An Effective Discrete Grey Wolf Optimization Algorithm for Solving the Packing Problem

This article proposes a novel discrete grey wolf optimization for the packing problem, called the two-dimensional strip packing (2DSP) problem without guillotine constraint. The 2DSP involves cutting pieces from a stock sheet with the objective of minimizing waste. To solve the 2DSP problem by the discrete grey wolf algorithm, many strategies are originally proposed. The searching and attacking operators in the algorithm are redesigned to guarantee coding effectiveness. A novel approach to measure the distance between the wolves is presented. In addition, an improved best-fit strategy is developed to solve this packing problem. The best-fit strategy divides the situation into five cases based on the width and length of the rectangle. Computational results on widely used benchmark instances show that the novel discrete grey wolf algorithm can solve the 2DSP problem effectively, and surpasses most of the previously reported meta-heuristic algorithms.