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

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 pro...