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

Author

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  • 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
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    References listed on IDEAS

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    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, April.
    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, June.
    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.
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