A block-based heuristic search algorithm for the two-dimensional guillotine strip packing problem

Abstract

Introduction:

This paper addresses the two-dimensional strip-packing (2DSP) problem of placing a set of rectangular pieces onto a fixed-width rectangular sheet to minimize the total length used.

Methodology:

We propose a Block-Based Heuristic Search Algorithm (BBHSA) to solve 2DSP problems with guillotine cut constraints. Initially, it converts the 2DSP problem into a series of 2D rectangular packing problems (2DRP), where the size of the sheet is fixed. In the BBHSA, rectangular pieces are aggregated into blocks, which are partial solutions without residual space. These blocks provide the ingredients for a good layout and are basic components in a tree-based constructive search process. Two basic operations, called placing & splitting and approximate binary search are used in the search process. Furthermore, several block-based placement rules are explored to speed up the search process and improve solution quality.

Result discussion:

To verify the performance of our proposed algorithm, we conducted extensive experiments using the zero-waste benchmark and non-zero-waste benchmark instances.

Final results:

The results show that BBHSA demonstrates computational effectiveness, particularly in zero-waste cases, achieving optimal solutions for almost all zero-waste benchmark instances reported in the existing literature.