Low-carbon diets across diverse dietary patterns: Addressing population heterogeneity under constrained optimization

Mathematical optimization is a useful tool for modeling diets that fulfill requirements for health and environmental sustainability, however, population-based optimization approaches fail to account for underlying dietary diversity in populations. This study proposes a methodological approach to consider diverse dietary intake patterns in mathematical optimization of nutritionally adequate low-carbon diets and investigates the differences between different population groups, along with trade-offs between greenhouse gas emission (GHGE) reduction and the inconvenience of dietary changes required to achieve optimized diets. A k-means clustering analysis was applied to individual dietary intake data from Denmark, which resulted in four clusters with different dietary patterns. This was followed by quadratic programming, wherein the total dietary changes required from the observed diet within each cluster were used as a proxy for consumer inconvenience (i.e., "inconvenience index") and were minimized while fulfilling nutrient constraints and incrementally tightened GHGE constraints. Across clusters, a steep increase of the inconvenience index was observed at GHGE levels below approximately 3 kg CO₂e/10 MJ, corresponding to GHGE reductions of 24-36 % in different clusters. In all clusters, the optimized diets with nutritional and GHGE constraints showed common traits of increased content of cereals and starches, eggs, and fish and decreased amounts of beef and lamb, cheese, animal-based fats, and alcoholic beverages, but differences across clusters were also observed, maintaining characteristics of the clusters' baselines. When additional health-based targets for food amounts were applied as constraints, the optimized diets converged towards the same type of diet. The total inconvenience of dietary changes required to fulfill constraints differed between clusters, indicating that specific sub-populations may be more effective targets for dietary transition. The method has potential for future integration of more sustainability aspects and different consumer preferences.