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Hybrid Nature-Inspired Optimization for the Cell Formation Problem with Machine Reliability and Alternative Routings
Paulo Figueroa-Torrez1, Broderick Crawford2, Orlando Durán3
1Departamento de Ciencias Industriales, Medio Ambiente y Energía, Universidad Católica Boliviana "San Pablo", Colón 734, Tarija, Bolivia.
Biomimetics (Basel, Switzerland)
|June 25, 2026
Summary
This study compares Black Widow Optimizer and Golden Eagle Optimizer for the complex Generalized Cell Formation Problem. A hybrid approach combining Golden Eagle Optimizer with Black Widow Optimizer
Area of Science:
- Operations Research
- Manufacturing Systems Engineering
- Computational Intelligence
Background:
- The Cell Formation Problem (CFP) is crucial for cellular manufacturing efficiency, flexibility, and reliability.
- Real-world complexities like alternative process routes and machine reliability lead to the NP-Hard Generalized Cell Formation Problem (GCFP) with machine reliability.
- Addressing the computational complexity of GCFP requires advanced optimization techniques.
Purpose of the Study:
- To comparatively evaluate the Black Widow Optimizer (BWO) and Golden Eagle Optimizer (GEO) for the GCFP with machine reliability.
- To investigate the potential of hybridizing metaheuristics by integrating BWO mechanisms into GEO to improve search behavior.
- To assess the performance and computational complexity of individual and hybrid algorithms.
Main Methods:
- Comparative analysis of BWO and GEO algorithms on the GCFP with machine reliability.
- Development and evaluation of a hybrid metaheuristic strategy combining BWO's mutation mechanism with GEO's search strategies.
- Application of the Wilcoxon-Mann-Whitney statistical test to validate performance differences.
- Calculation of Big-O computational complexity for algorithm assessment.
Main Results:
- The Black Widow Optimizer (BWO) demonstrated superior individual performance compared to the Golden Eagle Optimizer (GEO), with average relative percentage deviation (RPD) values of 0.855% and 1.068%, respectively.
- The hybrid strategy, integrating BWO's mutation mechanism into GEO, achieved the best performance with an RPD of 0.592%.
- Statistical validation confirmed significant performance differences among the evaluated algorithms.
Conclusions:
- Hybrid metaheuristics show significant potential for solving the Generalized Cell Formation Problem with machine reliability.
- Integrating specific mechanisms, like mutation from BWO into GEO, can enhance optimization performance in complex manufacturing problems.
- The findings contribute to developing more robust and efficient manufacturing systems through advanced computational approaches.