IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1184-d787144.html
   My bibliography  Save this article

Optimization of the Cognitive Processes in a Virtual Classroom: A Multi-objective Integer Linear Programming Approach

Author

Listed:
  • María Luisa Nolé

    (Institute for Research and Innovation in Bioengineering (i3B), Universitat Politècnica de València, Camí de Vera s/n, 46022 València, Spain)

  • David Soler

    (Institut Universitari de Matemàtica Multidisciplinar, Universitat Politècnica de València, Camí de Vera s/n, 46022 València, Spain)

  • Juan Luis Higuera-Trujillo

    (Institute for Research and Innovation in Bioengineering (i3B), Universitat Politècnica de València, Camí de Vera s/n, 46022 València, Spain
    Tecnológico de Monterrey, Escuela de Arquitectura, Arte y Diseño (EAAD), Monterrey 64849, Mexico)

  • Carmen Llinares

    (Institute for Research and Innovation in Bioengineering (i3B), Universitat Politècnica de València, Camí de Vera s/n, 46022 València, Spain)

Abstract

A fundamental problem in the design of a classroom is to identify what characteristics it should have in order to optimize learning. This is a complex problem because learning is a construct related to several cognitive processes. The aim of this study is to maximize learning, represented by the processes of attention, memory, and preference, depending on six classroom parameters: height, width, color hue, color saturation, color temperature, and illuminance. Multi-objective integer linear programming with three objective functions and 56 binary variables was used to solve this optimization problem. Virtual reality tools were used to gather the data; novel software was used to create variations of virtual classrooms for a sample of 112 students. Using an interactive method, more than 4700 integer linear programming problems were optimally solved to obtain 13 efficient solutions to the multi-objective problem, which allowed the decision maker to analyze all the information and make a final choice. The results showed that achieving the best cognitive processing performance involves using different classroom configurations. The use of a multi-objective interactive approach is interesting because in human behavioral studies, it is important to consider the judgement of an expert in order to make decisions.

Suggested Citation

  • María Luisa Nolé & David Soler & Juan Luis Higuera-Trujillo & Carmen Llinares, 2022. "Optimization of the Cognitive Processes in a Virtual Classroom: A Multi-objective Integer Linear Programming Approach," Mathematics, MDPI, vol. 10(7), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1184-:d:787144
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1184/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/7/1184/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Masatoshi Sakawa & Hitoshi Yano & Ichiro Nishizaki, 2013. "Stochastic Linear Programming," International Series in Operations Research & Management Science, in: Linear and Multiobjective Programming with Fuzzy Stochastic Extensions, edition 127, chapter 0, pages 149-196, Springer.
    2. Masatoshi Sakawa & Hitoshi Yano & Ichiro Nishizaki, 2013. "Multiobjective Linear Programming," International Series in Operations Research & Management Science, in: Linear and Multiobjective Programming with Fuzzy Stochastic Extensions, edition 127, chapter 0, pages 73-103, Springer.
    3. Masatoshi Sakawa & Hitoshi Yano & Ichiro Nishizaki, 2013. "Linear and Multiobjective Programming with Fuzzy Stochastic Extensions," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4614-9399-0, February.
    4. Oliveira, Carla & Antunes, Carlos Henggeler, 2007. "Multiple objective linear programming models with interval coefficients - an illustrated overview," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1434-1463, September.
    5. Masatoshi Sakawa & Hitoshi Yano & Ichiro Nishizaki, 2013. "Fuzzy Linear Programming," International Series in Operations Research & Management Science, in: Linear and Multiobjective Programming with Fuzzy Stochastic Extensions, edition 127, chapter 0, pages 105-148, Springer.
    6. Fátima Bernardo & Isabel Loupa-Ramos & Cristina Matos Silva & Maria Manso, 2021. "The Restorative Effect of the Presence of Greenery on the Classroom in Children’s Cognitive Performance," Sustainability, MDPI, vol. 13(6), pages 1-16, March.
    7. Sandra González-Gallardo & Ana B. Ruiz & Mariano Luque, 2021. "Analysis of the Well-Being Levels of Students in Spain and Finland through Interval Multiobjective Linear Programming," Mathematics, MDPI, vol. 9(14), pages 1-27, July.
    8. Alves, Maria Joao & Climaco, Joao, 2007. "A review of interactive methods for multiobjective integer and mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 99-115, July.
    9. Mikulás Luptácik, 2010. "Mathematical Optimization and Economic Analysis," Springer Optimization and Its Applications, Springer, number 978-0-387-89552-9, December.
    10. Carmen Llinares & Nuria Castilla & Juan Luis Higuera-Trujillo, 2021. "Do Attention and Memory Tasks Require the Same Lighting? A Study in University Classrooms," Sustainability, MDPI, vol. 13(15), pages 1-13, July.
    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. Soumendra Nath Sanyal & Izabela Nielsen & Subrata Saha, 2020. "Multi-Objective Human Resource Allocation Approach for Sustainable Traffic Management," IJERPH, MDPI, vol. 17(7), pages 1-16, April.
    2. Avik Pradhan & M. P. Biswal, 2017. "Multi-choice probabilistic linear programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 122-142, March.
    3. Milan Hladík, 2023. "Various approaches to multiobjective linear programming problems with interval costs and interval weights," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(3), pages 713-731, September.
    4. Dranichak, Garrett M. & Wiecek, Margaret M., 2019. "On highly robust efficient solutions to uncertain multiobjective linear programs," European Journal of Operational Research, Elsevier, vol. 273(1), pages 20-30.
    5. Christos Pelekis & Panagiotis Promponas & Juan Alvarado & Eirini Eleni Tsiropoulou & Symeon Papavassiliou, 2021. "A fragile multi-CPR game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 461-492, December.
    6. Morton, Alec, 2014. "Aversion to health inequalities in healthcare prioritisation: A multicriteria optimisation perspective," Journal of Health Economics, Elsevier, vol. 36(C), pages 164-173.
    7. Zhou, Feng & Huang, Gordon H. & Chen, Guo-Xian & Guo, Huai-Cheng, 2009. "Enhanced-interval linear programming," European Journal of Operational Research, Elsevier, vol. 199(2), pages 323-333, December.
    8. Richard Eglese & Sofoclis Zambirinis, 2018. "Disruption management in vehicle routing and scheduling for road freight transport: a review," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 1-17, April.
    9. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2018. "Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs," European Journal of Operational Research, Elsevier, vol. 270(1), pages 40-50.
    10. S. Razavyan, 2016. "A Method for Generating a Well-Distributed Pareto Set in Multiple Objective Mixed Integer Linear Programs Based on the Decision Maker’s Initial Aspiration Level," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-23, August.
    11. Wu, Hsien-Chung, 2009. "The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 49-60, July.
    12. S. Rivaz & M. Yaghoobi, 2013. "Minimax regret solution to multiobjective linear programming problems with interval objective functions coefficients," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 625-649, September.
    13. Cristina Matos Silva & Fátima Bernardo & Maria Manso & Isabel Loupa Ramos, 2023. "Green Spaces over a Roof or on the Ground, Does It Matter? The Perception of Ecosystem Services and Potential Restorative Effects," Sustainability, MDPI, vol. 15(6), pages 1-17, March.
    14. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    15. Filippi, C. & Guastaroba, G. & Speranza, M.G., 2016. "A heuristic framework for the bi-objective enhanced index tracking problem," Omega, Elsevier, vol. 65(C), pages 122-137.
    16. Di Martinelly, Christine & Meskens, Nadine, 2017. "A bi-objective integrated approach to building surgical teams and nurse schedule rosters to maximise surgical team affinities and minimise nurses' idle time," International Journal of Production Economics, Elsevier, vol. 191(C), pages 323-334.
    17. Julio B. Clempner, 2018. "Computing multiobjective Markov chains handled by the extraproximal method," Annals of Operations Research, Springer, vol. 271(2), pages 469-486, December.
    18. S. Rivaz & M. A. Yaghoobi & M. Hladík, 2016. "Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 237-253, September.
    19. P. Kumar & A. K. Bhurjee, 2022. "Multi-objective enhanced interval optimization problem," Annals of Operations Research, Springer, vol. 311(2), pages 1035-1050, April.
    20. Jorge, Jesús M., 2009. "An algorithm for optimizing a linear function over an integer efficient set," European Journal of Operational Research, Elsevier, vol. 195(1), pages 98-103, May.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:10:y:2022:i:7:p:1184-:d:787144. 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.