Metaheuristics for the Minimum Time Cut Path Problem with Different Cutting and Sliding Speeds

Abstract

The problem of efficiently cutting smaller two-dimensional pieces from a larger surface is recurrent in several manufacturing settings. This problem belongs to the domain of cutting and packing (C&P) problems. This study approached a category of C&P problems called the minimum time cut path (MTCP) problem, which aims to identify a sequence of cutting and sliding movements for the head device to minimize manufacturing time. Both cutting and slide speeds (just moving the head) vary according to equipment, despite their relevance in real-world scenarios. This study applied the MTCP problem on the practical scope and presents two metaheuristics for tackling more significant instances that resemble real-world requirements. The experiments presented in this study utilized parameter values from typical laser cutting machines to assess the feasibility of the proposed methods compared to existing commercial software. The results show that metaheuristic-based solutions are competitive when addressing practical problems, achieving increased performance regarding the processing time for 94% of the instances.

Evolutionary Algorithms for Optimization Sequence of Cut in the Laser Cutting Path Problem

“…We also present a heuristic approach based on Eulerian paths to generate high-quality initial individuals. Our methods outperform existing approaches, and our promising results are compared with those presented in [9] and discussed in detail in Section 4. 3.…”

“…Researchers have attempted to apply metaheuristics to various processing methods to minimize the inefficient "airtime" during the operation of cutting devices [12]. GA (genetic algorithm) and BRKGA (biased random-key genetic algorithm) have been used to determine the optimal arrangement of edges for a set of operations located in asymmetrical positions and diverse classes [9,13]. The ant colony optimization (ACO) algorithm has been employed to minimize tool switching time and tool airtime in hole-making operations [14], as well as to discover the optimal travel path by determining the best ordering for holecutting operations [15].…”

“…Similarly to [9], the execution will be performed on a laser cutting machine that moves along coordinates (x, y). The input parameters will define the head movement speed (V m ) and cutting speed (V c ).…”

“…The rest of this paper is organized as follows: Section 2 provides a formal definition of LCPP, Section 3 presents an overview of current approaches for tool path generation, and Section 4 highlights the critical aspects of the ABRKGA approach and the Eulerian concept for constructing an excellent initial population. Section 5 focuses on the test instances and compares the performance with the best-known solutions, presented in [9]. Finally, Section 6 draws conclusions based on the findings of this research.…”

“…In this context, we consider the concept, as mentioned earlier, to improve individual fitness, whereas solutions tend to have fewer unnecessary air moves. In [9], the authors construct the initial population with a random order of edges. This fact impacts several air movements.…”