GRASP Optimization for the Strip Packing Problem with Flags, Waste Functions, and an Improved Restricted Candidate List

Abstract

This research addresses the two-dimensional strip packing problem to minimize the total strip height used, avoiding overlapping and placing objects outside the strip limits. This is an NP-hard optimization problem. We propose a greedy randomized adaptive search procedure (GRASP), incorporating flags as a new approach for this problem. These flags indicate available space after accommodating an object; they hold the available width and height for the following objects. We also propose three waste functions as surrogate objective functions for the GRASP candidate list and use and enhanced selection for the restricted candidate list, limiting the object options to better elements. Finally, we use overlapping functions to ensure that the object fits in the flag because there are some cases where a flag’s width can be wrong due to new object placement. The tests showed that our proposal outperforms the most recent state-of-the-art metaheuristic. Additionally, we make comparisons against two exact algorithms and another metaheuristic.

Keywords

• strip packing problem
• NP-hard optimization
• GRASP
• object placing flag