Solving two-dimensional packing problem using particle swarm optimization

Particle swarm optimization is one of the evolutionary computations which is inspired by social behavior of bird flocking or fish schooling. This research focuses on the application of the particle swarm optimization to two-dimensional packing problem. Packing problem is a class of optimization problems which involve attempting to pack the items together inside a container, as densely as possible. In this study, when the arbitrary polygon-shaped packing region is given, the total number of items in the region is maximized. The optimization problem is defined not as the discrete-value optimization problem but as the continuousvalue optimization problem. The problem is solved by two algorithms, original and improved PSOs. In the original PSO, the particle position vector is updated by the best particle position in all particles (global best particle position) and the best position in previous positions of each particle (personal best position). The improved PSO utilizes, in addition to them, the second best particle position in all particles (global second best particle position) in the stochastic way. In the numerical example, the algorithms are applied to three problems. The results show that the improved PSO can pack more items than the original PSO and therefore, number of the successful simulations is also improved.