Greedy Adaptive Search: A New Approach for Large-Scale Irregular Packing Problems in the Fabric Industry

The 2-dimensional irregular packing problems are important in the fabric industry. Under several restrictions, fabric packing problems require placing a given set of parts within a fixed-width rectangular sheet, aiming at a minimum length use. In textile industry production, the fabric packing problems are usually large-scale with time limits, where the total number of parts is large, and a high-utilization solution should be computed in several minutes. However, there are few existing works on large-scale packing problems. In this paper, we propose a greedy adaptive search algorithm by constructing a new evaluation function and introducing a new restricted local search strategy. In our algorithm, with a given initial sequence of parts, we iteratively search the best-fit part in succeeding several parts and place it on sheet. Moreover, we employ a two-stage heuristic searching algorithm to search over all the possible sequences for a good initial sequence with high utilization. Numerical examples involve some large-scale industrial instances, together with some large-scale instances generated from benchmarks. Numerical tests show that our algorithm outperforms existing state-of-the-art solvers in large-scale packing problems. The results show the potential of our algorithm to large-scale packing problems in industrial production.