Optimized Resource Allocation for Sustainable Development in Beijing: Integrating Water, Land, Energy, and Carbon Nexus

Abstract

Chinese megacities face significant challenges in reducing carbon emissions while balancing economic growth and social welfare. This study constructs an innovative multi-objective optimization model, the SD-NSGA-III model, integrated with a System Dynamics (SD) model and using the Non-dominated Sorting Genetic Algorithm III (NSGA-III) to optimize resource allocation in Beijing. The model targets environmental, economic, and social goals by establishing a water–land–energy–carbon (WLEC) nexus for analyzing resource allocation strategies and carbon reduction pathways under various constraints. Scenario simulations under the efficiency-oriented scenario indicated a potential reduction in energy carbon emissions of 81.4% by 2030. The fairness-oriented scenario revealed significant trade-offs between equity and emission reductions, emphasizing the need for balanced strategies. Introducing constraints on resources and economic growth significantly reduced median energy carbon emissions to 80 million tons by 2030. These findings demonstrate the effectiveness of the SD-NSGA-III model in providing actionable strategies for achieving carbon neutrality and sustainable development in cities.

1. Introduction

The sustainable management of resources and the environment is a crucial concern in the development of megacities. In China, cities with an urban population exceeding 10 million are classified as megacities, which often serve as the core of urban agglomerations, engines of economic growth, and centers of innovation, technology, and culture [1]. However, these megacities face numerous challenges due to rapid development and intensive human activities, including resource scarcity, air pollution, supply–demand imbalances, sluggish growth, and widening income gaps. These challenges not only hinder urban development but also exacerbate social instability in China.

In recent years, driven by the dual-carbon strategy, megacities have actively pursued net-zero emissions. However, significant challenges, such as capacity, resource limitations, technology, and funding, hinder the achievement of net-zero emissions. Balancing carbon reduction with economic growth and social stability and replacing traditional resource allocation structures with new, integrated approaches to achieve coupled and coordinated development of the environment, economy, and society have become urgent issues.

As of 2023, the Chinese government has officially designated ten cities as megacities, which account for 20% of the national total in annual carbon emissions. These cities exhibit common characteristics, including high population density, concentrated economic activities, shortages of land and water resources, environmental pollution, and social inequality [2,3,4]. Beijing, as a representative megacity in China, ranks first in urban area and second in urban population among all megacities.

Beijing’s low-carbon transition began in 2012 when it was selected as a second-batch low-carbon pilot city by the National Development and Reform Commission (NDRC). In 2015, the Beijing Municipal Government released the “Implementation Plan for Promoting Energy Conservation, Low-Carbon, and Circular Economy Standardization Work in Beijing (2015–2022)”, proposing strategic measures to enhance resource utilization efficiency, environmental quality, and people’s well-being. Despite being ranked first in national low-carbon city pilot evaluations, Beijing’s low-carbon development lags behind other international megacities, such as New York, London, Paris, and Tokyo, with more stringent emission reduction tasks [5]. Key obstacles include shortages of water and land resources and resistance to green energy transformation [6,7].

As a model for the low-carbon transition of other Chinese megacities, effective assessment and in-depth analysis of Beijing’s resource allocation status and suitable carbon reduction paths are critical. Identifying suitable carbon reduction paths from the perspectives of resources, environment, economy, livelihood, and technology is a systematic task. Therefore, this paper utilizes the System Dynamics (SD) method to construct a water–land–energy–carbon relationship network for Beijing, simulating and analyzing the internal structure and interactions of the resource system. Based on a multi-objective optimization model, this paper analyzes Beijing’s carbon reduction from environmental, economic, and social perspectives. Balancing multiple objectives, we propose a “three-in-one” resource allocation scheme (Figure 1) suitable for Beijing’s sustainable development. This framework can provide insights for other megacities as well.

The remainder of this paper is organized as follows. Section 2 reviews the literature on resource management and sustainable development in megacities. Section 3 proposes a coupled multi-objective optimization model (SD-NSGA-III) and examines the resource allocation plan for Beijing. Section 4 reports the results and provides an in-depth discussion and analysis. Section 5 concludes this study and suggests directions for future research.

2. Literature Review

2.1. Research on Resource Management in Megacities

Megacities, as primary hubs of human and economic activities, face significant challenges in resource demand and management. The rapid industrialization of megacities has led to high consumption of essential urban development resources, such as water, land, and energy, resulting in increased environmental pressures and ecosystem degradation [8]. The academic community has conducted various studies on managing water, land, and energy resources in urban development.

The research indicates that megacities face several issues in water resource management, including supply–demand imbalances, water pollution, overexploitation, declining groundwater levels, and wetland desiccation [9,10,11]. Regarding land, the limited total available land restricts urban development, making low land use efficiency and disorderly urban expansion critical challenges [12,13]. In the energy sector, the high carbon emissions from traditional energy consumption in industrial, transportation, and building sectors expose megacities to severe environmental degradation and climate change risks. Therefore, energy management primarily focuses on energy use efficiency and renewable energy [14,15].

To address these challenges, scholars have proposed various solutions. These include water recycling, establishing reclaimed water systems and promoting water-saving technologies to alleviate water resource pressures [16,17]; advocating for compact urban development models and intensive land use to improve land use efficiency [18]; and addressing energy shortages and high carbon emissions by promoting energy structure adjustments and enhancing energy efficiency technologies [19]. However, these studies often treat different categories of resources as isolated components, neglecting the interconnections and interaction mechanisms between them. To address this issue, some scholars have proposed considering fundamental resources, such as water, land, and energy, as an integrated system and constructing a water–land–energy–carbon comprehensive management framework to more effectively mitigate urban environmental pressures and promote sustainable development [20,21].

Currently, there are some studies on the integrated management of resources in megacities, but these studies primarily employ static analysis methods [22,23], lacking in-depth consideration of the dynamic changes in urban resources. Since cities are ever-evolving complex systems with resource demand and supply changing over time due to technological advancements and policy shifts, it is essential to develop resource management strategies that not only meet current needs but also adapt to future changes, ensuring long-term sustainability in resource utilization [24,25].

2.2. Application of System Dynamics in Megacity Resource Management

System dynamics, as a method for studying the behavior of complex systems, uses mathematical models to simulate the interactions and dynamic changes among various factors within a system. It has been widely applied in the fields of environmental management and policy analysis. Sterman (2000) suggested that system dynamics models can capture the nonlinear characteristics of complex systems, providing decision-makers with tools for scenario analysis and strategy evaluation [26].

In the study of megacity resource management, system dynamics models can simulate the intricate relationships between resource consumption, environmental impact, and policy interventions, analyzing the interactions among various elements within the urban complex system [27]. Existing literature indicates that system dynamics can help understand the long-term effects of resource flows and management policies. For example, urban dynamics models are classic cases of early use of system dynamics to analyze urban issues, revealing the dynamic relationships among urban population, housing, and employment factors [28]. In recent years, system dynamics models have been widely applied to study urban sustainability, especially the sustainability of urban resources (water, land, energy) and waste management [29]. For instance, Luo et al. (2020) used a system dynamics model to analyze and predict the supply and demand of water resources in Beijing, proposing sustainable policy recommendations for the city’s water resources. Yao et al. used a system dynamics model to simulate land use changes in Hangzhou, proposing strategies to optimize land use and build an environment under a shared socioeconomic pathway. Freeman studied the socio-political feasibility of the UK’s energy structure transition through a system dynamics model [30,31,32].

Despite the significant progress made in applying system dynamics to urban resource management research, there are still some limitations in the existing studies. First, many studies simplify the description of complex relationships within the system when constructing models, overlooking the dynamic changes in certain key factors, which may lead to biased predictions. Second, existing models also face challenges in data acquisition and parameter calibration. Particularly when it comes to long-term predictions and policy evaluations, data uncertainty can have a substantial impact on model outcomes [33].

2.3. Application of Muti-Objective Model in Megacity Resource Management

In recent years, multi-objective optimization models have been widely applied in resource management research. These models provide systematic solutions by simultaneously considering multiple objectives, such as economic benefits, environmental impacts, and social welfare. For instance, Feng et al. (2023) utilized the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to optimize the management of water, land, energy, and CO₂ in Shenzhen and Sichuan, respectively, promoting regional agricultural sustainability [21]. However, most current studies focus on agricultural development and food security, with relatively few addressing comprehensive resource management for urban sustainability. Urban resource management research typically concentrates on single resource types, neglecting the interrelationships between different resources. This limitation hinders the scientific robustness and generalizability of the findings. Additionally, many studies rely heavily on idealized assumptions in model construction, overlooking the complexities and uncertainties in practical applications.

Recently, the improved Non-dominated Sorting Genetic Algorithm III (NSGA-III) has been widely adopted for multi-objective comprehensive management. Research indicates that the NSGA-III model excels in handling high-dimensional optimization problems by introducing the concept of reference points, allowing for more effective exploration and utilization of the solution space, resulting in more diverse optimization solutions [34]. Compared to NSGA-II, NSGA-III performs better in dealing with complexity and uncertainty, making it more adaptable to variable conditions in practical applications. Furthermore, the NSGA-III model can simultaneously consider multiple conflicting objectives, providing comprehensive resource optimization solutions and addressing the lack of integrative considerations in existing research.

In summary, the resource allocation pathways for achieving net-zero emissions in megacities are currently a focal point of academic and political attention. Although the academic community has extensively discussed carbon reduction in megacities, there is a lack of research on the comprehensive management of essential resources, such as water, land, and energy, under multiple objectives (environmental, economic, and social) to achieve carbon neutrality. Therefore, this study proposes an integrated resource management optimization model for megacities under China’s dual-carbon strategy, combining the SD and NSGA-III models, named the SD-NSGA-III model. This study has significant theoretical and practical implications for exploring sustainable carbon-reduction pathways in megacities.

3. Materials and Methods

3.1. Model Preparation

The goal of this study is to develop a systematic optimization model for the WLEC (water, land, energy, carbon) nexus in megacities to explore resource allocation pathways for achieving net-zero emissions and, ultimately, sustainable development. Therefore, this paper first identifies the sources of carbon emissions related to water, land, and energy in the development of megacities. To avoid double counting, carbon emission sources are categorized according to the GHG Protocol standards (https://ghgprotocol.org/standards-guidance, accessed on 15 January 2024) into direct emissions, indirect emissions, and other indirect emissions. By referencing the IPCC inventory and reviewing relevant literature, 28 carbon sources were identified, including 5 direct emission factors, 1 indirect emission factor, 14 other indirect emission factors, and 8 carbon sequestration factors. Secondly, the data on water resources, land resources, and energy carbon emissions in this study were sourced from the “Beijing Statistical Yearbook” (https://nj.tjj.beijing.gov.cn/), the “China Water Resources Bulletin” (http://szy.mwr.gov.cn/gbsj/index.html), the “China Energy Statistical Yearbook” (https://www.stats.gov.cn), and the National Bureau of Statistics (https://data.stats.gov.cn/index.htm).

Table 1. Calculation formula for carbon emissions and sequestration.

Sources of Carbon Emissions and Sequestration	Calculation Formula	NO	Sectors
Direct Sources of Carbon Emissions
Coal (Industrial Usage)	${E_{{CO}_2}^{coa}=\mu }^{coa}·q^{coa}$	(1)	E
Natural Gas (Heating and Cooking)	${E_{{CO}_2}^{nga}=\mu }^{nga}·q^{nga}$	(2)	E
Transportation (Public and Private Vehicles)	${E_{{CO}_2}^{tra}=\mu }^{tra}·q^{tra}$	(3)	L
Residential and Commercial Buildings (Heating Systems)	${E_{{CO}_2}^{rcb}=\mu }^{rcb}·q^{rcb}$	(4)	W, E
Waste Treatment and Landfill	${E_{{CO}_2}^{wtl}=\mu }^{wtl}·q^{wtl}$	(5)	E
Indirect Carbon Emissions
Electricity (Urban Grid)	${E_{{CO}_2}^{ele}=\mu }^{ele}·q^{ele}$	(6)	W, E
Other Indirect Carbon Emissions
Domestic Sewage (City Water Supply System)	${E_{{CO}_2}^{dse}=\mu }^{dse}·q^{dse}$	(7)	W
Production Wastewater	${E_{{CO}_2}^{pww}=\mu }^{pww}·q^{pww}$	(8)	W
Agricultural Irrigation (Surrounding Agricultural Activities)	${E_{{CO}_2}^{agi}=\mu }^{agi}·q^{agi}$	(9)	W, E
Agricultural Cultivation	${E_{{CO}_2}^{agc}=\mu }^{agc}·q^{agc}$	(10)	W, E
Agricultural Films	${E_{{CO}_2}^{agf}=\mu }^{agf}·q^{agf}$	(11)	L
Fertilizers	${E_{{CO}_2}^{fer}=\mu }^{fer}·q^{fer}$	(12)	E
Pesticides	${E_{{CO}_2}^{pes}=\mu }^{pes}·q^{pes}$	(13)	E
Petroleum (Transportation and Industrial Usage)	${E_{{CO}_2}^{pet}=\mu }^{pet}·q^{pet}$	(14)	E
Energy Consumption in Commercial Buildings	${E_{{CO}_2}^{ecb}=\mu }^{ecb}·q^{ecb}$	(15)	E
Urban Green Space and Park Management	${E_{{CO}_2}^{gsp}=\mu }^{gsp}·q^{gsp}$	(16)	W, L, E
Urban Lighting	${E_{{CO}_2}^{url}=\mu }^{url}·q^{url}$	(17)	E
Construction Activities	${E_{{CO}_2}^{cac}=\mu }^{cac}·q^{cac}$	(18)	L, E
Food Processing and Transportation	${E_{{CO}_2}^{fpt}=\mu }^{fpt}·q^{fpt}$	(19)	W, E
Water Resource Management	${E_{{CO}_2}^{wrm}=\mu }^{wrm}·q^{wrm}$	(20)	E
Sources of Carbon Sequestration
Grain Crops	${S_{{CO}_2}^{gcr}=\mu }^{gcr}·b^{gcr}$	(21)	W, L
Cash Crop	${S_{{CO}_2}^{ccr}=\mu }^{ccr}·b^{ccr}$	(22)	W, L
Other Crops	${S_{{CO}_2}^{ocr}=\mu }^{ocr}·b^{ocr}$	(23)	W, L
Surface and Water Facilities	${S_{{CO}_2}^{swf}=\mu }^{swf}·b^{swf}$	(24)	W, L, E
Woodland	${S_{{CO}_2}^{wol}=\mu }^{wol}·b^{wol}$	(25)	W, L
Grasslands	${S_{{CO}_2}^{gra}=\mu }^{gra}·b^{gra}$	(26)	W, L
Garden Area	${S_{{CO}_2}^{gar}=\mu }^{gar}·b^{gar}$	(27)	W, L
Unutilized Land	${S_{{CO}_2}^{unl}=\mu }^{unl}·b^{unl}$	(28)	L

provides information on the variables related to carbon emissions, their calculation formulas, and the involved sectors. Explanations of the variables and parameters involved in the formulas are detailed in

Table 2. Scenario parameter setting and principles.

Scenario	Fairness-Oriented	Efficiency-Oriented	Balanced
Lambda (λ)	0.2	0.8	0.5
Gini Coefficient	0.2	0.5	0.3
Selection Principle	Prioritize equity in resource allocation and carbon emission reduction	Maximize economic efficiency of resource use	Balance social equity and economic efficiency

.

3.2. Building the Water–Land–Energy–Carbon Nexus Using the SD Model

This subsection employs the SD model to construct the WLEC nexus of Beijing, laying the groundwork for the model coupling and optimization in the next subsection.

The SD model provides a framework to simulate the internal structure and dynamic behavior of complex systems, capturing interactions and feedback loops among system elements and their evolution [35,36]. Therefore, this study treats water, land, energy, and carbon as an integrated resource system consisting of four subsystems: the water resource system, the land resource system, the energy system, and the carbon system (Figure 1). There are dependencies and feedback loops within and between these subsystems, and the SD model helps identify the system’s internal equilibrium mechanisms (Figure 2).

First, state variables, flow variables, auxiliary variables, and parameters of each subsystem were defined based on real-world scenarios. The functional relationships and parameter values between variables were determined using historical data and relevant literature. Subsequently, the model simulated Beijing’s population and economic growth, resource consumption, land use dynamics, and carbon budget from 2006 to 2021, with a time step of one year. The historical data from 2006 to 2020 were used as a test set for model testing and simulation, while the data from 2020 to 2021 served as a validation set to verify the model’s accuracy and effectiveness. The results showed that the relative errors of the seven random variables were all below 0.5%, indicating good simulation results and high model accuracy.

3.3. Finding Optimal Resource Allocation Using the NSGA-III Model

Building on the network constructed in Section 3.2, this section couples the NSGA-III model with the SD model to solve for optimal strategies in comprehensive resource management. The NSGA-III is an effective optimization algorithm suitable for addressing complex problems with multiple conflicting objectives [37,38]. However, NSGA-III cannot simulate the dynamic behavior of systems. By coupling it with the SD model, the dynamic characteristics and time dependencies of the system can be incorporated into the decision-making process.

3.3.1. Objective Function

The core objective of this study is to establish a comprehensive management plan for Beijing’s water, land, and energy resources within the ‘three in one’ framework in environmental, economic, and social. Therefore, the objective functions are set from three dimensions: ecological environment, resource efficiency, and socio-economic development.

(1)

Ecological Environment Dimension

Objective Function 1: Minimization of Net Carbon Dioxide Emissions

We employ net carbon dioxide emissions as a crucial indicator to evaluate the city’s ecological environment. Minimizing net carbon dioxide emissions from urban economic activities is a crucial goal of this paper and can be represented by Formula (1):

$$Min{obj}_1=Min{\displaystyle \frac{TCE}{{\sum }_{i=1}^I{Y}_i}}$$

(29)

$$TCE={CE}_{dce}+{CE}_{ice}+{CE}_{oice}-{CS}_{cs}$$

(30)

$${CE}_{dce}=\left(1\right)+\left(2\right)+\left(3\right)+\left(4\right)+\left(5\right)$$

(31)

$${CE}_{ice}=\left(6\right)$$

(32)

$${CE}_{oice}=\left(7\right)+\left(8\right)+\left(9\right)+\cdots \left(19\right)+\left(20\right)$$

(33)

$${CS}_{cs}=\left(21\right)+\left(22\right)+\left(23\right)+\left(24\right)+\left(25\right)+\left(26\right)+\left(27\right)+\left(28\right)$$

(34)

(2)

Resource Efficiency Dimension

Objective Function 2: Maximization of Resource Economic Efficiency

In this part, the unit value of a resource is determined by the value of the carbon dioxide emissions produced per unit of resource consumption in the carbon market. The resources covered in this part include water and energy, while the primary role of land is carbon sequestration and is, thus, not included in the equation.

$$Min{obj}_2=Max\left(CEW+CEE\right)·vc$$

(35)

(3)

Socio-Economic Dimension

Objective Function 3: Maximization of Social Welfare from Carbon Emissions

The social welfare function is represented by the product of the power functions of carbon emissions economic efficiency and the equitable distribution of carbon emissions [39]. The equilibrium parameter lambda measures the balanced allocation of carbon emissions within the study area; when lambda equals 0, it signifies a sole focus on the economic efficiency of carbon emissions, whereas when lambda equals 1, it indicates a focus solely on the equality of carbon emissions [40,41]. The economic efficiency function is defined as the actual economic benefit generated by carbon emissions from all sectors divided by the potential maximum benefit. The equitable distribution function measures the extent to which the economic benefit per unit of carbon emission is fairly distributed across society, represented by the Gini coefficient of carbon emission benefit distribution. A higher Gini coefficient indicates a deviation from fairness, with a Gini coefficient of 1 signifying absolute inequality. The objective of carbon emissions is to maximize social welfare, which can be specifically represented by Formula (8):

$$Max{obj}_3=Max{\left({EE}_{car}\right)}^{\lambda }{\left(1-{Gini}_{car}\right)}^{1-\lambda }$$

(36)

$${EE}_{car}={\displaystyle \frac{\sum _{i=1}^I\sum _{m=1}^M{EB}_{im}}{Max\sum _{i=1}^I\sum _{m=1}^M{EB}_{im}}}$$

(37)

$${EB}_i={\sum }_{m=1}^M{EB}_{im}={\sum }_{m=1}^M{AEB}_{im}\cdot e_{im}$$

(38)

$${Gini}_{car}={\displaystyle \frac{1}{2I{\sum }_{i=1}^I\frac{Q_i}{{EB}_i}}}{\sum }_{i,j=1}^I\left|{\displaystyle \frac{Q_i}{{EB}_i}}-{\displaystyle \frac{Q_j}{{EB}_j}}\right|$$

(39)

3.3.2. Constraints

(1)

Energy Constraint

The energy constraint is expressed as a limitation on total energy consumption. According to the Comprehensive Work Plan for Energy Conservation and Emission Reduction during the 14th Five-Year Plan, the focus is on reducing energy consumption and improving efficiency. To achieve this, annual energy consumption is capped at baseline levels. Stricter energy limits will gradually tighten year by year, with further details on these progressive constraints provided in the next chapter. The energy constraint is as follows:

$${EC}_t\le {EC}_0$$

(40)

$${EC}_t\ge {EC}_{t+1}$$

(41)

(2)

Water Resource Constraint

Given Beijing’s water scarcity, limit annual usage to no more than the population size multiplied by the baseline per capita water consumption. The water resource constraint can be expressed as follows:

$${WC}_{t+1}\le {pop}_{t+1}·{AWC}_0$$

(42)

(3)

Farmland Protection Policy Constraint

According to the Beijing Government Work Report and related policy documents, a minimum arable land (farmland redline) has been established, and usually, the specified minimum area of farmland is stable. The farmland protection policy constraint can be expressed as follows:

$$S_t^{min}\le S_t\le S_t^{max}$$

(43)

(4)

Economic Growth Constraint

For megacities, especially those like Beijing with a special political status, economic growth is as important as environmental protection. Aligned with the Chinese government’s policy of pursuing steady economic progress, Beijing’s economy is expected to maintain positive growth; meanwhile, it will not exceed the highest level recorded over the past decade. The economic growth constraint can be expressed as follows:

$$0\le {GDP}_t\le {GDP}_{max}$$

(44)

4. Results and Discussion

4.1. Time Trends and Analysis of Resource-Related Carbon Emissions in Beijing

Based on the historical data, the SD model was used to simulate and predict the carbon emission trends of Beijing’s water, land, and energy systems as well as the net carbon absorption by land from 2006 to 2030. This analysis reveals the characteristics of carbon emission changes in different resource sectors of Beijing as it strives to achieve carbon neutrality along with the underlying driving factors (Figure 3).

Figure 3a shows the changes in carbon emissions from Beijing’s water resources. From 2006 to 2016, water resource carbon emissions rapidly increased, peaking in 2016, and then significantly decreased. This trend reflects Beijing’s success in reducing water consumption’s carbon emissions through the promotion of efficient water use technologies and policy regulation. This result indicates the effectiveness of policies in reducing carbon emissions in water resource management.

According to Figure 3b, carbon emissions from energy consumption increased annually from 2006 to 2020, peaking in 2020, before beginning to decline. This trend is closely related to adjustments in Beijing’s energy structure. As Beijing gradually reduced its reliance on fossil fuels and increased the use of renewable and clean energy, carbon emissions from energy consumption began to decrease. This change underscores the critical role of optimizing the energy structure in achieving carbon neutrality.

Figure 3c,d show the trends in land carbon emissions and land carbon sinks, respectively. Land carbon emissions have continuously increased since 2006, with a significant rise after 2019. This trend indicates a notable increase in land-related carbon emissions due to urban expansion and changes in land use. However, land carbon sinks declined before 2019 but gradually recovered and slightly increased afterward, possibly due to Beijing’s ecological restoration measures, such as greening and afforestation. These measures have effectively enhanced the land’s carbon sequestration capacity, although further efforts are needed to offset the growing land carbon emissions.

Figure 3e shows the changes in net carbon absorption. Net carbon absorption remained high before 2012, significantly declined between 2012 and 2020, and then gradually recovered. This trend may be related to the reduction in green spaces and the degradation of ecosystem services due to urbanization, while the subsequent recovery reflects the effectiveness of ecological restoration projects. This indicates that, although urban expansion negatively impacts net carbon absorption, effective ecological restoration measures can partially compensate for this loss.

Figure 3f summarizes the overall carbon emission trends in Beijing. Overall, total carbon emissions continuously increased from 2006 to 2020, peaking in 2020, before slightly declining. This trend aligns with the changes in carbon emissions across the various resource sectors discussed earlier, indicating that, despite the dual pressures of resource use and economic growth, Beijing has gradually stabilized and reduced carbon emissions through comprehensive management measures and policy regulation.

The carbon emission trends in Beijing’s various resource sectors during the pursuit of carbon neutrality reflect the effectiveness of different resource management policies and measures. Future efforts need to continue strengthening comprehensive management, promoting the efficient use and coordinated development of water, land, and energy resources to achieve sustainable development goals.

4.2. Scenario Simulation of Resource Allocation Scheme

Three different scenarios are defined to explore and understand the performance of carbon emission reduction strategies under different balances of fairness and efficiency [42]. Scenario 1 is fairness-oriented, with both λ and the Gini coefficient set to 0.2, indicating a priority for fairness over efficiency and a pursuit of highly equitable carbon emission distribution; Scenario 2 is efficiency-oriented, with λ set to 0.8 and the Gini coefficient at 0.5, indicating a consideration for economic efficiency and a tolerance for a certain level of inequality; Scenario 3 is a balanced scenario, with λ at 0.5 and the Gini coefficient at 0.3, balancing fairness and economic efficiency [43].

Scenario Simulation of Resource Allocation Without Constraints

Using the NSGA-III model, the Pareto front solution sets were calculated in this subsection under different scenarios to explore optimal resource allocation strategies for Beijing’s water, land, and energy resources under the carbon neutrality target. Finally, we conducted a detailed analysis of water resource carbon emissions, energy carbon emissions, and net land absorption for each scenario (Figure 4 and Figure 5).

In the fairness-oriented scenario (Scenario 1), the Pareto optimal solutions indicate significant trade-offs between minimizing net CO₂ emissions and maximizing resource economic efficiency to achieve higher equity. Specifically, the median water resource carbon emissions decrease markedly from approximately 8.40 tons of CO₂ in 2022 to approximately 3.85 tons in 2030, indicating that water resource carbon emissions must be substantially reduced under fairness-oriented strategies. However, while energy carbon emissions show a slight decrease, their overall variability remains high, reflecting greater uncertainty in energy carbon emissions in this scenario. Additionally, net land carbon absorption fluctuates from approximately 17.87 million tons of CO₂ in 2022 to approximately 14.83 million tons in 2030, highlighting volatility in land carbon sinks in this scenario.

In the efficiency-oriented scenario (Scenario 2), the Pareto optimal solutions suggest that, as resource economic efficiency increases, equity decreases, potentially leading to higher net CO₂ emissions. This implies that pursuing economic efficiency may inevitably result in some degree of carbon emissions and social welfare distribution inequity. In this scenario, the median water resource carbon emissions increase steadily from approximately 9.07 tons of CO₂ in 2022 to approximately 10.94 tons in 2025, indicating stable water resource carbon emissions while pursuing economic efficiency. The median net land carbon absorption remains relatively stable at approximately 20 million tons of CO₂. However, energy carbon emissions rise slowly from approximately 417.58 million tons of CO₂ in 2022 to approximately 499.39 million tons in 2030, suggesting that achieving carbon neutrality under an economic efficiency-first strategy is nearly impossible.

In the balanced scenario (Scenario 3), the Pareto optimal solutions demonstrate a good balance between social welfare, carbon emissions, and economic efficiency. In this scenario, the median water resource carbon emissions decrease from approximately 10.45 tons of CO₂ in 2022 to approximately 8.80 tons in 2030, showing effective emission reductions achieved through balancing fairness and efficiency. The median and variability of energy carbon emissions fall between the first two scenarios, fluctuating slightly from approximately 468 million tons of CO₂ in 2022 to approximately 481.09 million tons in 2030, indicating that emission control strategies aim for stable emissions in the balanced scenario. The median net land carbon absorption increases from approximately 19.87 million tons of CO₂ in 2022 to approximately 21.78 million tons in 2030, reflecting continuous improvements in land use.

In summary, the fairness-oriented scenario achieves social equity but faces greater resource use uncertainty and carbon emission pressure. The efficiency-oriented scenario improves resource utilization efficiency but may lead to higher carbon emissions and social welfare distribution inequity. The balanced scenario achieves better coordination and compromise among the various goals.

4.3. Scenario Simulation of Resource Allocation with Constraints

Building on the previous section, this subsection adds constraints on energy availability, water resource availability, arable land redlines, and economic growth to the model. By constructing scenarios that reflect real-world conditions, this section analyzes the optimal resource allocation strategies for Beijing under the carbon neutrality target and assesses their impact on urban sustainable development (Figure 6 and Figure 7).

When constraints were added to the fairness-oriented scenario (Scenario 1), the Pareto front became more compact, particularly between minimizing net CO₂ emissions and maximizing resource economic efficiency. This indicates that the range of feasible solutions narrowed with the addition of constraints. Although the maximum value for social welfare did not significantly decrease, the median energy carbon emissions dropped sharply from 414.73 million tons in 2022 to 97 million tons in 2030, demonstrating the significant impact of reducing limits. Net land carbon absorption remained stable, slightly increasing to 21.45 million tons by 2030, highlighting the critical role of land management in supporting sustained carbon absorption.

In the efficiency-oriented scenario (Scenario 2), the Pareto front became denser, suggesting that, to meet the constraints, the solutions were concentrated within a smaller range, potentially reducing diversity. Water resource carbon emissions showed significant fluctuations, reflecting the uncertainty introduced by policies balancing economic efficiency and constraint compliance. The median energy carbon emissions decreased from 445.84 million tons in 2022 to 83.22 million tons in 2030, illustrating the complex trade-offs between emission reduction and economic growth. Net land carbon absorption increased from 17.93 million tons in 2022 to 19.60 million tons in 2030, indicating adjustments in land management to address the challenges of energy emission reduction under efficiency-oriented policies.

In the balanced scenario (Scenario 3), the Pareto front maintained a good balance among the three objectives. The median water resource carbon emissions decreased from 103,700 tons in 2022 to 97,100 tons in 2030, while energy carbon emissions dropped from 445.09 million tons to 75.69 million tons, demonstrating steady emission reductions while achieving a balance between fairness and efficiency. Net land carbon absorption showed slight fluctuations, indicating continuous improvements in land use under carbon neutrality strategies.

The introduction of constraints had a significant impact on the decision variables, particularly the downward trend in energy carbon emissions, which aligned with the new constraint requirements. The stability of water resource carbon emissions was affected in the efficiency scenario. The stability of net land carbon absorption indicates that land use remains a crucial mechanism for maintaining carbon balance. Notably, although Beijing achieved its carbon peak target in 2020, accomplishing the 2060 carbon neutrality goal remains challenging under the current resource carbon emission structure and trends. Therefore, Beijing’s current resource allocation strategies need further optimization to achieve carbon neutrality and sustainable development goals.

In this section, the constraints on energy availability, water resources, land use, and economic growth were analyzed. These constraints are based on specific assumptions that significantly impact the model outcomes. The energy constraint assumes a reduction in fossil fuel use, transitioning towards renewable energy sources. The water resource constraint is based on the assumption that water availability will decrease, necessitating limits on water use to prevent overexploitation. The land use policy constraint aims to ensure that urban expansion does not compromise agricultural productivity or ecological sustainability. The economic growth constraint integrates environmental considerations into economic development, balancing economic outputs with resource inputs. Our findings underscore the importance of balancing equity and efficiency in resource management under carbon neutrality goals, aligning with the conclusions of Zhou and Feng [7,21]. Furthermore, similar to the results of Kong (2023) and Yue [14,39], our study demonstrates that, while efficiency-oriented scenarios highlight economic advantages, focusing solely on economic efficiency may lead to environmental degradation and social inequality. Conversely, prioritizing equity can help mitigate social disparities but may come at the cost of reduced economic output. Collectively, both objective functions and real constraints shape the feasible solution space of the SD-NSGA-III model, ensuring that simulated scenarios are both theoretically sound and practically viable. They highlight the trade-offs between different policy objectives and provide a comprehensive understanding of the pathways to achieve carbon neutrality and sustainable urban development.

While these constraints enhance the realism of the model, there are limitations. The simplifications inherent in the assumptions may not fully capture the complexity of real-world scenarios, potentially affecting the accuracy of the model’s predictions. Additionally, the availability and quality of data limit the precision of model parameters. Future research should focus on optimizing these parameters to improve the model’s applicability to diverse urban contexts. Moreover, exploring the impact of new technologies and policies on resource allocation and carbon reduction can enhance the model’s predictive capacity and policy relevance. By continuously refining the model and expanding its scope, more robust support for sustainable urban development and more precise decision-making tools can be provided for policymakers.

4.4. Policy Implications and Recommendations

Our study underscores the need for integrated resource management to achieve sustainable urban development. Policymakers should adopt a holistic approach recognizing the interdependencies among water, land, energy, and carbon (WLEC) resources. Developing policies that integrate water conservation with energy-efficient technologies can significantly reduce consumption and lower emissions. Investing in advanced water recycling technologies and incentivizing their adoption in industrial and domestic sectors can establish a robust reclaimed water system, reducing freshwater demand and water-related emissions.

Efficient land use and urban planning are crucial for maximizing land use and enhancing sustainability. Urban planners should prioritize high-density, mixed-use developments to prevent urban sprawl, and policies supporting green spaces and urban forests can enhance carbon sequestration and air quality. Accelerating the transition to renewable energy sources, such as solar and wind, is vital for reducing energy-related emissions. Subsidies, tax incentives, and regulatory support can promote renewable energy adoption.

Stringent emission reduction standards across all sectors are necessary for achieving carbon neutrality. Regular monitoring and penalties for non-compliance will ensure adherence to these standards. Promoting technological innovation in green technologies should be prioritized, with government support for research in energy efficiency, carbon capture, and sustainable agriculture. Raising public awareness through educational campaigns and community engagement is critical as is fostering collaboration between government, industry, academia, and civil society. These steps will help Beijing enhance its WLEC management and achieve sustainable development goals, setting a benchmark for other cities.

5. Conclusions and Outlook

This study developed a multi-objective optimization model for resource allocation in megacities, named the SD-NSGA-III model, and conducted an in-depth exploration of Beijing’s resource optimization under the carbon neutrality target. The results indicate that the SD-NSGA-III model can effectively optimize resource allocation while minimizing carbon emissions, maximizing resource economic efficiency, and maximizing social welfare, thereby defining the optimal allocation range.

The findings reveal that, without constraints on reducing energy carbon emissions, Beijing’s energy carbon emissions are projected to be approximately 400 million tons by 2030. However, with the introduction of annual reduction limits, the median energy carbon emissions significantly decrease to 80 million tons, demonstrating the substantial impact of these constraints. This highlights the necessity and urgency of implementing carbon emission reduction standards for energy consumption.

Through scenario simulations of efficiency-oriented, fairness-oriented, and balanced development paths, this study further explores how to effectively balance social welfare and economic efficiency while pursuing the carbon neutrality goal, providing specific recommendations for different scenarios. Particularly, in the analysis of the fairness-oriented and efficiency-oriented scenarios, this study emphasizes the importance of carefully considering the responsibilities and benefits distribution in carbon reduction strategies. Additionally, it points out that accelerating the transformation of the energy consumption structure is crucial for achieving more stringent carbon reduction targets.

The innovations of this study are as follows. First, it develops an integrated “three-in-one” framework for the allocation of water, land, energy, and carbon resources, capturing the complex interactions among these resources. Second, rather than limiting the analysis to a single urban development model, this study provides three alternative resource allocation pathways, enhancing its applicability to other cities. Third, it offers an in-depth exploration of the trade-offs between equity and efficiency in integrated resource management, a topic that has not been sufficiently addressed in previous studies.

This study has certain limitations. Firstly, the model parameters and scenario settings are based on current data and may not fully reflect the complexities of future changes. Secondly, the model’s generality and applicability need further validation in other cities. Future research should adjust and optimize model parameters for specific urban contexts to enhance its universality and practicality. Furthermore, it should explore the potential impacts of new technologies and policies on resource allocation and carbon reduction to improve the model’s predictive capacity and policy guidance value.

In summary, this study provides strong support for the optimal allocation of urban resources under the carbon neutrality goal and emphasizes the importance of integrated management strategies in promoting sustainable development. Future work should continue to refine the model, expand its application scope, and continuously explore new management strategies to advance urban sustainable development.