An iteratively doubling binary search for the two-dimensional irregular multiple-size bin packing problem raised in the steel industry

Abstract

This paper examines the two-dimensional irregular multiple-size bin packing problem, where the goal is to pack all the given irregular pieces into bins of various sizes such that the total area of the used bins is minimized. Meanwhile, the irregular pieces include holes, and the bins can be irregular, also. This problem is raised in the steel industry considering the reuse of leftover material. An iteratively doubling binary search is proposed to solve this problem. Moreover, a binary search strategy is introduced to search the bin combination with minimum area, and an iteratively doubling strategy is utilized to control the search effort on each bin combination. Once the bins are identified, a first-fit bottom-left method is utilized to generate the initial position for each piece. An overlap minimization approach, which includes a local search by exchanging the positions of two pieces, is adapted to minimize the overlap in the initial solution. Experiment results on existing instances show that our approach could find a better solution than existing methods. Several instances representing different application scenarios are generated, and the results show our approach’s effectiveness and generality.