A Three-Layered Multifactorial Evolutionary Algorithm with Parallelization for Large-Scale Engraving Path Planning

Abstract

Today, although laser engraving technology is widely used in 2D image engraving, when the image is larger and more complicated, most existing algorithms for engraving path planning have a huge computational burden and reduced engraving efficiency. Accordingly, this article addresses the trajectory optimization problem in large-scale image engraving. First, we formulate the problem as an improved model based on the large-scale traveling salesman problem (TSP). Then, we propose a three-layered algorithm called 3L-MFEA-MP, structured as follows: an upper layer, the genetic algorithm (GA); a middle layer, the GA; and a bottom layer, the parallel multifactorial evolutionary algorithm. Experiments on four classic large-scale TSP datasets show that our algorithm exhibits superior performance in terms of the path length and engraving time compared with other algorithms. In particular, compared with the single-thread algorithm, the proposed parallel algorithm reduced the engraving time by 80%. Moreover, the engraving machine experiment demonstrated that the engraving time of our algorithm on mona-lisa 100K, vangogh 120K, and venus 140K was approximately one tenth that of the traditional dot engraving method. The results indicate that the proposed algorithm can reduce the computational burden and improve engraving efficiency in engraving path planning.

An Adaptive Layered Clustering Framework with Improved Genetic Algorithm for Solving Large-Scale Traveling Salesman Problems

“…In this section, to investigate the performance of ALC_-IGA on large-scale instances, the new ALC_IGA is compared to three state-of-the-art algorithms, which are TLACS [7], an accelerating genetic algorithm evolution via ant-based mutation and crossover (ER-ACO) [28] and a 3L-MFEA-MP [51]. The ALC_IGA and TLACS were implemented in Matlab R2022a and parallelized by the parallel computing toolbox in Matlab.…”

“…Naturally, based on clustering algorithms, the two-layered method could be expanded to the three-layered. This concept was realized recently by Liang et al [51]. Firstly, they applied k-medoids algorithm to divide the large-scale instance into some medium-scale groups, and then applied k-medoids algorithm for all medium-scale groups again to divide them into small-scale groups.…”

“…In recent years, some two-layered algorithms have been proposed, and they significantly reduce the time expenditure for large-scale TSPs. Liang et al [51] recently proposed a three-layered algorithm with k-means and indicated that it outperforms two-layered algorithms by numerical experiments. Notwithstanding, both two-layered and threelayered algorithms may still have medium-scale or large-scale groups.…”

“…The drawbacks of the above two-layered algorithms include high computational complexity, poor accuracy, and problematic parameter tuning. Naturally, two-layered algorithms can be developed to three-layered or multiple-layered, very recent works can be seen in [51] and [52]. Admittedly, in order to fully utilize all the CPUs of computers, parallelizability is becoming extremely essential for algorithms designed to solve large and complicated problems.…”