<![CDATA[This study addresses the challenge of enhancing transportation efficiency during large-scale events, with a particular focus on the Hajj pilgrimage. Every year, more than two million pilgrims visit Makkah in Saudi Arabia to perform their Hajj rituals. The Haj ritual requires transporting vast numbers of pilgrims within a limited time, compounded by diverse transportation preferences that make timely, optimal scheduling complex. To tackle this, the study employs three optimization algorithms -Harmony Search (HS), Differential Evolution (DE), and Black Widow Optimization (BWO) - to optimize transportation schedules based on individual preferences. A comprehensive mathematical model was developed for this purpose, incorporating both hard and soft constraints that reflect the scheduling requirements and preferences of pilgrims. Experimental results show that the DE algorithm consistently outperforms HS and BWO, achieving the highest mean scores in 100% of scenarios with a population size of 100, 66.7% of scenarios with a population size of 20, and 16.7% of scenarios with a population size of 5. In contrast, BWO struggles to adapt to varying parameter settings, producing consistently lower-quality solutions. DE, in particular, performs exceptionally well with lower crossover probabilities, demonstrating its ability to balance exploration and exploitation effectively. On the other hand, HS yields better results when higher exploration probabilities are used, highlighting its strength in broader search space exploration. In contrast, the performance of BWO remains largely unaffected by variations in exploration and exploitation parameters, leading to consistently inferior solutions. These findings underscore the importance of dynamic parameter tuning for large-scale optimization tasks, suggesting that such approaches are promising for addressing complex scheduling challenges in major events like Hajj.]]>
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