A hybrid flow shop scheduling optimization using puma optimizer: Addressing energy efficiency and workforce restrictions

The Hybrid Flow Shop Scheduling Problem (HFSP) is a complex challenge in production and manufacturing, requiring efficient scheduling solutions that optimize productivity while considering real-world constraints. This study proposes an advanced optimization framework utilizing the Puma Optimizer, a metaheuristic algorithm enhanced with an adaptive control mechanism for intelligently selecting phases and operators. This feature makes it well-suited for discrete optimization problems such as HFSP. Our approach integrates heuristic decoding and adaptive local search, balancing exploration and exploitation to generate high-quality schedules. The proposed mathematical model optimizes makespan and total tardiness while energy consumption is incorporated as a constraint to enhance sustainability. Extensive computational experiments demonstrate the superior performance of the proposed algorithm compared to traditional methods, achieving shorter makespan and lower tardiness while ensuring workforce feasibility. These results highlight the Puma Optimizer’s adaptability and potential to set new benchmarks for HFSP, offering a scalable and effective solution for modern production systems.