Phi-Functions for 2D Objects Formed by Line Segments and Circular Arcs. (6th May 2012)

• Record Type: Journal Article
• Authors: Chernov, N.; Stoyan, Yu.; Romanova, T.; Pankratov, A.
• Other Names: Liao Ching-Jong Academic Editor.
• Is Part Of: Advances in operations research. Volume 2012(2012)
• Publication Date: 2012-05-06
• Subjects: Operations research -- Periodicals; Operations research; Periodicals; 003
• DOI: 10.1155/2012/346358
• Languages: English
• ISSNs: 1687-9147

Abstract

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.