A hybrid scheduling approach for mega event transportation: integrating harmony search and black widow optimization

Optimization techniques have been extensively employed to address various challenges in human life across numerous domains. This study introduces a novel hybrid optimization algorithm that combines the strengths of harmony search (HS) and black widow optimization (BWO). The primary contribution lies in combining the cannibalism mechanism of BWO into the improvisation process of HS, enhancing HS's ability to explore and refine solutions within the search space. The proposed Harmony Search Black Widow Optimization (HSBWO) algorithm is adapted and applied to a real-world optimization problem in transportation scheduling during the Hajj pilgrimage, particularly focusing on increasing the capacity of pilgrims' housing sites in the Muzdalifah area by reusing the sites multiple times. Efficiently relocating a vast number of pilgrims to housing sites within a limited timeframe while meeting several hard and soft constraints is critical. Experimental results demonstrate that HSBWO consistently achieved the highest average scores across all tested scenarios compared to HS and BWO, with significant improvements in both solution quality and convergence rates. Statistical analysis using ANOVA confirmed that the performance differences were statistically significant at α equal to 0.05. Specifically, HSBWO outperformed HS with improvements in average fitness values ranging from 3.1% to 55.2%, while improvements over the BWO algorithm ranged from 6.4% to 56.0%, depending on the applied scenarios and population sizes.