Heuristics: intelligent search strategies for computer problem solving
Heuristics: intelligent search strategies for computer problem solving
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Approximate Algorithms for the 0/1 Knapsack Problem
Journal of the ACM (JACM)
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
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The efficient packing of regular shaped two dimensional objects is the core problem of several kinds of industry such as steel. thin-film and paper. This special kind of packing problem consists in cutting small rectangular stripes of different length and width from bigger coiled rectangles of raw material by combining them in such a way that trim loss is as low as possible. Previous attempts to apply "exact" discrete optimization techniques such as Simplex Partial Columns Generation were not able to produce good cutting plans in large instances. We tackled this Roll Cutting Problem developing a new "dimension decomposition technique" that has been successfully experimented in a big steel industry first and then replicated in other steel and thin-film factories. This "unfolding" technique consists in splitting the overall search for good cutting plans in two separate graph search algorithms. one for each physical dimension of the rectangles. Searching individually in each dimension improves the overall search strategy allowing the effective pruning of useless combinations. Experimental evidence of how dimensional splitting strengthens the overall search strategy is given.