diversification), diving for prey (exploitation/intensification), and fostering symbiotic relations. In this study, we introduce the Pied Kingfisher Optimizer (PKO), a novel swarm-based meta-heuristic algorithm that draws inspiration from the distinctive hunting behavior and symbiotic relationships observed in pied kingfishers in the natural world.

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