Abstract: The purpose of this paper is to solve the equilateral rectangular packing problem
characterized by surface orbit arised in practical production. We focus on the optimization system based
on adaptive genetic algorithm and graph theory, and greatly improve the cutting efficiency. Our method
target the optimization of the machining path, in this method, the path optimization problem is turned
into an undirected graph connectivity problem, and using genetic algorithm to find the optimized
machining path. The optimal solution of the final search is used to arrange the rectangular parts
according to BL positioning strategy. Through the improvement of genetic algorithm, such as: ① the
judgment of the legitimacy of the initial individual genes, and using the depth first traversal results
evaluation of individual performance. ② The crossover and mutation operators use adaptive mechanism,
and the object that performs the mutation operation is limited to a broken point set on a chromosome,
which greatly improves the performance of the algorithm. Finally, the experiments show that the
algorithm can provide the available solution in most cases, and it is also a very reliable method.

Key words: equilateral rectangle packing, feature machining, path optimization, adaptive genetic
algorithm