Abstract

ALVAREZ-MARTINEZ, David; TORO-OCAMPO, Eliana Mirledy  and  GALLEGO-RENDON, Ramón Alfonso. Unconstrained Two-Dimensional Knapsack Problem. Ing. Univ. [online]. 2010, vol.14, n.2, pp.327-344. ISSN 0123-2126.

Cutting and packing problems are common in operations research, due to their big spectrum of application in the industry and its highly mathematical and computational complexity for the academy. In this study we present the unconstrained twodimensional cutting stock problem of rectangular items, with and without weights associated to the items, bearing in mind the possibility to rotate items at 90°, and with guillotine cuts (also known as unconstrained two-dimensional guillotineable single knapsack problem). For this problem, we describe the mathematical model recognized by the academic community. We develop an appropriate encoding of the problem so it is possible to work on it using metaheuristic hybrid algorithm particle swarm optimization and simulated annealing. To check the efficiency of this methodology, case studies were taken from specialized literature, where the presented solution method could be analyzed and compared with current problems. The results obtained had an excellent quality and had never been reported.

Keywords : Unconstrained two-dimensional knapsack problem; particle swarm optimization; simulated annealing.

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