On genetic algorithms for the packing of polygons

Article Abstract:

A genetic algorithm, the embedded-shrinking algorithm, for packing polygon-shaped figures into a rectangular module is investigated. Since the problem requires satisfying a bottom-left condition on the movement of rectangles to the bottom or the left, deterministic procedures are used to transform the permutation of polygons into a packing pattern. It embeds the polygons into rectangles of minimum area and applies the polygon-cut algorithm to test whether shifts to draw the rectangles closer are successful.

Cases, Mathematical programming

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Mathematical model and method of searching for a local extremum for the non-convex oriented polygons allocation problem

Article Abstract:

The problem of optimally placing arbitrarily spatially formed polygons in a given space is investigated within a mathematical programming framework. Specifically, the problem, which is encountered in cutting and packing situations, is modelled using linear inequalities structures to account for non-overlapping of items. It is solved by determining 'a local minimum of the problem from any feasible initial point' using active set principles.

Case studies, Cutting

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Regular packing of congruent polygons on the rectangular sheet

Article Abstract:

Research was conducted to examine the regular packing of congruent polygons on the rectangular sheet. The problem of searching for the dense lattice fragment packing was addressed taking into account only the packings for which the polygons form rows parallel to one of the sheet sides. The mathematical model of the problem is developed and the approximate approach towards solving it is recommended.

Lattice theory, Polygons

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