A multi criteria genetic algorithm based approach for the rectangular cutting stock problem

The problems called as material cutting and packing or trim loss is one of the common usage of resource drawback. It is possible that the convertion of many problems depending on the variety of problems and application areas which is basically in the same logical structure but under-named of different names in resources to a metarial cutting problem. In this study, first of all, a lot of studies which were performed on two dimensional rectangular stock cutting problems are classified with variety aspects and the next step is to present a developing multi-criteria approach which includes genetic algorithm based. In this developing method; to define sequence of parts which are assigned to sheet material; genetic algorithm is used and by using three different nesting algorithms existed in literature, nesting of parts to the sheet metarial carried out according to this defined sequence. Three different nesting plan acquired regarding to sequence defined with genetic algorithm. The value of the availability function are calculated that trim loss, cost, number of plan, and the re-usability rates about nesting plans evaluated with respect to TOPSIS, a technic that is multi-criteria decision-making application. In this way, for the problem on hand, regarding to four different criteria nesting algorithm usage that gives the best feedback is achieved. The developing algorithm is tested on the problems in the literature and real life problem. The obtained results show that the developing approach is successful in respect of the solution quality.Keywords: Material Cutting Problems, Genetic Algorithm, Bottom Left Fill, Difference Process, Touching Perimeter, TOPSIS