A parallel multi-population genetic algorithm for a constrained two-dimensional orthogonal packing problem
- 486 Downloads
This paper addresses a constrained two-dimensional (2D), non-guillotine restricted, packing problem, where a fixed set of small rectangles has to be placed into a larger stock rectangle so as to maximize the value of the rectangles packed. The algorithm we propose hybridizes a novel placement procedure with a genetic algorithm based on random keys. We propose also a new fitness function to drive the optimization. The approach is tested on a set of instances taken from the literature and compared with other approaches. The experimental results validate the quality of the solutions and the effectiveness of the proposed algorithm.
KeywordsPacking Cutting Two-dimensional packing Two-dimensional cutting Non-guillotine cutting Genetic algorithm
Unable to display preview. Download preview PDF.
- Amaral A, Letchford AN (2001) An improved upper bound for the two-dimensional non-guillotine cutting problem. Technical report, Lancaster University, UK. Available online at http://www.lancs.ac.uk/staff/letchfoa/ngc.doc
- Fekete SP, Schepers J (1997b) On higher-dimensional packing I: Modeling. Technical Report ZPR 97-288, Mathematisches Institut, Universitat zu Köln Google Scholar
- Fekete SP, Schepers J (1997c) On higher-dimensional packing II: Bounds. Technical Report ZPR97-289, Mathematisches Institut, Universitat zu Köln Google Scholar
- Fekete SP, Schepers J (2004c) An exact algorithm for higher-dimensional orthogonal packing. Technical report, Mathematisches Institut, Universitat zu Köln. Working paper. Available online at http://www.math.tu-bs.de/~fekete
- Gonçalves JF, Resende MGC (2009) Biased random key genetic algorithms for combinatorial optimization. Technical report, AT&T Labs Research Technical Report, Florham Park, NJ 07733 USA Google Scholar
- Lai KK, Chan JWM (1997a) An evolutionary algorithm for the rectangular cutting stock problem. Int J Ind Eng 4:130–139 Google Scholar
- Spears WM, Dejong KA (1991) On the virtues of parameterized uniform crossover. In: Proceedings of the fourth international conference on genetic algorithms, pp 230–236 Google Scholar