Swarm manifold PSO for solving two-dimensional guillotine cutting problem

Particle swarm optimization (PSO) is an evolutionary computational model which owns a very fast converging characteristic. Guillotine cut refers to an ancient execution device and here is to place as many rectangles into a main frame as possible. Hence, the main purpose is to place a set of rectangles into a main frame and reduce the waste empty spaces as many as possible. It is well known that the 2D_GCP is an NP hard problem. In this paper, we propose a hybrid approach of PSO named swarm manifold PSO (SMPSO) for solving two-dimensional guillotine cutting problem (2D_GCP). The proposed SMPSO for solving the 2D_GCP performs much faster than invoking brute-force algorithm, and more accurate than the traditional random PSO and genetic algorithm (GA).