Multi-Objective Optimization of Defective Multi-Inventory Mother-Plate Cutting

The increasing complexity of steel manufacturing and the rising demand for customized high-grade plates have intensified the need for efficient and defect-aware cutting optimization. In practical production, mother plates frequently contain multiple surface defects, and the cutting process is further constrained by delay-sensitive operations such as tool-change sequences and defect-tolerance requirements. To address these challenges, this study formulates the Defective Multi-Inventory Mother-Plate Two-Dimensional Cutting Stock Problem (DMMP-2CSP) as a multi-objective model that simultaneously maximizes cutting profit and minimizes tool changes under strict geometric and defect-avoidance constraints. We develop an Improved Multi-Objective Grey Wolf Optimizer (IMOGWO) featuring continuous random-keys encoding with hierarchical decoding to handle multi-plate, multi-defect layouts; a Large-Language-Model-guided Fourth-Leader Boost mechanism that adaptively mitigates stagnation through domain-informed auxiliary-leader generation; and an NSGA-II fusion module incorporating non-dominated sorting, crowding-distance control, and stochastic variation to balance exploration and exploitation throughout the search. Extensive experiments on industrial-scale datasets demonstrate that IMOGWO consistently produces well-distributed Pareto-optimal solutions, significantly improves cutting profit, reduces tool-change frequency, and achieves superior overall performance compared with classical Multiobjective Grey Wolf Optimizer, Multiobjective Particle Swarm Optimization, Multi-Objective Cuckoo Search, and Multi-Objective Snake Optimizer baselines.