IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i15p1760-d601633.html
   My bibliography  Save this article

Multi-Objective Optimization of Plastics Thermoforming

Author

Listed:
  • António Gaspar-Cunha

    (IPC—Institute of Polymer and Composites, University of Minho, 4800-050 Guimarães, Portugal)

  • Paulo Costa

    (IPC—Institute of Polymer and Composites, University of Minho, 4800-050 Guimarães, Portugal)

  • Wagner de Campos Galuppo

    (IPC—Institute of Polymer and Composites, University of Minho, 4800-050 Guimarães, Portugal)

  • João Miguel Nóbrega

    (IPC—Institute of Polymer and Composites, University of Minho, 4800-050 Guimarães, Portugal)

  • Fernando Duarte

    (IPC—Institute of Polymer and Composites, University of Minho, 4800-050 Guimarães, Portugal)

  • Lino Costa

    (ALGORITMI Center, University of Minho, 4800-050 Guimarães, Portugal)

Abstract

The practical application of a multi-objective optimization strategy based on evolutionary algorithms was proposed to optimize the plastics thermoforming process. For that purpose, in this work, differently from the other works proposed in the literature, the shaping step was considered individually with the aim of optimizing the thickness distribution of the final part originated from sheets characterized by different thickness profiles, such as constant thickness, spline thickness variation in one direction and concentric thickness variation in two directions, while maintaining the temperature constant. As far we know, this is the first work where such a type of approach is proposed. A multi-objective optimization strategy based on Evolutionary Algorithms was applied to the determination of the final part thickness distribution with the aim of demonstrating the validity of the methodology proposed. The results obtained considering three different theoretical initial sheet shapes indicate clearly that the methodology proposed is valid, as it provides solutions with physical meaning and with great potential to be applied in real practice. The different thickness profiles obtained for the optimal Pareto solutions show, in all cases, that that the different profiles along the front are related to the objectives considered. Also, there is a clear improvement in the successive generations of the evolutionary algorithm.

Suggested Citation

  • António Gaspar-Cunha & Paulo Costa & Wagner de Campos Galuppo & João Miguel Nóbrega & Fernando Duarte & Lino Costa, 2021. "Multi-Objective Optimization of Plastics Thermoforming," Mathematics, MDPI, vol. 9(15), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1760-:d:601633
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/15/1760/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/15/1760/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Beume, Nicola & Naujoks, Boris & Emmerich, Michael, 2007. "SMS-EMOA: Multiobjective selection based on dominated hypervolume," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1653-1669, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liagkouras, Konstantinos & Metaxiotis, Konstantinos, 2021. "Improving multi-objective algorithms performance by emulating behaviors from the human social analogue in candidate solutions," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1019-1036.
    2. Gong, Wenyin & Cai, Zhihua, 2009. "An improved multiobjective differential evolution based on Pareto-adaptive [epsilon]-dominance and orthogonal design," European Journal of Operational Research, Elsevier, vol. 198(2), pages 576-601, October.
    3. Andrea Ponti & Antonio Candelieri & Ilaria Giordani & Francesco Archetti, 2023. "Intrusion Detection in Networks by Wasserstein Enabled Many-Objective Evolutionary Algorithms," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    4. Yunsong Han & Hong Yu & Cheng Sun, 2017. "Simulation-Based Multiobjective Optimization of Timber-Glass Residential Buildings in Severe Cold Regions," Sustainability, MDPI, vol. 9(12), pages 1-18, December.
    5. Sergio Cabello, 2023. "Faster distance-based representative skyline and k-center along pareto front in the plane," Journal of Global Optimization, Springer, vol. 86(2), pages 441-466, June.
    6. Houssem R. E. H. Bouchekara & Yusuf A. Sha’aban & Mohammad S. Shahriar & Makbul A. M. Ramli & Abdullahi A. Mas’ud, 2023. "Wind Farm Layout Optimization/Expansion with Real Wind Turbines Using a Multi-Objective EA Based on an Enhanced Inverted Generational Distance Metric Combined with the Two-Archive Algorithm 2," Sustainability, MDPI, vol. 15(3), pages 1-32, January.
    7. Braun, Marlon & Shukla, Pradyumn, 2024. "On cone-based decompositions of proper Pareto-optimality in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 317(2), pages 592-602.
    8. Jesús Martínez-Frutos & David Herrero-Pérez, 2016. "Kriging-based infill sampling criterion for constraint handling in multi-objective optimization," Journal of Global Optimization, Springer, vol. 64(1), pages 97-115, January.
    9. José Antonio Castán Rocha & Alejandro Santiago & Alejandro H. García-Ruiz & Jesús David Terán-Villanueva & Salvador Ibarra Martínez & Mayra Guadalupe Treviño Berrones, 2024. "Pareto Approximation Empirical Results of Energy-Aware Optimization for Precedence-Constrained Task Scheduling Considering Switching Off Completely Idle Machines," Mathematics, MDPI, vol. 12(23), pages 1-53, November.
    10. Dubois-Lacoste, Jérémie & López-Ibáñez, Manuel & Stützle, Thomas, 2015. "Anytime Pareto local search," European Journal of Operational Research, Elsevier, vol. 243(2), pages 369-385.
    11. Hyoungjin Kim & Meng-Sing Liou, 2013. "New fitness sharing approach for multi-objective genetic algorithms," Journal of Global Optimization, Springer, vol. 55(3), pages 579-595, March.
    12. Miettinen, Kaisa & Molina, Julián & González, Mercedes & Hernández-Díaz, Alfredo & Caballero, Rafael, 2009. "Using box indices in supporting comparison in multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 197(1), pages 17-24, August.
    13. Tangpattanakul, Panwadee & Jozefowiez, Nicolas & Lopez, Pierre, 2015. "A multi-objective local search heuristic for scheduling Earth observations taken by an agile satellite," European Journal of Operational Research, Elsevier, vol. 245(2), pages 542-554.
    14. Luan, Wenpeng & Tian, Longfei & Zhao, Bochao, 2023. "Leveraging hybrid probabilistic multi-objective evolutionary algorithm for dynamic tariff design," Applied Energy, Elsevier, vol. 342(C).
    15. Cosson, Raphaël & Santana, Roberto & Derbel, Bilel & Liefooghe, Arnaud, 2024. "On bi-objective combinatorial optimization with heterogeneous objectives," European Journal of Operational Research, Elsevier, vol. 319(1), pages 89-101.
    16. Allmendinger, Richard & Handl, Julia & Knowles, Joshua, 2015. "Multiobjective optimization: When objectives exhibit non-uniform latencies," European Journal of Operational Research, Elsevier, vol. 243(2), pages 497-513.
    17. Weihua Qian & Hang Xu & Houjin Chen & Lvqing Yang & Yuanguo Lin & Rui Xu & Mulan Yang & Minghong Liao, 2024. "A Synergistic MOEA Algorithm with GANs for Complex Data Analysis," Mathematics, MDPI, vol. 12(2), pages 1-30, January.
    18. Rahat, Alma A.M. & Wang, Chunlin & Everson, Richard M. & Fieldsend, Jonathan E., 2018. "Data-driven multi-objective optimisation of coal-fired boiler combustion systems," Applied Energy, Elsevier, vol. 229(C), pages 446-458.
    19. Raimundo, Marcos M. & Ferreira, Paulo A.V. & Von Zuben, Fernando J., 2020. "An extension of the non-inferior set estimation algorithm for many objectives," European Journal of Operational Research, Elsevier, vol. 284(1), pages 53-66.
    20. Xiang Yu & Xueqing Zhang, 2017. "Multiswarm comprehensive learning particle swarm optimization for solving multiobjective optimization problems," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-21, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1760-:d:601633. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.