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Designing sustainable diet plans by solving triobjective integer programs

Author

Listed:
  • Luca Benvenuti

    (Sapienza, University of Rome)

  • Alberto Santis

    (Sapienza, University of Rome)

  • Marianna Santis

    (University of Florence)

  • Daniele Patria

    (Sapienza, University of Rome)

Abstract

We present an algorithm for triobjective nonlinear integer programs that combines the $$\varepsilon $$ ε -constrained method with available oracles for biobjective integer programs. We prove that our method is able to detect the nondominated set within a finite number of iterations. Specific strategies to avoid the detection of weakly nondominated points are devised. The method is then used to determine the nondominated solutions of triobjective 0–1 models, built to design nutritionally adequate and healthy diet plans, minimizing their environmental impact. The diet plans refer to menus for school cafeterias and we consider the carbon, water and nitrogen footprints as conflicting objectives to be minimized. Energy and nutrient contents are constrained in suitable ranges suggested by the dietary recommendation of health authorities. Results obtained on two models and on real world data are reported and discussed.

Suggested Citation

  • Luca Benvenuti & Alberto Santis & Marianna Santis & Daniele Patria, 2024. "Designing sustainable diet plans by solving triobjective integer programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(3), pages 703-721, December.
    • Handle: RePEc:spr:mathme:v:100:y:2024:i:3:d:10.1007_s00186-024-00879-8
    DOI: 10.1007/s00186-024-00879-8
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    References listed on IDEAS

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    1. Satya Tamby & Daniel Vanderpooten, 2021. "Enumeration of the Nondominated Set of Multiobjective Discrete Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 72-85, January.
    2. De Santis, Marianna & Grani, Giorgio & Palagi, Laura, 2020. "Branching with hyperplanes in the criterion space: The frontier partitioner algorithm for biobjective integer programming," European Journal of Operational Research, Elsevier, vol. 283(1), pages 57-69.
    3. William Pettersson & Melih Ozlen, 2020. "Multiobjective Integer Programming: Synergistic Parallel Approaches," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 461-472, April.
    4. Gabriele Eichfelder & Peter Kirst & Laura Meng & Oliver Stein, 2021. "Correction to: A general branch-and-bound framework for continuous global multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 229-229, May.
    5. Eichfelder, Gabriele & Warnow, Leo, 2023. "Advancements in the computation of enclosures for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 310(1), pages 315-327.
    6. Boland, Natashia & Charkhgard, Hadi & Savelsbergh, Martin, 2017. "The Quadrant Shrinking Method: A simple and efficient algorithm for solving tri-objective integer programs," European Journal of Operational Research, Elsevier, vol. 260(3), pages 873-885.
    7. Gabriele Eichfelder & Peter Kirst & Laura Meng & Oliver Stein, 2021. "A general branch-and-bound framework for continuous global multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 195-227, May.
    8. Melih Ozlen & Benjamin A. Burton & Cameron A. G. MacRae, 2014. "Multi-Objective Integer Programming: An Improved Recursive Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 470-482, February.
    9. Özlen, Melih & Azizoglu, Meral, 2009. "Multi-objective integer programming: A general approach for generating all non-dominated solutions," European Journal of Operational Research, Elsevier, vol. 199(1), pages 25-35, November.
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