A general heuristic for two-dimensional nesting problems with limited-size containers

Leandro R. Mundim, Marina Andretta, Maria Antónia Carravilla and José Fernando Oliveira

International Journal of Production Research, 2018, vol. 56, issue 1-2, 709-732

Abstract: Cutting raw-material into smaller parts is a fundamental phase of many production processes. These operations originate raw-material waste that can be minimised. These problems have a strong economic and ecological impact and their proper solving is essential to many sectors of the economy, such as the textile, footwear, automotive and shipbuilding industries, to mention only a few. Two-dimensional (2D) nesting problems, in particular, deal with the cutting of irregularly shaped pieces from a set of larger containers, so that either the waste is minimised or the value of the pieces actually cut from the containers is maximised. Despite the real-world practical relevance of these problems, very few approaches have been proposed capable of dealing with concrete characteristics that arise in practice. In this paper, we propose a new general heuristic (H4NP) for all 2D nesting problems with limited-size containers: the Placement problem, the Knapsack problem, the Cutting Stock problem, and the Bin Packing problem. Extensive computational experiments were run on a total of 1100 instances. H4NP obtained equal or better solutions for 73% of the instances for which there were previous results against which to compare, and new benchmarks are proposed.

Date: 2018
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DOI: 10.1080/00207543.2017.1394598

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