A backtracking heuristic algorithm for two-dimensional strip packing with rotation

A backtracking heuristic algorithm (BHA) was proposed for a two-dimensional rectangular strip packing problem with rotations and without guillotine cutting, which has many applications. An improved fitness strategy was used to select the fittest rectangle to be packed on a strip with a certain height. Next, a backtracking constructive heuristic was repeatedly used at a higher height until all the rectangles were packed. A multi-start improvement procedure then found the best solution by taking a different rectangle as the first rectangle, whereas the sequence of the other rectangles remained unchanged. Finally, in order to further expand the scope of the solution, a simple randomized local search procedure based on random sequences of rectangles with the first rectangle unchanged was applied to search for the optimal solution. BHA has only two parameters; it is simple and effective. Computational results on benchmark problems (zero-waste instances and non-zero-waste instances) with different scales (from 10 to 75,032 rectangles) indicate the following: (1) though it is non-deterministic, the difference between the results after each running is tiny and (2) the proposed algorithm outperforms most of the other algorithms under comparison on the whole, especially for large-scale instances with more than 1000 rectangles, which is further verified by statistical analysis and greatly meaningful in mass industrial production like metal cutting.