In Cutting and Packing problems "small" items have to be assigned to "large" objects under both geometric constraints (assuring that the items do not overlap and are contained inside the objects) and quantitative constraints (e.g. at least a given quantity of each item type has to be cut). The objective of the problem may be either related to the minimization of the value of the large objects that are used or to the maximization of the value of the small items that are cut. The solution of the problem is one or more cutting patterns, describing the geometric disposition of the small items in/on the large objects. Nesting problems are two-dimensional Cutting and Packing problems where the small items have irregular shapes, usually described by polygons (aka irregular packing problems).
In the last 5-6 years the number of publications on nesting problems have significantly increased, with more research groups in the world looking at these problems and proposing new solution approaches. Not only new heuristic algorithms have been publish, but also exact techniques, based on Mixed Integer Problems models have been developed, aiming the resolution until optimality of nesting problems or the
integration of these models with heuristics, under what is currently known as a matheuristics framework.
In this talk an overview of these most recent developments will be given, both concerning exact methods and heuristic approaches.
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