Optimizing the Classic and the Energy-Efficient Permutation Flowshop Scheduling Problem with a Hybrid Tyrannosaurus Rex Optimization Algorithm

This paper introduces a Hybrid Tyrannosaurus Rex Optimization Algorithm (Hybrid TROA) combined with Variable Neighborhood Search (VNS), two variations of the Path Relinking strategy, and a randomized Nawaz–Enscore–Ham (NEH) heuristic to address the Permutation Flowshop Scheduling Problem (PFSP). The TROA is a novel bio-inspired meta-heuristic algorithm modeled on the hunting behavior of the prehistoric Tyrannosaurus Rex. Leveraging the potential of this newly developed and efficient algorithm, we propose a framework in which an initial population of solutions is generated using the randomized NEH heuristic. These solutions are then further optimized through VNS and Path Relinking, yielding highly satisfactory results for the PFSP. First, we consider two optimization criteria separately: the makespan and the total flow time. Next, we conduct a comparative study of the Hybrid TROA against other prominent meta-heuristics, along with a statistical analysis using non-parametric tests, to determine the best-performing method for each objective. According to our findings, the Hybrid TROA proves to be the most suitable method in this study for minimizing both targets. Finally, recognizing that contemporary industry demands both high productivity and energy efficiency, we propose an energy-efficient version of the classic PFSP, simultaneously considering two criteria for optimization: the makespan and total energy consumption. Our study introduces a novel objective function that achieves balanced optimization by integrating both criteria.