Nesting Arbitrary Shapes Using Geometric Mating

Abstract

A genetic algorithm-based optimization method is proposed for solving the problem of nesting arbitrary shapes. Depending on the number of objects and the size of the search space, realizing an optimal solution within a reasonable time may not be possible. In this paper, a mating concept is introduced to reduce the solution time. Mating between two objects is defined as the positioning of one object relative to the other by merging common features that are assigned by the mating condition between them. A constrained move set is derived from a mating condition that allows the transformation of the object in each mating pair to be fully constrained with respect to the other. Properly mated objects can be placed together, thus reducing the overall computation time. Several examples are presented to demonstrate the efficiency of utilizing the mating concept to solve a nesting optimization problem.