Developing a novel optimisation approach for keeping heterogeneous diets healthy and within planetary boundaries for climate change

The study addresses how to operationalise healthy and climate-friendly diets that are acceptable across heterogeneous population groups. While the EAT-Lancet Commission proposes a global plant-forward reference diet, applying a uniform average-based optimisation may overlook within-population dietary variability and lead to unrealistic changes for some subgroups. The authors propose combining data-driven dietary clustering with linear programming (LP) to tailor nutritionally adequate, health-promoting, and low-greenhouse-gas-emission (GHGE) diets that remain culturally acceptable. The primary aim was to optimise diets for distinct eating-pattern clusters and compare them with a total-population optimisation, assessing whether tailored cluster-based solutions are more realistic. Diets were constrained to meet Nordic DRVs, Swedish Food-Based Dietary Guidelines (FBDGs), and an IPCC-aligned GHGE threshold of 1.57 kg CO₂eq/day, and compared with the EAT-Lancet diet.

Design: Modelling study integrating hierarchical clustering and linear programming (LP) to create nutritionally adequate, health-promoting, climate-friendly, and culturally acceptable diets. Data source: Swedish national dietary survey Riksmaten Vuxna 2010–11; 4-day web-based food diary, 1797 adults (56% female; mean age 48 years). Nutrient intakes linked to the Swedish Food Agency Food Composition Database (Riksmaten Vuxna 2010–11). Environmental data: CO₂eq for 2078 foods from the RISE Climate Database (LCA-based; 100-year GWP factors for CO₂, CH₄, N₂O); excluded packaging, transport from store to home, meal preparation, and household food waste. Prices: 2020 retail prices from Matpriskollen; average price per item across retailers/variants; used for cost estimates, not as constraints. Food grouping: For modelling/description, 24 food categories per RISE schema; additionally mapped to EAT-Lancet categories for comparisons (whole grains, tubers, vegetables, fruits, dairy foods, red meat, poultry, eggs, fish, legumes, nuts, added fats, added sugars). Mixed dishes apportioned by dominant or proportional recipe shares. Clustering: Exploratory validation with clValid identified hierarchical clustering as best algorithm; Canberra distance with Ward’s method chosen (highest Dunn index). NbClust supported 2–3 clusters; three clusters selected. Food groups used in clustering: Red meat, Processed meat, Vegetables, Fruits and berries, Dairy, Pulses, Nuts and seeds, Seafood, Mixed animal fats, Sugar and sweets, Rice, Potatoes, Cereals/grains, Eggs, Poultry, and Whole grains. To avoid sparsity bias, only groups consumed by ≥75% were included, except Pulses and Nuts and seeds retained as key indicators. Intakes standardised per energy (g/MJ). Statistical comparisons across clusters: Kruskal–Wallis with Dunn post-hoc (BH-adjusted) for non-normal variables (food groups, CO₂eq, income); ANOVA with Tukey post-hoc for age; chi-squared for sex. Healthiness assessed using SHEIA15 (score 0–9; low <4, medium 4–7, high >7). Optimisation models: LP implemented with OpenSolver (CBC solver) in Excel 2016. Decision variables: absolute amount of each individual food item (per total population or per cluster). Objective: minimise total relative deviation (TRD) from baseline reported intake to maximise similarity (cultural acceptability). Constraints: (1) DRVs (NNR 2012) covering 97.5% of population; sex-specific DRVs weighted by sex distribution; total daily energy fixed to baseline level within each group; (2) Swedish FBDGs; (3) Acceptability: each food item could be reduced to 0 g; increases capped at +200% relative to baseline except Pulses, Nuts and seeds, Dairy substitutes, Meat substitutes, and Vegetable oils (no upper limit); (4) For the second set of models, an added total CO₂eq cap of ≤1.57 kg/day. Cost calculated ex-post. Outputs included average relative deviation (ARD = TRD/number of foods) as a proxy for similarity/acceptability, and identification of active constraints (binding at 100%). Models: For total population and for each of three clusters, two stages were run: (i) meeting DRVs and FBDGs (TotPop, Classic, NutRich, LowClim) and (ii) additionally meeting the GHGE limit (TotPop+, Classic+, NutRich+, LowClim+).

- Clusters identified: three roughly equal-sized clusters (n=707, 534, 556). Characterisations: • Classic Baseline: higher red/processed meat and potatoes; lower fruits/vegetables; higher CO₂eq; medium SHEIA15. • NutRich Baseline: higher nutrient-dense animal products, nuts, vegetables; highest CO₂eq; high SHEIA15. • LowClim Baseline: higher vegetables and pulses (also some sugar/sweets); lowest CO₂eq; high SHEIA15. - Baseline GHGE: 2770 g/day (LowClim) to 3361 g/day (Classic). All baseline diets were below recommended carbs, fibre, iron; vitamin D below DRV except LowClim met 100%. All exceeded saturated fat and sodium DRVs. - Optimisation without GHGE cap (meet DRVs + FBDGs): GHGE reduced 8–24% relative to baseline; costs modestly increased by ~1–3% (Classic −1%); ARD low (~2.6–3.6%) except Classic ARD 19.7%. - Optimisation with GHGE cap (≤1.57 kg CO₂eq/day): GHGE reduced 43–53% vs baseline; costs decreased ~8–13%; ARD modestly increased vs uncapped but remained 5.8% (LowClim+) to 22.8% (Classic+). Only about 5–12% of foods were changed (increased/reduced/removed) relative to baseline in capped models. - Food group shifts in capped models: substantial decreases in animal-source foods; Classic+ diet: −82% red meat, −81% processed meat, −62% poultry, dairy reduced to about one-third of baseline; all optimised diets increased plant foods (vegetables +6% to +159%; potatoes +106% to +131%; fruits/berries +127% to +183%). Cereals/grains increased most in TotPop+ (+56%), modestly in LowClim+ (+8%). Rice reduced by ~70% in all capped diets except unchanged in LowClim+. Pulses increased 15-fold in Classic+. - Active constraints frequently included lower bounds for iron and vitamin D and upper bounds for added sugars and sodium. - Cluster-specific optimised diets differed from the total-population optimised diet (TotPop+), indicating that tailoring by cluster changes both magnitude and direction of required dietary shifts. - All optimised diets diverged considerably from the EAT-Lancet reference diet pattern.

The combined clustering and LP approach directly addressed the heterogeneity of dietary patterns, producing tailored solutions that are potentially more acceptable than a single average-based optimisation. Meeting DRVs and current Swedish FBDGs alone reduced GHGE by up to 24% but was insufficient to reach the IPCC-aligned threshold of 1.57 kg CO₂eq/day; adding an explicit GHGE cap was necessary. Importantly, the GHGE-constrained optimisations maintained relatively low deviations from baseline (low ARD) and changed a small share of foods, suggesting cultural acceptability could be high, and reduced diet costs compared to baseline, countering the perception that sustainable diets are necessarily more expensive. The optimised diets did not align closely with the EAT-Lancet pattern, likely due to explicit nutrient adequacy constraints, cultural acceptability bounds, inclusion of mixed dishes in the food database, and the focus on GHGE rather than multiple environmental dimensions; moreover, EAT-Lancet is a global reference not tailored to Swedish contexts. Tailoring by clusters revealed different required shifts than those inferred from total-population averages, supporting the value of this approach for policy and guidance aimed at diverse consumer groups.

This study introduces a novel, cluster-based optimisation framework that integrates nutrient adequacy, health promotion, climate impact, affordability, and cultural acceptability. Fully optimised diets meeting DRVs, FBDGs, and a 1.57 kg CO₂eq/day cap achieved 43–53% GHGE reductions while largely preserving existing food patterns and lowering costs. Across all clusters, shifts predominantly replaced animal-source foods with plant-based options, but the magnitude and composition of changes varied by dietary pattern, indicating that cluster-specific recommendations may be more realistic than a single average-based solution. The optimised diets diverged from the EAT-Lancet reference, highlighting multiple viable pathways to sustainable diets and the importance of cultural context. Future research should incorporate additional environmental indicators and consider inclusion of newer fortified plant-based alternatives to further enhance nutrient adequacy and acceptability.

- Environmental assessment limited to GHGE; other impacts (land use, water use, eutrophication, acidification, biodiversity, ecotoxicity, animal welfare) were not included due to data limitations. - CO₂eq estimates excluded packaging, transport from store to home, household meal preparation, and food waste. - Optimisation restricted to foods present in the baseline diets, excluding newer meat/dairy alternatives that could aid nutrient adequacy and acceptability. - Food grouping and inclusion of mixed dishes differ from the EAT-Lancet’s basic food categories, limiting direct comparability. - Context-specific findings (Swedish dietary data 2010–11; prices from 2020) may limit generalisability to other settings or time periods.