Abstract
Aiming at the constrained two-dimensional guillotine cutting problem of rectangular items, a heuristic algorithm with block corner-occupying pattern is presented in this paper. It can maximize the pattern value for the totally included items, but the occurring frequency of each item type doesn’t exceed its upper bound. Several rows and columns of identical items are packed at the left-bottom corner of the sheet, and the remaining part is divided into two sub-sheets. The sub-sheets are then packed and divided in the same way till no items can be packed. This upper bound and normal size methods applied in the algorithm will avoid the unnecessary calculation. The algorithm is compared with 9 literature algorithms with benchmark instances and random instances. Computational results show that, compared with the 8 heuristic algorithms, the pattern value of this algorithm is increased by 0.787% to 6.119% and the calculation time is reasonable. Compared with the exact algorithm, for large size instances the pattern value of this algorithm is 0.090% lower than it, but the calculation time is only 0.079% of it.
Highlights
In industrial production, for instance, the cutting of sheet metal, glass, and plywood, two-dimensional cutting problem often occurs
HEURISTIC ALGORITHM In this paper, all possible size of sub-sheet generated in optimal corner-occupying pattern is listed from small size to large
With regarding to the RGC_2DC problem, a block corneroccupying cutting heuristic algorithm is presented, where rectangular item is rotated by 90 degrees for higher pattern value
Summary
For instance, the cutting of sheet metal, glass, and plywood, two-dimensional cutting problem often occurs. A heuristic algorithm based on dynamic programming for the block corner-occupying cutting pattern is constructed. BLOCK CORNER-OCCUPYING CUTTING PATTERN Without loss of generality, the length of the sheet and items are defined as the horizontal direction, and the width as the vertical direction. S rows and t columns of type-i items are placed at the left-bottom corner of the sheet x × y, the unoccupied region is divided into sub-sheet A and B by a cutting line along the upper boundary (Figure 1a) or right boundary (Figure 1b). HEURISTIC ALGORITHM In this paper, all possible size of sub-sheet generated in optimal corner-occupying pattern is listed from small size to large. The normal size and the pattern value upper bound of the sub-sheet are used to exclude unnecessary calculations
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