Designing sustainable diet plans by solving triobjective integer programs
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 strateg...
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| Vydané v: | Mathematical methods of operations research (Heidelberg, Germany) Ročník 100; číslo 3; s. 703 - 721 |
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| Hlavní autori: | , , , |
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| Jazyk: | English |
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01.12.2024
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| 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. |
|---|---|
| AbstractList | We present an algorithm for triobjective nonlinear integer programs that combines the 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. 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. |
| Author | Benvenuti, Luca De Santis, Marianna Patria, Daniele De Santis, Alberto |
| Author_xml | – sequence: 1 givenname: Luca surname: Benvenuti fullname: Benvenuti, Luca – sequence: 2 givenname: Alberto surname: De Santis fullname: De Santis, Alberto – sequence: 3 givenname: Marianna orcidid: 0000-0002-1189-5917 surname: De Santis fullname: De Santis, Marianna – sequence: 4 givenname: Daniele surname: Patria fullname: Patria, Daniele |
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| Cites_doi | 10.1080/0305215X.2021.1939695 10.1016/j.orl.2022.04.007 10.1186/s12859-018-2007-7 10.1287/ijoc.2020.0953 10.1080/11026480410000986 10.1038/s41597-021-00909-8 10.1016/j.cor.2021.105396 10.1007/s10898-020-00984-y 10.1007/s10957-023-02285-2 10.1002/mcda.1780 10.1089/SUS.2013.9852 10.1016/j.ejor.2016.03.035 10.1016/j.ijhydene.2005.04.017 10.1137/19M1264709 10.1016/j.amc.2009.03.037 10.1007/s11081-021-09598-z 10.1007/s12532-015-0093-3 10.1016/j.ejor.2023.02.032 10.1007/s10957-013-0364-y 10.1002/9781118341704 10.1016/j.foreco.2020.118714 10.1016/j.ejor.2019.10.034 10.1016/j.ejor.2008.10.023 10.1016/j.ddtec.2013.02.001 |
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-constrained method with available oracles for... We present an algorithm for triobjective nonlinear integer programs that combines the ε-constrained method with available oracles for biobjective integer... |
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| SubjectTerms | Algorithms Constraints Diet Integer programming Linear programming Optimization Water consumption |
| Title | Designing sustainable diet plans by solving triobjective integer programs |
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