Hybrid Nature-Inspired Optimization for the Cell Formation Problem with Machine Reliability and Alternative Routings

The Cell Formation Problem plays a fundamental role in cellular manufacturing due to its impact on efficiency, flexibility, and reliability. Its complexity increases under real-world conditions involving alternative process routes and machine reliability constraints, leading to the Generalized Cell Formation Problem with machine reliability. Researchers have classified the Cell Formation Problem as an NP-Hard problem. To address this computational complexity, this study presents a comparative and hybrid evaluation of the Black Widow Optimizer and the Golden Eagle Optimizer for the Generalized Cell Formation Problem with machine reliability, examining whether mechanisms derived from the Black Widow Optimizer can enhance the search behavior of the Golden Eagle Optimizer. The Black Widow Optimizer provides strong intensification through procreation, cannibalism, and mutation mechanisms, whereas the Golden Eagle Optimizer provides a balanced search process through its cruise and attack strategies. Experimental results show that the Black Widow Optimizer achieved better individual performance than the Golden Eagle Optimizer, with average RPD values of 0.855% and 1.068%, respectively. However, the hybrid strategy based on incorporating the mutation mechanism into the Golden Eagle Optimizer produced the best result, reaching an RPD of 0.592%. The study also employed the Wilcoxon–Mann–Whitney statistical test to validate the performance differences among algorithms, and the respective Big-O computational complexity was calculated. These findings highlight the potential of hybrid metaheuristics for designing robust and efficient manufacturing systems.