Construction heuristics for generating tool paths for laser cutters

Abstract

This paper deals with generating paths for cutting irregular parts nested on thin or thick metal sheets. The objective is to minimise the total time required to cut all parts from the metal sheet explicitly taking the cost of piercing and pre-cutting into account. The problem is modelled as a generalised travelling salesperson problem with special precedence constraints. A set of construction heuristics is presented that incorporates the constraints originating from inner-outer contours, common cuts, piercing points and pre-cuts. Computational tests on a set of real-life cutting problems show that our solution approach is able to generate tool paths that for thick plates spend on average 33.4% less time than those generated by a commercial package for air movements, pre-cuts and sharp angle macros with cutting and piercing times being equal.

A review of cutting path algorithms for laser cutters

“…Both the composition of the total time and the main precedence constraints are discussed in depth by Dewil et al [6]. These will be briefly discussed in the following two paragraphs.…”

“…The papers that consider common cuts and collisions are either complete CAM system descriptions [76][77][78][79][80], or consider an EDM application where the cutter never stops cutting [66,68], or our own work which focuses on considering simultaneously as many problem aspects as possible [6,[71][72][73][74][75]. Similarly, the papers that consider piercings and bridges are CAM system descriptions [76][77][78][79][80], our own previous work [6,73,75], and one more paper [64]. Thermal effects are only considered by three papers [50][51][52] in addition to our own previous work [74,75].…”

“…Similarly, the papers that consider piercings and bridges are CAM system descriptions [76][77][78][79][80], our own previous work [6,73,75], and one more paper [64]. Thermal effects are only considered by three papers [50][51][52] in addition to our own previous work [74,75]. In the next sections, each class of problems will be discussed in detail.…”

“…A constraint optimization model is presented and solved using Ilog OPL Studio v3. 6 In [71], Dewil et al present an element insertion construction heuristic and a set of local moves embedded in a tabu search framework for the laser cutting path problem without considering piercing costs, pre-cuts, and sharp angle costs. In [72], these heuristics are expanded to include the additional costs.…”

About a Routing Problem of the Tool Motion on Sheet Cutting

“…Некоторые эвристические алгоритмы решения обобщенной задачи курьера (или обобщенной задачи коммивояжера GTSP), разработанные специально для маршру-тизации инструмента машин листовой резки, описаны в [17][18][19][20]26]. Однако среди них отсутствуют точные алгоритмы, позволяющие получать оптимальные решения для задач небольшой размерности.…”