Research on an Improved Grey Wolf Optimizer Based on Probabilistic Hesitant Fuzzy Sets for Laser Cutting Path Optimization

Laser Cutting Path Optimization (LCPO) is a discrete combinatorial optimization problem in industrial engineering that requires simultaneous determination of cutting sequence and direction under practical uncertainty. To address the limitations of current laser cutting systems for LCPO, such as non-productive idle movements and disordered cutting sequences, this paper proposes a multi-strategy grey wolf optimizer (pDE-GWO) combining dynamic inertia weight, adaptive search step size, and elite individual preservation. The proposed algorithm incorporates Probabilistic Hesitant Fuzzy Sets (PHFS) to model the relationship between the objective function and uncertain decision information, leveraging the uncertainty and preference ambiguity inherent in PHFS to guide the evolutionary process, thereby transforming path-length evaluation into a probability-based hesitant decision process. The algorithm is evaluated using benchmark experiments, ablation analysis, and laser-cutting simulations. The results demonstrate that pDE-GWO improves convergence quality and robustness for LCPO.