The data on food consumption and expenditure utilized in this study are derived from the microdata of the Urban Household Income and Expenditure Survey conducted by the National Bureau of Statistics in China. This survey spans six provinces or autonomous regions, namely Guangdong, Sichuan, Jilin, Hebei, Henan, and Xinjiang. A significant strength of this dataset is its comprehensiveness, which surveyed households recorded their complete dietary consumption and expenditures daily throughout the year. This dataset encompasses detailed records of food expenditures and various family characteristic variables. Characterized by its large sample size and high quality, the data accurately reflect the Chinese diets and have been extensively used in empirical studies concerning food consumption in China (Han et al., 2019; Zheng and Henneberry, 2012; Zhu et al., 2022; Zhu et al., 2021).

The residents’ diet categories in this study primarily include seven major food groups: cereals, oils and fats, meat and poultry, dairy and eggs, aquatic products, fruits and vegetables, and other foods. To paint a detailed picture of consumers’ diets, these seven major food groups were further subdivided into 20 sub-categories (Table 2). To ensure data integrity and reduce the influence of extreme values, the approach adopted from Zheng and Henneberry (2012) was employed, wherein samples with food price and expenditure variables exceeding five standard deviations from the mean were excluded. This filtering process yielded a total of 6,535 samples suitable for analysis. Additionally, to explore diets across different income strata, households were categorized into low, middle, and high-income groups according to the income group division method of the National Bureau of Statistics in China. These groups represent the lowest 20%, middle 60%, and highest 20% of the total household income distribution, respectively. Furthermore, due to the lack of price data in this survey, a quality-adjusted price was used (Cox and Wohlgenant, 1986; Gao et al., 1995; Zheng and Henneberry, 2009; Zhu et al., 2021). First, the unit value for 20 food items was calculated by dividing food expenditure by the quantity consumed for each item. Next, based on these unit values without considering quality factors, the quality-adjusted price was estimated using hedonic price regression. These price variables are later used to calculate demand price elasticity parameters and dietary costs.

Table 2 presents a detailed breakdown of the current diets and food expenditures for the overall sample and across the three income groups. The data reveal notable disparities in both food consumption expenditures and dietary structures among the different income groups. The average per capita food expenditure for all samples stands at 8.73 yuan/day. Specifically, the expenditure for the low-income group is 6.61 yuan/day, while the expenditures for the middle and high-income groups are 8.98 yuan/day and 9.97 yuan/day, respectively. There is a prevalent trend towards higher consumption of plant-based products, such as cereals, fruits and vegetables, with comparatively lower consumption of animal-based products. Notably, the consumption of most food types tends to increase with income across the groups, with some exceptions such as wheat, edible animal oil, mutton, and alcohol, which are consumed more by the middle-income group than by the high-income group.

In this study, nutrient analysis encompasses 19 distinct categories, including energy, protein, fat, carbohydrates, dietary fiber, cholesterol, and various vitamins and minerals (vitamin A, vitamin C, vitamin E, calcium, phosphorus, potassium, sodium, magnesium, iron, zinc, selenium, copper, and manganese). To integrate these nutrients into the multi-objective programming model, it is imperative to convert food consumption data into nutrient content. The conversion coefficients for each nutrient, along with the edible portion coefficients for each food, are derived from the China Food Composition Tables (National Institute for Nutrition and Health, 2021). Additionally, the nutrient intake guidelines, including recommended and maximum intake levels for each nutrient, are sourced from the Chinese DRIs Tables (2013 Edition) (Chinese Nutrition Society, 2014).

A primary objective of this study is to construct a diet pattern that not only promotes health but also minimizes greenhouse gas (GHG) emissions from the food system. Accurate GHG emission conversion coefficients are essential for this purpose. This research utilizes the food system GHG emission coefficients reported by Song et al. (2017), which are based on a global life cycle assessment (LCA) method and drawn from an extensive database of 1,237 articles maintained by the Barilla Center for Food & Nutrition (BCFN). These coefficients encompass the entire supply chain from production to consumption, accounting for GHGs such as CO₂, N₂O, and CH₄ produced during agricultural activities, as well as CO₂ emissions from energy consumption in subsequent stages of the supply chain. An advantage of these coefficients is their incorporation of uncertainty measures, employing triangular probability distributions and Monte Carlo simulations to enhance the reliability of the GHG emissions assessment (Eggleston et al., 2006; Song et al., 2015). The specific parameters are detailed in Table 3. To validate the reliability of these GHG emission conversion coefficients, a sensitivity analysis is conducted as part of the robustness tests.

To accurately reflect consumers’ dietary habits and preferences, this study incorporates demand price elasticity as a critical parameter in the diet programming model. This approach follows the methodologies established by Green et al. (2015) and Irz et al. (2015). Chalmers and Revoredo-Giha (2019) suggest that different socio-economic groups exhibit distinct demand price elasticities, necessitating tailored calculations to accurately mirror the food consumption preferences of these groups. Consequently, this study estimates demand price elasticities for low, middle, and high-income groups, integrating these parameters into the model to reflect the inertia in changing consumption habits. The economic model employed is comprehensive and robust, built upon the Stone index implicit Marshallian demand system (EASI) as proposed by Lewbel and Pendakur (2009), and uses a two-stage consistent estimation method by Shonkwiler and Yen (1999) to address the issue of zero consumption values. This model combines the strengths of widely utilized models such as Almost Ideal Demand System (AIDS) and Quadratic Almost Ideal Demand System (QUAIDS) and is capable of discerning complex impacts of income, price, and other variables on food consumption behavior (Zhen et al., 2014). The data employed for estimating demand price elasticity are consistent with the food consumption and expenditure data previously mentioned, ensuring coherence in matching parameters with dietary data. To address potential endogeneity concerns related to the association between expenditure share and expenditure, price, the Dubin-Wu–Hausman (DWH) method is used, and the Generalized Method of Moments (GMM) is applied for estimation (Zhu et al., 2022). Estimates of own-price elasticity of Marshallian demand are provided in Table 3.

The development of a sustainable healthy diet necessitates a holistic approach that bridges multiple systems. This approach is primarily focused on the food system, yet extends into socio-economic, nutrition-health, and climate-environment systems, integrating foundational theories from diverse disciplines. The overarching goal is to formulate diets that are not only aligned with established eating habits and cost-effective, but also confer benefits to both environmental and health outcomes. This conceptual framework is illustrated in Figure 1.

Initially, the food system is deeply intertwined with the socio-economic system. Grounded in consumer behavior theory and welfare economics, individuals aim to maximize their utility from food consumption or minimize the costs associated with their food purchases. Within the confines of their financial resources, individuals choose foods that reflect their dietary preferences, exemplifying the quintessential consumption behavior of a rational actor within society. As socio-economic conditions evolve, they prompt a diversification among consumer demographics, leading to varying income levels and consequently, distinct patterns of food consumption. Therefore, a sustainable healthy diet should aim to maximize economic welfare across these diverse income groups while accommodating their dietary preferences. This necessitates that the optimized diets should not significantly elevate the cost of food and should preserve consistency in the consumption of various food types. Our study aims to minimize both the economic costs and the alterations in food consumption patterns in the pursuit of optimized diets.

Moreover, the food system is closely linked to the nutrition-health system. The primary role of food is to supply the essential energy required for human survival and to support health through a diverse array of nutrients. Drawing on the theories of nutritional balance and dietary transition, it is crucial for individuals to consume a balanced mix of nutrients to foster healthy development, with nutritional health influenced by factors such as income, dietary preference and nutritional awareness (Popkin, 1993; Popkin, 2006). Consequently, a sustainable healthy diet should also strive to maximize health welfare for all income groups by ensuring nutrient intakes are within recommended levels. Thus, the optimized diets should offer a more balanced nutrient intake and significantly improve the overall dietary quality. In this study, adequate nutrient intake is incorporated as a constraint within our diet optimization model.

Finally, with the intensification of global climate change and shifts in diets, the food system’s greenhouse gas emissions increasingly impact the climate-environment system. The entire life cycle of food, from production to consumption, generates greenhouse gases, contributing to global warming, glacier melt, sea-level rise, and various other environmental challenges (Garnett, 2011; Xiong et al., 2020). From the perspective of environmental economics, consumption behaviors that negatively affect the environment are economically inefficient and can result in significant negative externalities when environmental welfare losses are substantial, jeopardizing the welfare of both current and future generations. This is contrary to the theory of sustainable development, which advocates for a balance between economic growth and environmental preservation. Therefore, a sustainable healthy diet should also aim to maximize environmental welfare by reducing greenhouse gas emissions. According to environmental economic theory, internalizing these external costs into consumer food choices is a critical strategy for addressing these externalities. Consequently, our study incorporates the reduction of food system greenhouse gas emissions as a key optimization objective.

Building upon this conceptual framework, Figure 2 presents the technical roadmap for developing a sustainable healthy diet for Chinese residents. This roadmap includes four main components: (1) Data and parameter acquisition, involving the collection of data on food consumption, expenditures, nutrient and greenhouse gas emission conversion coefficients, and food demand elasticity parameters to support the construction of the diet; (2) The establishment of a multi-objective programming model that recognizes income group disparities and includes three types of optimization objectives, alongside nutrient intake constraints, providing a methodological foundation for diet development; (3) The design of scenarios, which considers five different types of scenarios based on the optimization objectives and the programming model; (4) The evaluation of the resulting diets, assessing them from socio-economic, nutrition-health, and climate-environment perspectives, and confirming the robustness of the results through a sensitivity analysis of the parameters.

Prior studies on programming models for sustainable healthy diets typically employed single-objective linear or nonlinear frameworks, addressing diet optimization at a uniform group level(Chalmers and Revoredo-Giha, 2019; Green et al., 2015; Yin et al., 2021). However, significant disparities exist in dietary preferences across different income groups, and decision-making in this context is inherently multi-objective. Decisions are influenced by a range of considerations beyond merely reducing greenhouse gas emissions or minimizing deviations from existing dies. Economic considerations, such as the cost of food purchases, often play a critical role, and decision outcomes can be seen as an amalgamation of these varied factors. This study, therefore, proposes the development of a multi-objective programming model that explicitly incorporates income group differences. The core premise is that residents from diverse income brackets, constrained by specific limitations and guided by the relative significance of each objective, collaboratively determine the most suitable diet. In this study, we define three primary objectives: minimizing food expenditure, minimizing changes in diets, and reducing greenhouse gas emissions from the food system.

Multi-objective programming involves balancing and prioritizing multiple goals. On one hand, it is crucial to determine a target level for each objective, which represents the decision-makers’ perception of acceptable values for each goal. In this model, the target values for food expenditure, changes in diets, and greenhouse gas emissions are derived from the results of single-objective optimizations that do not consider the other objectives. Consequently, achieving an optimal balance in the multi-objective model necessitates trade-offs, and the outcomes are likely to approach but not fully achieve the values determined by single-objective optimizations (Rardin, 2018). On the other hand, establishing a priority sequence for these objectives is essential. Drawing on Maslow’s hierarchy of needs in psychology, which posits that human behavior is motivated by the fulfilment of hierarchical needs (Maslow, 1943), the prioritization in this model reflects different levels of consumer needs. At the most basic level, economical and sufficient food meets the fundamental physiological needs. Once these are met, the focus shifts to intermediate social needs, such as maintaining established dietary habits, which provide comfort beyond mere survival. At the highest level, minimizing greenhouse gas emissions reflects a need for self-actualization, where individuals express their environmental philosophy through their dietary choices. Thus, the prioritization of objectives in this study is structured as follows: first, minimize food expenditure; second, minimize changes in diets; and third, reduce greenhouse gas emissions from the food system.

Building upon the conceptual framework and pertinent theoretical underpinnings, this research delineates three distinct objective functions within its model:

In Equation 1, C represents the total expenditure on food consumption as defined by this study; q_i denotes the consumption quantity of food i within the sustainable healthy diet, which is also the decision variable; p_i indicates the purchase price of food i.

In Equation 2, ∆D measures the weighted sum of squares of deviations from the current diet to the target diet (changes in dietary structure). The larger the value of this indicator, the greater the deviation from the current diet, indicating a greater dissatisfaction with personal food preference. The weight is the ratio of the food expenditure share to the price elasticity of food demand, reflecting the difficulty for consumers to deviate from their eating habits. w_i represents the share of expenditure for food i in the total food expenditure, φ represents the absolute value of the Marshallian own-price elasticity of demand for food i, which is estimated based on the EASI model based on the estimating procedure from Zhu et al. (2022). x_i denotes the current consumption of food i.

In Equation 3, G denotes the per capita greenhouse gas emissions from the food system, while ζ_i represents the greenhouse gas emissions conversion factor per unit of food i.

The model incorporates constraints predominantly focused on the dietary intake of various nutrients:

In Equation 4, R_j represents the recommended intake of nutrient j, UL_j represents the maximum intake of nutrient j. η_ij indicates the content of nutrient j in food i, r_i represents the edible proportion of food i.

Additionally, the research introduces constraints on the consumption range for food items:

In Equation 5, a_i is the 20% quintile of the current consumption quantity of food i, and b_i is 180% of the current consumption quantity of food i. Considering the potential health hazards of excessive intake of certain foods, the constraints also stipulate that the consumption of alcoholic beverages and oils and fats should not increase. It should be noted that given the complexity of the optimization objectives and constraints, the multi-objective programming might not be able to find the optimal solution; thus, the constraints are set as soft constraints in this study, meaning that the nutritional constraints are met as much as possible. Therefore, the evaluation of the optimization results is conducted through the overall improvement of dietary quality (Vieux et al., 2013).

In refining the multi-objective programming model, this study integrates the methodological approach of Reynolds et al. (2019) to address the dietary preferences of different income groups. By calculating the diets specific to each income bracket and subsequently taking a weighted average based on the sample sizes of these groups, we derive a comprehensive, healthy, and sustainable diet that represents the general populace of Chinese residents.

To evaluate the efficacy of the multi-objective programming model that incorporates income group differences, as applied in this study, it is compared against the outcomes of a traditional single-objective programming model that overlooks such distinctions. To this end, five scenarios have been established (Table 4). Notably, scenario 5 (S5) implements the multi-objective programming model with consideration of income group differences. In contrast, scenario 1 (S1) operates without regard to income group disparities, employing a multi-objective programming model at an aggregate sample level. Additionally, scenario 2 (S2), scenario 3 (S3), and scenario 4 (S4) each utilize a single-objective programming model that acknowledges income group differences but focuses exclusively on distinct optimization objectives: minimizing food expenditure (S2), minimizing changes in diets (S3), and minimizing greenhouse gas emissions from the food system (S4), respectively. It is important to note that all five scenarios adhere to the same set of constraints, which ensure that the diets meet a basic level of balanced nutrient intake. This consistent constraint framework allows for an equitable comparison of the scenarios, highlighting the impact of integrating multiple objectives versus focusing on a single objective.

In this study, the multi-objective programming model, which incorporates variations among income groups, along with the five designed scenarios, has facilitated the derivation of several sustainable healthy diets. It is imperative to conduct a comprehensive evaluation of these diets, focusing on several critical aspects: economical affordability, cultural acceptability, environmental sustainability, and nutritional health statuses. Furthermore, the robustness of these outcomes is rigorously assessed through sensitivity analysis of key parameters. This analysis explores how changes in these parameters might influence the stability and viability of the resulting diets, ensuring that the sustainable healthy dies are both practical and resilient under varying conditions.

The economical affordability is evaluated using the percentage change in food expenditure (changes in dietary costs), ∆C, as expressed in Equation 6:

To assess the cultural acceptability, a weighted sum of squares of deviations from current diets to the target diet (changes in dietary structure), ∆D, is used, as shown in Equation 7. A smaller ∆D value indicates greater alignment with consumers’ dietary habits:

The environmental sustainability is measured by the percentage change in per capita greenhouse gas emissions from the food system (changes in dietary emissions), ∆G, as formulated in Equation 8:

The variables and parameters in Equations 6–8 maintain their meanings consistent with the previous sections.

Furthermore, the nutritional health status is assessed using indicators that reflect dietary quality. Based on the methods of Vieux et al. (2013) and Chalmers and Revoredo-Giha (2019), changes in nutrient intake due to dietary changes can be translated into dietary quality indicators, specifically the Mean Adequacy Ratio (MAR) and the Mean Excess Ratio (MER), to measure overall nutritional quality improvement.

The MAR, used to evaluate nutrient intakes below recommended levels, is defined as:

The MER, for assessing nutrient intakes above recommended levels, is:

In Equations (9, 10), a higher MAR indicates better dietary quality; a lower MER suggests higher dietary quality. N_k denotes the average intake of nutrient k; RDA_k is the recommended intake quantity for nutrient k in the Chinese Dietary Guidelines during the MAR calculation, if N_k changes to N_k^*, exceeding the RDA_k, then N_k^* is set to RDA_k to ensure that high intake of one nutrient cannot compensate for other nutrients, making the MAR more rational. Similarly, for the MER calculation, if N_k changes to N_k^*, falling below the RDA_k, then N_k^* is set to RDA_k to ensure that low intake of one nutrient cannot offset deficiencies in other nutrients, making the MER more rational.

Lastly, the study conducts sensitivity analysis on the primary scenario outcomes by adjusting the greenhouse gas emission coefficient ζ_i and the price elasticity coefficient φ by a magnitude of ±10% to test the robustness of the results.

This section evaluates the alignment of the sustainable healthy diet with the FAO’s foundational principles, including environmental sustainability, nutritional health, economical affordability, and cultural acceptability. According to Equations 6–10, the evaluation results are summarized in Table 5. According to Table 5, the scenario focused on minimizing the deviations from current diet (S2) reported the lowest weighted sum of squared deviations, totaling only 1352.5. The multi-objective programming scenario that considers income group differences (S5) recorded a slight increase in the weighted sum of squared deviations to 1524.9, which remains substantially lower than those observed in the other scenarios. In terms of changes in food expenditure, the scenario aimed at minimizing these costs (S3) determined that the diet could reduce expenses by 30.3%. In contrast, the single-objective programming scenarios (S2 and S4) saw increases of 5.0 and 3.1% in food expenditure. The multi-objective programming scenario (S5), which incorporates income group differences, achieved a modest cost reduction of 1.1%, successfully meeting the essential goal of economical affordability. All scenarios effectively reduced greenhouse gas emissions from the food system, with reductions ranging from 0.1 to 14.1%. The scenario exclusively targeting the minimization of these emissions (S4) demonstrated the most significant reduction. The multi-objective scenario (S5) also showed a notable decrease in emissions by 12.8%, aligning with the 5 to 28% reduction range reported by Song et al. (2017). Regarding improvements in dietary quality under nutritional constraints, the diets across all scenarios significantly enhanced the existing diet, aligning it more closely with nutritional health standards. Initially, the diet’s MAR and MER stood at 78.6 and 56.4, respectively. Post-scenario implementation, MAR values increased to between 84.4 and 88.4, while MER values decreased to between 45.1 and 57.8. Notably, the MAR and MER for the multi-objective scenario (S5) were 84.4 and 46.4, respectively, indicating substantial improvements in dietary quality.

The diets for different income groups, as calculated by the multi-objective programming model, are detailed in Table 6. For the low-income group, minimal changes in diets were required to achieve a sustainable healthy diet. However, this resulted in a 2.0% increase in food expenditure and an 11.1% increase in greenhouse gas emissions. The primary cause is the need to supplement protein and fats through animal products, escalating both costs and emissions. The improvements in MAR confirm effective nutrient enhancement. This suggests the necessity for income subsidies to mitigate the increased food costs when optimizing the diets for the low-income group. Conversely, the middle- and high-income groups experienced only minor changes in diets, yet saw reductions in food expenditure and greenhouse gas emissions ranging from 0.4 to 4.8% and 14.5 to 23.4%, respectively. The MAR and MER indicators also reflected an enhancement in diet quality, highlighting the significant role of dietary improvements in the high-income group in optimizing overall diets.

This section details the robustness check of the diets derived from the multi-objective programming scenario (S5), which incorporates variations by income group, using a sensitivity analysis of key parameters. This analysis involves four distinct outcomes, designated as GHG_coef+, ELA_coef+, GHG_coef−, and ELA_coef−. These outcomes capture the impact of changes in greenhouse gas emission coefficients (ζ_i) and the Marshallian own-price elasticities of food demand (φ). Specifically, these outcomes correspond to a 10% increase in the value of ζ_i (GHG_coef+), a 10% increase in the absolute value of φ(ELA_coef+), a 10% decrease in the value of ζ_i (GHG_coef−), and a 10% decrease in the absolute value of φ(ELA_coef−; Table 7).

The effects of these adjustments on the diets under scenarios S5 and R1 through R4 are compiled in Table 8. Firstly, the weighted sum of squared deviations from current diets across the four robustness checking scenarios ranges between 1047.8 and 2370.9, with the S5 scenario yielding 1524.9, closely aligning with the mean value of 1617.2. This indicates that the S5 scenario reflects a typical outcome within the range of tested conditions. Secondly, the average change in food expenditure across the robustness checking scenarios is marginally positive at 0.10%. This result is influenced by an increase in food consumption expenditure in scenario R3, while the changes observed in the other three scenarios (R1, R2, and R4) are consistent in direction and magnitude with those of the S5 scenario. Thirdly, all robustness checking scenarios demonstrate a reduction in greenhouse gas emissions from the food system, with decreases spanning from 7.5 to 15.4%. The average reduction across the scenarios is 11.70%, closely aligned with the 12.80% reduction observed in the S5 scenario. This consistency underscores the reliability of the model’s performance in terms of environmental sustainability. Lastly, the average values of the MAR and MER indicators across the robustness checking scenarios are 84.9 and 48.7, respectively. These figures exhibit minimal deviation from the values of 84.4 and 46.4 recorded for the S5 scenario, indicating a stable improvement in diet quality across varying conditions. In summary, the results affirm that the diets formulated under the multi-objective programming scenario (S5), which takes into account income group differences, are robust and reliable. This reliability is demonstrated by the consistency of outcomes across a range of sensitivity analyses, reinforcing the dependability of the model in guiding dietary improvements that are both healthy and sustainable.