A Modular Adaptive Hybrid Metaheuristic Based on Distributed Population Evolution for 2D Irregular Packing Problems

This paper addresses the NP-hard 2D irregular packing problem with non-convex geometric constraints. We propose a distributed hybrid metaheuristic based on an island population structure, integrating a genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA), and a grey wolf optimizer (GWO), with a novel Modular Adaptive Optimization Module (MAOM). The passivity and stability of the MAOM are rigorously proven via a Lyapunov energy function. The convergence rate of the island model is proven to be O(Tmax/K), demonstrating linear speedup. Extensive experiments on 11 benchmark datasets show that the proposed algorithm achieves material utilization ranging from 61.73% to 79.42% with excellent stability (CV<0.03). Statistical tests confirm significant improvements over traditional metaheuristics (p<0.05). This work provides a theoretically grounded and practically effective approach for 2D irregular nesting.