Active-set sequential quadratic programming method with compact neighbourhood algorithm for the multi-polygon mass production cutting-stock problem with rotatable polygons

The cutting-stock problem, which considers how to arrange the component profiles on the material without overlaps, can increase the utility rate of the sheet stock, and is thus a standard constrained optimisation problem. In some applications the components should be placed with specific orientations, but in others the components may be placed with any orientation. This study presents an overlap index and it is much more suitable for the active-set SQP method which can reduce the time spend for constraint consideration. Using this method, various object orientations can be considered easily and the number of object on the sheet stock can be improved by up to eight percent.