# Mhand Hifi

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In this paper we propose two exact algorithms for solving both two-staged and three staged unconstrained (un)weighted cutting problems. The two-staged problem is solved by applying a dynamic programming procedure originally developed by Gilmore and Gomory [Gilmore and Gomory, Operations Research, vol. 13, pp. 94–119, 1965]. The three-staged problem is(More)
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• In this work, we develop a new version of the algorithm proposed in 17] for solving exactly some variants of (un)weighted constrained two-dimensional cutting stock problems. We introduce one-dimensional bounded knapsacks in order to obtain an improved initial lower bound for limiting initially the size of the search space, an improved upper bound at each(More)
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(More)
• Comp. Opt. and Appl.
• 2006
In this paper, we approximately solve the multiple-choice multi-dimensional knapsack problem. We propose an algorithm which is based upon reactive local search and where an explicit check for the repetition of configurations is added to the local search. The algorithm starts by an initial solution and improved by using a fast iterative procedure. Later,(More)
• Computers & OR
• 2004
In this paper, we study the problem of cutting a rectangular plate R of dimensions (L;W ) into as many circular pieces as possible. The circular pieces are of n di4erent types with radii ri; i = 1; : : : ; n. We solve the constrained circular problem, where di the maximum demand for piece type i is speci+ed, using two heuristics: a constructive(More)
• Comp. Opt. and Appl.
• 2010
In this paper, we propose to solve large-scale multiple-choice multidimensional knapsack problems. We investigate the use of the column generation and effective solution procedures. The method is in the spirit of well-known local search metaheuristics, in which the search process is composed of two complementary stages: (i) a rounding solution stage and(More)
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