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Designing sustainable diet plans by solving triobjective integer programs

Luca Benvenuti (luca.benvenuti@uniroma1.it), Alberto Santis (alberto.desantis@uniroma1.it), Marianna Santis (marianna.desantis@unifi.it) and Daniele Patria (daniele.patria@uniroma1.it)
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Luca Benvenuti: Sapienza, University of Rome
Alberto Santis: Sapienza, University of Rome
Marianna Santis: University of Florence
Daniele Patria: Sapienza, University of Rome

Mathematical Methods of Operations Research, 2024, vol. 100, issue 3, No 5, 703-721

Abstract: 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.

Keywords: Multiobjective integer programming; Criterion space algorithm; Environmental sustainability (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00186-024-00879-8

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