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1 2019

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A one-pass heuristic for nesting problems

Kierkosz Igor, Łuczak Maciej

Operations Research and Decisions

2019

Vol. 29, No. 1

37--60

A two-dimensional cutting (packing) problem with items of irregular shape and rectangular sheets is studied. Three types of problems are considered: single-sheet problems without restrictions on the number of elements, single-sheet problems with restrictions on the number of elements, and cutting stock problems (restricted number of items and unrestricted number of sheets). The aim of the optimization is to maximize the total area of the elements cut from a single plate or to minimize the number of sheets used in cutting. A one-pass algorithm is proposed which uses the popular concept of a no-fit polygon (NFP). The decision on whether an item is cut from a sheet in a given step depends on the value of a fitting function. The fitting function depends on the change in the NFP of individual items. We test eight different criteria for the evaluation of partial solutions. On the basis of numerical experiments, the algorithm that generates the best solution for each of the considered problem types is selected. The calculation results for these algorithms are compared with results obtained by other authors.