Mathematical Optimization to Explore Tomorrow's Sustainable Diets: A Narrative Review

Abstract

A sustainable diet is, by definition, nutritionally adequate, economically affordable, culturally acceptable, and environmentally respectful. Designing such a diet has to integrate different dimensions of diet sustainability that may not be compatible with each other. Among multicriteria assessment methods, diet optimization is a whole-diet approach that simultaneously combines several metrics for dimensions of diet sustainability. This narrative review based on 67 published studies shows how mathematical diet optimization can help with understanding the relations between the different dimensions of diet sustainability and how it can be properly used to identify sustainable diets. Diet optimization aims to find the optimal combination of foods for a population, a subpopulation, or an individual that fulfills a set of constraints while minimizing or maximizing an objective function. In the studies reviewed, diet optimization was used to examine the links between dimensions of diet sustainability, identify the minimum cost or environmental impact of a nutritionally adequate diet, or identify food combinations able to combine ≥2 sustainability dimensions. If some constraints prove difficult to fulfill, this signals an incompatibility between nutrient recommendations, over-monotonous food-consumption patterns, an inadequate supply of nutrient-rich foods, or an incompatibility with other dimensions. If diet optimization proves successful, it can serve to design nutritionally adequate, culturally acceptable, economically affordable, and environmentally friendly diets. Diet optimization results can help define dietary recommendations, tackle food security issues, and promote sustainable dietary patterns. This review emphasizes the importance of carefully choosing the model parameters (variables, objective function, constraints) and input data and the need for appropriate expertise to correctly interpret and communicate the results. Future research should make improvements in the choice of metrics used to assess each aspect of a sustainable diet, especially the cultural dimension, to improve the practicability of the results.

Reaching culturally acceptable and adequate diets at the lowest cost increment according to income level in Brazilian households

“…associated with changes in diet composition in a non-linear pattern: small divergence of optimized diets in comparison to observed diets resulted in lower differences in costs. Similar non-linear inverse relationship between cost and deviation from the observed diet was found in a study with French women: to meet nutritional constraints, the minimum departure from the observed diet was 495% at a cost of 4.99 euros, but to achieve nutritional constraints at the lowest possible cost (i.e., 3.18 euros), the deviation markedly increased to 2,870% [18].…”

“…Linear programming (LP) is an analytic method for the optimization of variables, subject to constraints expressed as target values that should be met. It helps in the assessment of the feasibility of complex problems involving multiple variables and constraints (such as cost and nutrient contents) and to find their optimal solution [18]. Results from studies with diet optimization may support decisions on food policies and nutritional guidelines after considering constraints of cost and acceptability, indicating what could be more effective and efficient in terms of diet changes, i.e., higher quality and acceptability and lower cost.…”

Affordability of the EAT–Lancet reference diet: a global analysis

“…This cost of nutrient adequacy is an updated version of the least-cost diet concept originally suggested by Stigler 17 that has since been used for a wide range of purposes. [18][19][20][21][22] To compare with the EAT-Lancet reference diet, we defined the cost of nutrient adequacy as the lowest-cost combination of foods needed to meet all requirements of 20 essential nutrients for a healthy 60 kg woman at 30 years old, in energy balance at 2503 kcal per day (appendix). The quantity of each food needed to deliver nutrients in the required proportions was calculated by linear programming, to give a lower bound on the daily cost of meeting a healthy woman's minimum estimated average requirements, while staying below the maximum upper level of toxicity risk for each micronutrient and within acceptable macronutrient distribution range for protein, fats, and carbohydrates.…”

Optimising healthy and safe fish intake recommendations: a trade-off between personal preference and cost

“…Mathematical optimisation of food intakes ('diet optimisation') have been applied to analyse several aspects of diet sustainability (18) . Mathematical optimisation methods are suitable for this purpose, thanks to their ability to deal with several factors simultaneously; they provide a multi-dimensional approach.…”

“…Diet modelling has been applied at individual (19)(20)(21)(22) and population level (23)(24)(25) . The majority of the previous diet optimisation studies have considered nutritional recommendations as criteria, and few studies also included contaminant exposure limits (18) . Several diet optimisation studies have assessed the cultural acceptability dimension of diet sustainability by modelled combinations of foods that deviate as little as possible from observed intake (19)(20)(21)(22)(23)(24) .…”