Efficient 2D irregular layout by vector superposition NFP and mixed-integer programming

Abstract

As a typical combinatorial optimization problem, two-dimensional (2D) irregular layout is a common problem in the engineering field. No-fit polygon (NFP) is a common geometric tool for solving layout problems. Although it is necessary to calculate NFP frequently in the process of layout, the search efficiency of the NFP generation algorithm is affected. The existing unfitting polygon algorithms have difficulties in dealing with complex contours, especially irregular contours with cavities. The large-scale layout process takes the long time with the low material utilization. A vector superposition NFP (VS-NFP) method is proposed in this paper to improve the solution efficiency of 2D irregular layout problems with complex contours. Based on the VS-NFP, an improved mixed integer programming (MIP) model is built. The model increases compression constraints for high solution search efficiency. A hybrid algorithm based on the VS-NFP and MIP is proposed to solve the problem. Comparing with the existing methods, the proposed method shortens the search time and improves the material utilization. The proposed method is verified in the application of large-scale layout problems.