Incremental Move for 2D Strip-Packing

When handling 2D packing problems, numerous incomplete and complete algorithms maintain a so-called bottom-left (BL) property: every rectangle placed in a container is propped up bottom and left. While it is easy to make a rectangle BL when it is is added in a container, it is more expensive to maintain all the placed pieces BL when a rectangle is removed. This prevents researchers from designing incremental moves for metaheuristics or efficient complete optimization algorithms. This paper investigates the possibility of violating the BL property. Instead, we propose to maintain only the set of "maximal holes", which allows incremental additions and removals of rectangles. To validate our alternative approach, we have designed an incremental move, maintaining maximal holes, for the strip-packing problem, a variant of the famous 2D bin-packing. We have also implemented a generic metaheuristic using this move and standard greedy heuristics. Experimental results show that the approach is competitive with the best known incomplete algorithms, especially the other metaheuristics (able to escape from local minima).