A Quick Heuristic-Dynamic Programming for Two-Dimensional Cutting Problem

The two-dimensional rectangular cutting problem with defects is discussed. The goal is to cut a small rectangular block of a given height and width from a large rectangular object containing a plurality of defects on the premise of satisfying several constraints, so that the sum of the area of the cut small rectangular blocks are maximized. The constraint is that each cutting operation must be guillotine, and the number of small rectangular blocks of each type is not limited and maintains a given direction. The problem is regarded as covering the original plate with small rectangular block, and a Quick Heuristic-Dynamic Programming (QHDP) algorithm is proposed. Firstly, a one-dimensional knapsack problem is established according to the height and width of small rectangular blocks, respectively, and an efficient discretization sets is generated respectively. Then, each value in the sets is used as a possible cutting line coordinate for sub-problem division. The algorithm calculates 14 typical examples. The experimental results show that it has obtained the optimal solution of all the examples, and the calculation time is less than one tenth of the best algorithm in the current literature. The algorithm complexity is analyzed and proved.