Heuristic for constrained two-dimensional three-staged patterns

Abstract

Three-staged cutting patterns are often used in dividing large plates into small rectangular items. Vertical cuts separate the plate into segments in the first stage, horizontal cuts split each segment into strips in the second stage, and vertical cuts divide each strip into items in the third stage. A heuristic algorithm for generating constrained three-staged patterns is presented in this paper. The optimization objective is to maximize the pattern value that is the total value of the included items, while the frequency of each item type should not exceed the specified upper bound. The algorithm uses an exact procedure to generate strips and two heuristic procedures to generate segments and the pattern. The pattern-generation procedure first determines an initial solution and then uses its information to generate more segments to extend the solution space. Computational results show that the algorithm is effective in improving solution quality.

Keywords:

• three-staged patterns
• cutting stock
• cutting and packing
• single large object placement problem

Acknowledgements

This research is part of Projects 61363026 and 71371058 supported by National Natural Science Foundation of China. It is also supported by the scientific research project 201010LX003 of the universities in Guangxi.