Abstract
A polyomino is a connected figure consisting of unit squares joined at the edges. We consider the following polyomino packing problem (PPP): Given a region R and a set S of n distinct polyominoes with associated values. How should copies of the polyominoes be placed into R so as to maximize their total value, whereby they are not allowed to overlap each other? A lagrangean relaxation is presented which provides upper bounds for (PPP) using subgradient optimization. For the special case of packing copies of one polyomino into a rectangle, we present an exact tree search procedure which allows medium sized problems to be solved. We briefly describe tabu search heuristics for (PPP) which produce very good solutions.
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© 1992 Physica-Verlag Heidelberg
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Wolffram, J. (1992). Packing Polyominoes. In: Gritzmann, P., Hettich, R., Horst, R., Sachs, E. (eds) Operations Research ’91. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-48417-9_49
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DOI: https://doi.org/10.1007/978-3-642-48417-9_49
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-0608-3
Online ISBN: 978-3-642-48417-9
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