L-PFO: Enhancing Polar Fox Optimization with Linear Population Size Reduction for Complex Benchmark Problems

Abstract

This study presents an improved variant of the Polar Fox Optimization (PFO) algorithm, named L-PFO, by incorporating the Linear Population Size Reduction (LPSR) mechanism. The original PFO algorithm, which is inspired by the adaptive survival strategies of Arctic wildlife in harsh environmental conditions, exhibits strong capabilities in exploring the search space. However, its performance is notably inconsistent in high-dimensional and multimodal optimization problems due to limitations in maintaining a balanced trade-off between exploration and exploitation. To address these shortcomings, the L-PFO algorithm dynamically adjusts the population size during the optimization process through a linear reduction strategy, thereby promoting convergence stability and refining local search efficiency. The proposed algorithm is empirically validated using eight well-known benchmark test functions that reflect varying levels of complexity and modality. Performance metrics including best, average, and standard deviation values are calculated over 30 independent runs to assess the algorithm’s robustness and generalization capacity. The experimental results demonstrate that the L-PFO algorithm consistently outperforms the original PFO in terms of convergence speed, solution accuracy, and stability across most test functions. In particular, significant improvements are observed on challenging functions where the original PFO algorithm struggled with premature convergence or high variance among runs. The integration of LPSR enhances the algorithm's adaptability and resilience against local optima traps, making it more suitable for complex optimization tasks. Overall, the proposed L-PFO algorithm provides a more reliable and scalable metaheuristic framework with minimal parameter dependency, indicating its potential applicability in various real-world engineering and computational optimization problems