Nesting in the sheet metal industry: dealing with constraints of flatbed laser-cutting machines

Abstract

Abstract This paper deals with the 2D nesting problem for flatbed laser-cutting machines and integrating the constraints related to the manufacturing process into a nesting algorithm. Literature concerned with nesting problems has mainly focused on minimizing the raw material area used to cut a given set of parts. However, minimizing the raw material costs does not necessarily minimize the cutting costs, as some costs related to the manufacturing process are also fixed with the nesting. These costs stem from the rather low process reliability of flatbed laser-cutting machines and include for example the damage to the slats or the downtime of the machine due to collisions of the cutting head with tilted parts. All of these constraints are related to the exact position of the raw metal sheet in relation to the supporting points of the slats. This work assumes that the position of all supporting points is known. The constraints are explained and modeled, and two variants of an evolutionary algorithm are introduced that can find solutions to the optimization problem using local search. The first one uses fixed pressure points and the other variable pressure points. It is shown that the approach with variable pressure points yields better results.