1. Introduction
Water resources, energy, and food, as the most important material resources to satisfy the essential needs of humans, play a crucial role in economic and social development [
1]. However, with the population growth, rapid economic development, and climate change around the world, these put great pressures on the supply of water resources, energy, and food, which have gradually formed a highly sensitive and fragile relationship [
2,
3]. The relevant research studies have shown that the demands of global water, energy, and food are predicted to grow by 40%, 50%, and 35% by 2030, respectively, while the supply of water, energy, and food will face severe challenges owing to serious ecological environmental changes [
4]. The imbalance between supply and demand of water, energy, and food has become an urgent problem to be solved. In January 2011, the Global Risk Report proposed that the “water resource–energy–food risk group” was one of the three key risk groups for the first time, emphasizing that the relationship of water resource–energy–food was very significant to the sustainable development of the regional economy and society, and only considering the optimization of a single resource would lead to unpredictable serious consequences [
5]. In November of the same year, the Bonn conference firstly summarized the relationship among water, energy, and food as a nexus, and it actively explored how to balance the synergies among water, energy, and food from the perspective of the water–energy–food nexus [
6].
At present, most scholars only study the nexus between two of the resources, such as the water–energy nexus [
7,
8,
9,
10,
11,
12,
13,
14], water–food nexus [
15,
16,
17,
18,
19], and energy–food nexus [
20,
21,
22,
23,
24,
25]. According to the relevant literature, it can be concluded that for the water–energy nexus, refining, processing, and cooling of energy consume the water resources. Especially, with the rapid increase of electricity demand, the cooling water of thermal power generation also increases quickly. As for the water–energy nexus, the agriculture department is the largest water consumption department in the world, accounting for 70% of the total water consumption [
26]. In terms of the energy–food nexus, energy plays an important role in the process of packaging, distribution, storage, etc., of the agricultural department.
At present, research on the water–energy–food nexus are increasing year by year, mainly focusing on the definition and challenge of the water–energy–food nexus. For example, De Amorim et al. [
27] defined the water–energy–food nexus and analyzed the impact of global risks on the water–energy–food nexus. Heard et al. [
28] summarized and analyzed the water–energy–food nexus in the urban system, and they thought that it was very important to analyze the water–energy–food nexus by establishing the comprehensive index system and model. Kurian [
29] provided a framework to study the water–energy–food nexus and emphasized the importance of an interdisciplinary approach in the research of the water–energy–food nexus. Endo et al. [
30] reviewed the water–energy–food nexus and studied the challenges and prospects of the water–energy–food nexus. Pahl-wostl [
31] defined water–energy–food security from the perspective of the water–energy–food nexus. Chi et al. [
32] believed that although progress had been made, there were still limitations in the research of the water–energy–food nexus that faced four challenges in the future, including the definition of a system boundary, the uncertainty related to modeling, the analysis limitation of the internal mechanism of the nexus, and the evaluation of system performance. Zhi et al. [
33] built a “water–energy–food” symbiotic system framework based on the symbiosis theory and put forward the regional system adaptation concept of “water–energy–food” from the perspectives of stability, coordination, and sustainability. In addition, some scholars adopted correlative models to conduct quantitative researches on the water–energy–food nexus. For instance, Bazilian et al. [
34] established the Climate- Land-Energy-Water (CLEW) model to study the water–energy–food nexus. Ziv et al. [
35] adopted the method of fuzzy cognitive mapping (FCM) to analyze the water–energy–food nexus and found that the energy-related elements had the greatest impact on the water–energy–food nexus. Chen et al. [
36] constructed an evaluation index system of the vulnerability and coordination of the water–energy–food system based on the Pressure-State-Response (PSR) model and used a cloud matter-element model to evaluate the degree of coordination, taking the northwest region as a case study. Meanwhile, some scholars have made use of case studies to research the water–energy–food nexus. For example, Taniguchi et al. [
37] studied the water–energy–food nexus by taking 20 cases in the Asia-Pacific region as the research subject. Owen et al. [
38] took the UK as an example and analyzed the interactions among water, energy, and food by using the input–output method. Additional, some scholars carried out the studies on Inner Mongolia from the water–energy–food nexus perspective. For example, Chen et al. [
39] used the Slacks-Based Measure (SBM) super-efficiency model and Malmquist-Luenberger (ML) index analysis method to evaluate the total factor productivity (TFP) of the water–energy–food system in Inner Mongolia; they applied the Tobit model to study the influential factors of the water–energy–food system and found that there was a serious difference in TFP between Inner Mongolia cites. Furthermore, the mechanization level and degree of opening up have positive effects on the TFP, while the enterprise scale and the output of the third industry have negative effects on the TFP. Shang et al. [
40] quantified the temporal patterns of socioeconomic growth, energy consumption, and food and water footprints of Inner Mongolia from 1987 to 2015, and they found that water resource use increased four-fold, energy consumption increased approximately seven-fold, and large areas of natural grasslands were converted to agricultural, industrial, and urban land use, which were exacerbated by large-scale coal production.
Now, some research studies on the optimization of water–energy–food have also been paid more and more attention by scholars. For example, Hang [
41] proposed a systematic mathematical modeling-based approach for designing local production systems and developed a superstructure-based optimization model specifically for design of the food–energy–water nexus in a local context, which considered each supply subsystem individually and allows insights into the potential interactions between them. Zhang and Vesselinov [
42] put forward a comprehensive evaluation method to optimize the production of water, energy, and food in the study of water–energy–food security, with the goal of minimizing energy supply, water supply, food production and the comprehensive cost of carbon dioxide emissions. Zhang et al. [
43] used an integrated water–food–energy nexus model and optimization method to combine real-time drought monitoring with irrigation management to overcome the negative impact of agricultural drought. Karan et al. [
44] built the water–energy–food system and proposed a stochastic mathematical model to forecast demand and output, which was applied to both dry and humid environments. Mo et al. [
45] combined multi-objective programming, nonlinear programming, and intuitive fuzzy number, and constructed a comprehensive Agricultural Water-Energy-Food Sustainable Management (AWEFSM) optimization model of water–energy–food considering the constraints of limited water resources and energy in the agricultural system, taking northwest China as an example for empirical study. Mo et al. [
46] established an optimization model for sustainable management of the water–energy–food nexus under uncertainty conditions to achieve maximum economic benefits and the minimum environmental impact. Therefore, a number of optimization models, such as the linear programming model, nonlinear programming model, dynamic programming model, and stochastic programming model, have been used to promote optimization research to the maximization or minimization of certain objectives [
47]. Since the optimization of research on the water–energy–food system depends on various aspects, such as economy, environment, water, energy, food, and so on, the multi-objective programming model, which is able to solve multiple conflicting objectives functions, can be used to solve the optimization problem.
In conclusion, there are few scholars who pay close attention to the optimization studies of the water–energy–food system from a regional perspective. In addition, the field of studies about the water–energy–food system is still in its infancy in China. Therefore, in this paper, Inner Mongolia in China was selected as a research area to demonstrate a multi-objective optimization study of a water–energy–food system. Firstly, synergy theory was applied to establish the framework of the water–energy–food system. Then, the multi-objective programming model was constructed with objectives and constraints. Finally, a genetic algorithm was designed for accurately assessing the most promising results. The research can provide a theoretical framework and technical support for the comprehensive management and sustainable development of a water–energy–food system in Inner Mongolia in the future. The paper is organized as follows.
Section 2 introduces the study area and data sources.
Section 3 describes the methodology. The main results and discussion are presented in
Section 4.
Section 5 gives the conclusions of the study.
2. Study Area and Data Sources
Inner Mongolia (37°24′–53°23′ N, 97°12′–126°04′ E) is located in the north of China (
Figure 1), including nine prefectural cities and three alliances, namely, Hohhot, Baotou, Hulunbuir, Wuhai, Chifeng, Tongliao, Ulaan Chal, Baynnur, Ordos, Xing’an, Xilin Gol, and Alax. Inner Mongolia is a vast territory with an area of 1,183,000 km
2. The terrain of Inner Mongolia stretches from the northeast to the southwest in a narrow and slender shape, with a linear distance of 2400 km from east to west and a span of 1700 km from north to south.
The spatial and temporal distribution of water resources in Inner Mongolia is very uneven, which does not adapt to the distribution of population and farmland. Inner Mongolia is a major province of energy production in China. It not only has abundant energy resources such as coal, oil, and natural gas, but also has an optimistic prospect for the development and utilization of new energy sources such as wind energy, solar energy, and bio-energy. There are 808 billion tons of confirmed coal reserves in Inner Mongolia, ranking the first in China. The reserve of petroleum geological resources is 614 million tons, and that of natural gas is 1.67 trillion m3, ranking the third in China. Hence, Inner Mongolia has provided an important pillar for China’s energy development. Food grown in Inner Mongolia mainly includes corn, wheat, potato, soybean, millet, and sorghum. The corn production in Inner Mongolia accounts for nearly 80% of all food production, which has gradually developed into an “eldest brother” in the food structure in Inner Mongolia. Therefore, Inner Mongolia is a typical region to study the optimization research of a water–energy–food system, and it will promote the sustainable development of a water–energy–food system in Inner Mongolia.
This study constructed an optimization model of a water–energy–food system in Inner Mongolia based on a multi-objective programming model with 2017 as the level year and 2020 as the planning year. The data mainly included a variety of parameters in this paper. The sources of datasets included the Statistical Yearbook of Inner Mongolia, Economic and Social Development Bulletins of Inner Mongolia, Environmental Bulletin of Inner Mongolia, 13th Five-Year Plan, and Water Resources Bulletin of Inner Mongolia.
6. Conclusions
In this paper, synergy theory was applied to establish the framework of a water–energy–food system, and the multi-objective programming model was adopted to construct the optimization model of a water–energy–food system in Inner Mongolia, which was designed with the goals of minimizing the integrated deviation degree and pollutant emissions from the energy subsystem, maximizing the water economic benefit, energy production, and food production, taking the economy, environment, water, energy, and food as constraints. Then, a genetic algorithm was designed for accurately assessing the most promising results. Therefore, this paper draws the main conclusions and proposes policy suggestions to improve the sustainable development of the water–energy–food system in Inner Mongolia.
Firstly, it can be seen that the cooperation degree of a regional water–energy–food system is getting better and better, because the pollutant emission from the water–energy–food system is reducing. Besides, the agricultural department remains the largest water consumer, although its proportion declines, while the water consumption of the industrial department and domestic department shows an increasing trend. There is still a large space to save water in agricultural, industrial, and domestic departments. Therefore, the government should continue to vigorously promote water conservation in agriculture, industry, and life to comprehensively improve the efficiency and benefits of water resources utilization. First of all, Inner Mongolia should comprehensively promote the development of water-saving agriculture through a combination of engineering, administrative, economic, technological, and managerial measures, increase financial support for water-saving agricultural practices, and ensure the implementation of water-saving agricultural irrigation. Next, Inner Mongolia is supposed to vigorously promote water-saving transformation in industry, encourage enterprises to increase water-saving in production technology, advocate recycling, and improve water utilization efficiency. Third, Inner Mongolia should promote the renovation of water-saving facilities in urban areas and do a good job in the construction and renovation of sewage treatment and reuse facilities.
Secondly, it can be revealed that the production of coal, natural gas, and power in Inner Mongolia are all showing an increasing trend. However, the proportions of coal, natural gas, and power change inconsistently, where the proportions of coal and natural gas increase, while that of power decreases. In addition, there are substantial increases of food production in Inner Mongolia, but the food planting structure is not reasonable. Among them, corn production is in the eldest brother position, while the proportion of wheat and soybean production is low. Thus, Inner Mongolia firstly should give full play to the basic supporting role of coal, encourage the use of new technologies, new equipment, and new processes, and reduce the pollutant emission based on its resource advantages dominated by coal. Then, the construction scale of clean energy such as wind energy, solar energy, and biomass energy should be rationally planned and drawn up. Furthermore, Inner Mongolia is supposed to promote the diversification of its food planting structure. It is valuable to boost the planting of other crops such as beans, cereals, and potato to meet social demand.
Lastly, it can be concluded that there are differences between the planned values and optimal values of decision variables. The optimal values of water consumption of all departments are higher than the planned values, the same as the optimal corn production. Besides, the optimal production of coal and natural gas is inferior to planned values, the same as the optimal soybean production. Therefore, in the future, Inner Mongolia should allocate a water quota for various industries in a scientific way, strictly control water consumption for industry, reduce agricultural irrigation water, and moderately guarantee water for life and ecology. Then, Inner Mongolia should adjust the agricultural planting structure according to its own water resource endowment conditions. On the one hand, the planting area of water-consuming food crops such as corn should be appropriately reduced. On the other hand, that of drought-tolerant crops such as soybean should be increased. Finally, Inner Mongolia should adhere to the concept of green development and vigorously develop natural gas, wind energy, and other clean energy, taking building a green, low-carbon, safe, and efficient energy system as the development goal.
All in all, the present study identified the framework of the water–energy–food system and carried out optimization research from the overall perspective of the water–energy–food system. Therefore, this paper is of great value to the research of the water–energy–food system. From the perspective of methodology, a multi-objective programming model has been successfully applied to reflect the complexities of the water–energy–food system and it has been proven to be effective in the case study, so this methodology has reference value in the future research of water–energy–food optimization. From the perspective of synergy theory, at present, very few research studies construct the framework of a water–energy–food system based on the synergetic theory, and few of them take into account the synergetic effects within a water–energy–food system. Hence, this study provides a new research idea for water–energy–food academic research in the future. However, due to the lack of data, water pollutant emission and solid waste discharge as important factors were not considered in the objective functions. Meanwhile, although eight parameters have been taken into account in our model, there are also some other factors that should be considered to make the results more complete. Hence, the study has its own limitations, which calls for improvement in future related studies. First, a more reasonable model that considers the more comprehensive objective functions and constraints for a water–energy–food system is desired. Second, an application of optimization research of a water–energy–food system in other typical regions would be recommended in future research.