Effective nesting of rectangular parts in multiple rectangular sheets using genetic and heuristic algorithms

In this paper, a hybrid approach, employing both genetic and heuristic algorithms, is proposed for nesting of different rectangular parts in multiple rectangular sheets with the objective of utilizing the sheet material effectively. The proposed genetic approach gives the best sequence of sheets and parts to generate an effective nested pattern with a heuristic algorithm. The heuristic approach arranges each of the parts in the bottom-left-most position of the sheet(s) by considering the sequence of sheets and parts given by the genetic algorithm. The effectiveness of the proposed approach is shown by comparing the results obtained with the present approach to those obtained by Jakobs' approach when all the parts are nested in a single sheet. Finally, the application of the current approach for nesting of rectangular parts in multiple sheets is illustrated.