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

Abstract EN

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.