Log in

Fidelity-adaptive evolutionary optimization algorithm for 2D irregular cutting and packing problem

  • Published:
Journal of Intelligent Manufacturing Aims and scope Submit manuscript

Abstract

The cutting and packing problems (CPP) widely appear in various industrial fields, such as additive manufacturing (AM) and the fashion industry. The evolutionary optimization (EO) algorithms inspired by biological evolution are popular to solve such combinatorial optimization problems these years. Most of the research focused on the improvement of nesting strategies (NS) and EO algorithms, while the relationship between NSs and evolutionary optimization stages is the neglected crucial point. In this paper, a fidelity-adaptive evolution optimization (FAEO) method is proposed to speed up the optimization process by using different nesting strategies at the appropriate optimization stages. In FAEO methods, two switching methods are designed to convert NSs. The neighbourhood-elite evaluation (NEE) and staged-archive (S-A) methods are developed to accelerate individual internal assessment. The experimental results and relevant analysis of the cases from ESICUP by the combination of genetic algorithm (GA) and skyline-derived NSs prove the effectiveness, rapidity, and industrial value of the FAEO algorithm compared with the benchmark algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Algorithm 1
Fig. 6
Algorithm 2
Algorithm 3
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability

The data that support the findings of this study are openly available at https://www.euro-online.org/websites/esicup/data-sets/#1535972088237-bbcb74e3-b507.

References

  • Abeysooriya, R. P., Bennell, J. A., & Martinez-Sykora, A. (2017). Efficient local search heuristics for packing irregular shapes in two-dimensional heterogeneous bins. In T. Bektaş, S. Coniglio, A. Martinez-Sykora, & S. Voß (Eds.), Computational Logistics. ICCL 2017. Lecture Notes in Computer Science (10572) (pp. 557–571). Cham: Springer.

    Google Scholar 

  • Araújo, L. J. P., Atkin, E. Ö. J. A. D., & Baumers, M. (2018). Analysis of irregular three-dimensional packing problems in additive manufacturing: A new taxonomy and dataset. International Journal of Production Research, 57(18), 5920–5934.

    Article  Google Scholar 

  • Baldacci, R., Boschetti, A., Ganovelli, M., & Maniezzo, V. (2014). Algorithms for nesting with defects. Discrete Applied Mathematics., 163(1), 17–33.

    Article  MathSciNet  Google Scholar 

  • Bennell, J. A., & Oliveira, J. F. (2008). The geometry of nesting problems: A tutorial. European Journal of Operational Research., 184(2), 397–415.

    Article  MathSciNet  Google Scholar 

  • Bennell, J., Scheithauer, G., Stoyan, Y., & Romanova, T. (2010). Tools of mathematical modeling of arbitrary object packing problems. Annals of Operations Research., 179, 343–368.

    Article  MathSciNet  Google Scholar 

  • Błażewicz, J., Hawryluk, P., & Walkowiak, R. (1993). Using a tabu search approach for solving the two-dimensional irregular cutting problem. Annals of Operations Research., 41, 313–325.

    Article  Google Scholar 

  • Bouganis, A., & Shanahan, M. (2007). A vision-based intelligent system for packing 2-D irregular shapes. IEEE Transactions on Automation Science and Engineering., 4(3), 382–394.

    Article  Google Scholar 

  • Canellidis, V., Giannatsis, J., & Dedoussis, V. (2013). Efficient parts nesting schemes for improving stereolithography utilization. Computer-Aided Design, 45(2013), 875–886.

    Article  Google Scholar 

  • Chekanin, V. A., & Chekanin, A. V. (2015). Development of optimization software to solve practical packing and cutting problems. In: International Conference on Artificial Intelligence and Industrial Engineering, Atlantis, July 26–27.

  • Cherri, L. H., Cherri, A. C., & Soler, E. M. (2018). Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations. Journal of Global Optimization., 72, 89–107.

    Article  MathSciNet  Google Scholar 

  • Delorme, M., Iori, M., & Martello, S. (2018). BPPLIB: A library for bin packing and cutting stock problems. Optimization Letters, 12, 235–250.

    Article  MathSciNet  Google Scholar 

  • Dowsland, K. A., & Dowsland, W. B. (1992). Packing problems. European Journal of Operational Research, 56(1), 2–14.

    Article  MathSciNet  Google Scholar 

  • Duan, L., Hu, H. Y., Qian, Y., Gong, Y., Zhang, X., Wei, J., & Xu, Y. (2019). A multi-task selected learning approach for solving 3D flexible bin packing problem. Proceedings of the 18th International Conference on Autonomous Agents and Multiagent Systems (pp. 1386–1394). AAMAS: Montreal.

    Google Scholar 

  • Evtimov, G., & Fidanova, S. (2018). Heuristic algorithm for 2D cutting stock problem. In I. Lirkov & S. Margenov (Eds.), Large-scale scientific computing. LSSC 2017. Lecture Notes in Computer Science (10665) (pp. 350–357). Cham: Springer.

    Google Scholar 

  • Fang, J., Rao, Y., Liu, P., & Zhao, X. (2021). Sequence transfer-based particle swarm optimization algorithm for irregular packing problems. IEEE Access., 9, 131223–131235.

    Article  Google Scholar 

  • Gardeyn, J., & Wauters, T. (2021). A goal-driven ruin and recreate heuristic for the 2D variable-sized bin packing problem with guillotine constraints. European Journal of Operational Research, 301, 432–444.

    Article  MathSciNet  Google Scholar 

  • Guo, B., Hu, J., Wu, F., & Peng, Q. (2020). Automatic layout of 2D free-form shapes based on geometric similarity feature searching and fuzzy matching. Journal of Manufacturing Systems, 56, 37–49.

    Article  Google Scholar 

  • Guo, B., Ji, Y., Hu, J., Wu, F., & Peng, Q. (2019). Efficient free-form contour packing based on code matching strategy. IEEE Access, 7, 57917–57926.

    Article  Google Scholar 

  • Hopper, E., & Turton, B. C. H. (1999). A Genetic algorithm for a 2D industrial packing problem. Computers & Industrial Engineering., 37, 375–378.

    Article  Google Scholar 

  • Hopper, E., & Turton, B. C. H. (2001). An empirical study of meta-heuristics applied to 2D rectangular bin packing. European Journal of Operational Research, 128(1), 34–57.

    Article  Google Scholar 

  • Hu, H., Zhang, X., Yan, X., Wang, L., & Xu, Y. (2017). Solving a new 3d bin packing problem with deep reinforcement learning method. ar**v: 1708.05930

  • Illich, S., While, L., & Barone, L. (2007). Multi-objective strip packing using an evolutionary algorithm. In: IEEE Congress on Evolutionary Computation. Singapore, September 25–28.

  • Jakobs, S. (1996). On genetic algorithms for the packing of polygons. European Journal of Operational Research., 88(1), 165–181.

    Article  Google Scholar 

  • Jones, D. R. (2014). A fully general, exact algorithm for nesting irregular shapes. Journal of Global Optimization., 59, 367–404.

    Article  MathSciNet  Google Scholar 

  • Júnior, A. N., Silva, E., Francescatto, M., Rosa, C. B., & Siluk, J. (2021). The rectangular two-dimensional strip packing problem real-life practical constraints: A bibliometric overview. Computers and Operations Research., 137, 105521.

    Article  MathSciNet  Google Scholar 

  • Leao, A. A. S., Toledo, F. M. B., Oliveira, J. F., Carravilla, M. A., & Alvarez-Valdés, R. (2020). Irregular packing problems: A review of mathematical models. European Journal of Operational Research., 282(3), 803–822.

    Article  MathSciNet  Google Scholar 

  • Lee, W.-C., Ma, H., & Cheng, B.-W. (2008). A heuristic for nesting problems of irregular shapes. Computer-Aided Design., 40, 625–633.

    Article  Google Scholar 

  • Liu, X., Liu, J., Cao, A., & Yao, Z. (2015). HAPE3D—A new constructive algorithm for the 3D irregular packing problem. Frontiers of Information Technology & Electronic Engineering., 16, 380–390.

    Article  ADS  Google Scholar 

  • Liu, Y., Chu, C., & Wang, K. (2011). A new heuristic algorithm for a class of two-dimensional bin-packing problems. The International Journal of Advanced Manufacturing Technology., 57, 1235.

    Article  Google Scholar 

  • Lodi, A., Martello, S., & Vigo, D. (2004). TSpack: A unified Tabu search code for multi-dimensional bin packing problems. Annals of Operations Research., 131, 203–213.

    Article  MathSciNet  Google Scholar 

  • Martins, T. C., & Tsuzuki, M. S. G. (2010). Simulated annealing applied to the irregular rotational placement of shapes over containers with fixed dimensions. Expert Systems with Applications., 37, 1955–1972.

    Article  Google Scholar 

  • Mezghani, S., Haddar, B., & Chabchoub, H. (2022). The evolution of rectangular bin packing problem—A review of research topics, applications, and cited papers. Journal of Industrial and Management Optimization. Advance online publication.

  • M’Hallah, R., & Bouziri, A. (2014). Heuristics for the combined cut order planning two-dimensional layout problem in the apparel industry. International Transactions in Operational Research., 23(1–2), 321–353.

    MathSciNet  Google Scholar 

  • Oh, Y., Witherell, P., Lu, Y., & Sprock, T. (2020). Nesting and scheduling problems for additive manufacturing: A taxonomy and review. Additive Manufacturing., 36, 101492.

    Article  CAS  Google Scholar 

  • Oliveira, J. F. C., & Ferreira, J. A. S. (1993). Algorithms for nesting problems. In R. V. V. Vidal (Ed.), Applied simulated annealing: Lecture notes in economics and mathematical systems (Vol. 369, pp. 255–273). Springer.

    Chapter  Google Scholar 

  • Oliveira, J. F., Gomes, A. M., & Ferreira, J. S. (2000). TOPOS—A new constructive algorithm for nesting problems. Or Spektrum., 22, 263–284.

    Article  MathSciNet  Google Scholar 

  • Ren, H., & Zhong, R. (2022). Covering, cornersearching and occupying: A three-stage intelligent algorithm for the 2d multishape part packing problem. PLoS ONE, 17(5), e0268514.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Ross, P., Schulenburg, S., Blázquez, J. M., & Hart, E. (2002). Hyper-heuristics: Learning to combine simple heuristics in bin-packing problems. In Proceedings of GECCO 2002, New York, July 9–13.

  • Sato, A. K., Martins, T. D. C., & Tsuzuki, M. D. S. G. (2016). A pairwise exact placement algorithm for the irregular nesting problem. International Journal of Computer Integrated Manufacturing., 29(11), 1177–1189.

    Article  Google Scholar 

  • Sato, A. K., Martins, T. D. C., & Tsuzuki, M. D. S. G. (2019). Massive parallelization accelerated solution for the 2D irregular nesting problem. IFAC-PapersOnLine, 52(10), 119–124.

    Article  Google Scholar 

  • Terashima-Marín, H., Ross, P., Farías-Zárate, C. J., López-Camacho, E., & Valenzuela-Rendón, M. (2010). Generalized hyper-heuristics for solving 2D regular and irregular packing problems. Annals of Operations Research., 179(1), 369–392.

    Article  MathSciNet  Google Scholar 

  • The Association of the European Operational Research Societies. ESICUP -Information-Data sets (2D Irregular). Retrieved 1988, from https://www.euro-online.org/websites/esicup/data-sets/#1535972088237-bbcb74e3-b507.

  • Tsao, Y.-C., Delicia, M., & Vu, T.-L. (2022). Marker planning problem in the apparel industry: Hybrid PSO-based heuristics. Applied Soft Computing, 123(3), 108928.

    Article  Google Scholar 

  • Vasantha, G. V. A., Jagadeesan, A. P., Corney, J. R., Lynn, A., & Agrawal, A. (2015). Crowdsourcing solutions to 2D irregular strip packing problems from Internet workers. International Journal of Production Research., 54(14), 4104–4125.

    Article  Google Scholar 

  • Wei, L., Hu, Q., Leung, S. C. H., & Zhang, N. (2017). An improved skyline-based heuristic for the 2D strip packing problem and its efficient implementation. Computers & Operations Research., 80, 113–127.

    Article  MathSciNet  Google Scholar 

  • Wei, L., Oon, W.-C., Zhu, W., & Lim, A. (2011). A skyline heuristic for the 2D rectangular packing and strip packing problems. European Journal of Operational Research., 215(2), 337–346.

    MathSciNet  Google Scholar 

  • Wu, S., Zhan, Z., & Zhang, J. (2021). SAFE: Scale-adaptive fitness evaluation method for expensive optimization problems. IEEE Transactions on Evolutionary Computation, 25(3), 478–491.

    Article  ADS  Google Scholar 

  • Xu, Y., Yang, G. K., Bai, J., & Pan, C. (2011). A review of the application of swarm intelligence algorithms to 2D cutting and packing problem. In: ICSI 2011: Advances in swarm intelligence, Chongqing, June 12–15.

  • Yang, Y., Liu, B., Li, H., Li, X., Wang. G., & Li, S. (2022). A nesting optimization method based on digital contour similarity matching for additive manufacturing. Journal of Intelligent Manufacturing. Advance online publication.

  • Yau, H.-T., & Hsu, C.-W. (2022). Nesting of 3D irregular shaped objects applied to powder-based additive manufacturing. The International Journal of Advanced Manufacturing Technology., 118, 1843–1858.

    Article  Google Scholar 

  • Zhang, Y. C., Gupta, R. K., & Bernard, A. (2016). Two-dimensional placement optimization for multi-parts production in additive manufacturing. Robotics and Computer-Integrated Manufacturing., 38, 102–117.

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge Haochen Li for his help in algorithm design.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Yizhe Yang or Bingshan Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, Y., Liu, B., Li, X. et al. Fidelity-adaptive evolutionary optimization algorithm for 2D irregular cutting and packing problem. J Intell Manuf (2024). https://doi.org/10.1007/s10845-024-02329-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10845-024-02329-y

Keywords

Navigation