64 research outputs found
An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem
The irregular strip packing problem is a combinatorial optimization problem that requires to place a given set of two-dimensional polygons within a rectangular container so that no polygon overlaps with other polygons or protrudes from the container, where each polygon is not necessarily convex. The container has a fixed width, while its length can change so that all polygons are placed in it. The objective is to find a layout of the set of polygons that minimizes the length of the container. We propose an algorithm that separates overlapping polygons based on nonlinear programming, and an algorithm that swaps two polygons in a layout so as to find their new positions in the layout with the least overlap. We incorporate these algorithms as components into an iterated local search algorithm for the overlap minimization problem and then develop an algorithm for the irregular strip packing problem using the iterated local search algorithm. Computational comparisons on representative instances disclose that our algorithm is competitive with other existing algorithms. Moreover, our algorithm updates several best known results
Packing squares independently
Given a set of squares and a strip of bounded width and infinite height, we
consider a square strip packaging problem, which we call the square independent
packing problem (SIPP), to minimize the strip height so that all the squares
are packed into independent cells separated by horizontal and vertical
partitions. For the SIPP, we first investigate efficient solution
representations and propose a compact representation that reduces the search
space from to , with the number of given squares,
while guaranteeing that there exists a solution representation that corresponds
to an optimal solution. Based on the solution representation, we show that the
problem is NP-hard, and then we propose a fully polynomial-time approximation
scheme (FPTAS) to solve it. We also propose three mathematical programming
formulations based on different solution representations and confirm the
performance of these algorithms through computational experiments. Finally, we
discuss several extensions that are relevant to practical applications.Comment: 15 page
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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものである京都大学0048新制・論文博士博士(工学)乙第10101号論工博第3416号新制||工||1146(附属図書館)UT51-99-G578(主査)教授 茨木 俊秀, 教授 岩間 一雄, 教授 加藤 直樹学位規則第4条第2項該当Doctor of EngineeringKyoto UniversityDFA
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