Multi-objective optimization of a two-dimensional cutting problem using genetic algorithms

The work presented here describes a method of optimizing the layout of rectangular parts placed on a rectangular sheet to cut out various parts. Two types of cutting problems have been investigated (i) in which guillotine cutting (cutting from edge to edge) is required (mostly metallic sheets where each cut is made individually for one single sheet), and (ii) the one in which guillotine cutting is not essential (e.g. cuts which can be made using a punch) i.e. for materials like paper or rubber where the sheets to be cut can be laid side by side or on top of one another and one single cut can be made. The optimization of the layout of rectangular parts is achieved with respect to two design objectives involving minimization of (i) the length of the mother sheet required, and (ii) also the total number of cuts required to obtain all the parts from the mother sheet. A tree encoded multi-objective genetic algorithm has been used to study both guillotine and non-guillotine cutting cases, using a binary representation of the variables, and it is shown for the known cases that the globally optimum solutions are obtained.