A Distributed Hybrid Algorithm for Composite Stock Cutting

The composite stock cutting problem is defined as allocating rectangular and irregular patterns onto a large composite stock sheet of finite dimensions in such a way that the resulting scrap will be minimized. In this paper, we introduce a new hybrid algorithm called Mean Field Genetic Algorithm (MGA) which combines the benefit of rapid convergence property of Mean Field Annealing (MFA) and the effective genetic operations of Simulated annealing-like Genetic Algorithm (SGA). In SGA, the typical genetic algorithm is modified such that the new evolved state is accepted by the Metropolis Criteria in order to keep the thermal equilibrium of MFA. We adopt Bottom-up Left-justified (BL) algorithm because BL algorithm represents the order of patterns to be packed as a list which can be implemented by the spin matrix of MFA and a string of SGA. However BL algorithm has been developed for rectangular patterns. So in this paper, first we make the bounding box including each irregular pattern. Next, after finding an optimal list by using the proposed MGA algorithm, spaces among patterns are removed. The new hybrid algorithm was more promising as the problem size and complexity increases and its distributed algorithm achieves almost linear speedup as the problem size increases.