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A recursive exact algorithm for weighted two-dimensional cutting
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DOI：10.1016/0377-2217(95)00343-6.png)
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Abstract
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Gilmore and Gomory's algorithm is one of the better actually known exact algorithms for solving unconstrained guillotine two-dimensional cutting problems. Herz's algorithm is more effective, but only for the unweighted case. We propose a new exact algorithm adequate for both weighted and unweighted cases, which is more powerful than both algorithms. The algorithm uses dynamic programming procedures and one-dimensional knapsack problem to obtain efficient lower and upper bounds and important optimality criteria which permit a significant branching cut in a recursive tree-search procedure. Recursivity, computational power, adequateness to parallel implementations, and generalization for solving constrained two-dimensional cutting problems, are some important features of the new algorithm.
Keywords:
knapsack
two-dimensional cutting
dynamic programming
exact algorithms
heuristics
recursivity
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