Simulated Annealing with Adaptive Neighborhood Applied to the Placement over Containers with Fixed Dimensions

This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular bi-dimensional items inside a bi-dimensional container. This problem is approached with an heuristic based on Simulated Annealing (SA) with adaptive neighborhood. Traditional “external penalization” techniques are avoided through the application of the no–fit polygon, that determinates the collision-free area for each polygon before its placement. The SA controls continuous and discrete parameters. The rotation applied and the translation of the polygon are continuous parameters, and the sequence of placement is represented as a set of discrete parameters. For each non–placed item, a limited depth binary search is performed to find a scale factor that when applied to the item, would allow it to be fitted in the container.