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

N. Chernov | Zendy; Yu. G. Stoyan | Zendy; Т. Romanova | Zendy; Alexander Pankratov | Zendy

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

Author(s) -

N. Chernov,

Yu. G. Stoyan,

Т. Romanova,

Alexander Pankratov

Publication year - 2012

Publication title -

advances in operations research

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.379

H-Index - 14

eISSN - 1687-9155

pISSN - 1687-9147

DOI - 10.1155/2012/346358

Subject(s) - simple (philosophy) , line (geometry) , class (philosophy) , quadratic equation , order (exchange) , function (biology) , mathematics , combinatorics , computer science , algorithm , pure mathematics , geometry , artificial intelligence , philosophy , epistemology , finance , evolutionary biology , economics , biology

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 modelin 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

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