Phi-Functions for 2D Objects Formed by Line Segments and Circular Arcs

N. Chernov, Yu. Stoyan, T. Romanova and A. Pankratov

Advances in Operations Research, 2012, vol. 2012, 1-26

Abstract:

We study the cutting and packing (C&P) problems in two dimensions by using phi-functions. Our phi-functions describe the layout of given objects; they allow us to construct a mathematical model in which C&P problems become constrained optimization problems. Here we define (for the first time) a complete class of basic phi-functions which allow us to derive phi-functions for all 2D objects that are formed by linear segments and circular arcs. Our phi-functions support translations and rotations of objects. In order to deal with restrictions on minimal or maximal distances between objects, we also propose adjusted phi-functions. Our phi-functions are expressed by simple linear and quadratic formulas without radicals. The use of radical-free phi-functions allows us to increase efficiency of optimization algorithms. We include several model examples.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaor:346358

DOI: 10.1155/2012/346358

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