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Φ-functions for complex 2D-objects. (English) Zbl 1125.90382
Summary: Within two-dimensional cutting and packing problems with irregular shaped objects, the concept of Φ-functions has been proven to be very helpful for several solution approaches. In order to construct such Φ-functions a previous work [Yu. G. Stoyan et al., Appl. Math. 29, No. 2, 199–218 (2002; Zbl 1053.90009)], in which so-called primary objects are considered, is continued. Now Φ-functions are constructed for pairs of objects which can be represented as a finite combination (union, intersection, complement) of primary objects which allows the handling of arbitrary shaped objects by appropriate approximations of sufficient accuracy.
MSC:
90B80Discrete location and assignment
90C26Nonconvex programming, global optimization