A beam search implementation for the irregular shape packing problem

The paper investigates the irregular shape packing problem, also frequently referred to as the nesting problem. A review of the literature highlights two distinct approaches for representing the problem; as an order list of pieces to be packed that is decoded by a placement rule (construction heuristic), or as a layout where pieces have allocated coordinate positions on the stock sheet. The former strategy is explored in this paper. Success of such an approach is dependant on two critical characteristics; the construction heuristic and the packing order. A construction heuristic based taken from the literature is presented and modified through a more powerful nofit polygon generator and new evaluation criteria that encourage certain desirable behaviours. A beam search algorithm is implemented to search over the packing order. Beam search is analogous to branch and bound where the tree is searched breadth first and aggressively pruned at each level. Using this approach many parallel partial solutions can be generated and compared using the new constructive heuristic. Computational results for benchmark problems show that the algorithm generates highly competitive solutions in significantly less time than the best results currently in the literature.