<![CDATA[Optimization is fundamental to solving complex problems across engineering, economics, and computer science. However, navigating optimization landscapes characterized by numerous local extrema, such as valley-shaped functions, remains a significant computational challenge. To address this, this study implements the Flower Pollination Algorithm (FPA)—a robust nature-inspired metaheuristic—to efficiently solve valley-shaped optimization problems. The algorithm's performance is rigorously evaluated against four deceptive benchmark functions: Rosenbrock, Dixon-Price, Six-Hump Camel, and Three-Hump Camel, utilizing Python-based computational simulations. The evaluation focuses on convergence speed, solution accuracy, and the algorithm's capability to escape local optima. Experimental results demonstrate that FPA achieves exceptional accuracy and high computational efficiency. Specifically, FPA secured near-optimal fitness values of 0.00027 for the Rosenbrock function in under 0.83 seconds, and an impressive fitness of for the Three-Hump Camel function within 500 iterations. Furthermore, it successfully identified the true global minimum of -1.0316 for the Six-Hump Camel function at early stages. These empirical findings confirm FPA's strong global exploration capabilities, providing a solid foundation for its future application in more complex, high-dimensional engineering optimization tasks.]]>
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