Assessing the complex adaptability of regional water security systems based on a unified co-evolutionary model

In recent years, due to fluctuations in the natural water cycle and the destruction of the water balance, regional water security is becoming increasingly serious; water security refers to a region (or country) under certain socioeconomic conditions and includes the ability to withstand water disasters and the sustainable use of water resources to ensure sustainable economic, social, and ecological development (Petersen-Perlman et al. 2012; Anand et al. 2013; Fu et al. 2013). Water security systems are complex systems including water resources, socioeconomic and eco-environmental subsystems, which must be individually examined to comprehensively and systematically analyze and study the regional water security situation. Additionally, water resource systems are the basis for the development of subsystems in water security systems; socioeconomic systems aim to maximize the benefits of the subsystems. In the context of sustainable development, eco-environmental systems provide an environment for the good functioning of water security systems. Thus, water security systems are highly integrated with complex adaptive characteristics (Giacomoni et al. 2013; Cheng et al. 2015).

This paper introduces a cooperative evolutionary algorithm to study the operational mechanisms and development of water security systems. Co-evolution refers to the combined evolution of both organisms and the environment under long-term mutual adaptation, whereas evolution corresponds to the individual development of organisms and the environment (Ehrlich & Raven 1964). The co-evolutionary algorithm is an evolutionary computational method that was first proposed in the 1990s to simulate the co-evolution phenomenon in ecological evolution (Hillis 1990; Panait 2010). The method calculates the fitness of individuals according to the collaborative relationship between individuals. Compared with the genetic algorithm, the co-evolutionary algorithm can simulate ecological evolution more effectively, and the algorithm is more adaptive and can overcome the premature convergence of the genetic algorithm. Therefore, some researchers have introduced cooperative evolutionary computations in research on optimization problems; for example, an innovative variation of the co-evolutionary genetic algorithm (CGA) was proposed by Baek & Yoon (2002) to determine adaptive scheduling strategies in a complex multi-machine system. The CGA effectively suppressed premature convergence and produced dispatching rules for spatial adaptation that outperformed other heuristic methods. In a study of the optimal allocation of water resources, a CGA was proposed by Wang et al. (2014) to improve the utilization of water resources. A hybrid CGA was proposed by Korayem et al. (2016) to determine the optimal moving paths of concentrated nanoparticles in a complex environment. Infeasible initial paths significantly reduced the efficacy of the path planning algorithm, especially in large and complex environments. Tian & Gong (2014) proposed a new CGA that uses two types of alternating co-evolution to generate test data for path coverage. This proposed method displayed the highest success rate, lowest requirement for human evaluation, and lowest time consumption.

Based on an individual competitive relationship or partnership, co-evolutionary algorithms can be divided into competitive co-evolutionary algorithms (CCEAs) and cooperative co-evolutionary algorithms (Chandra et al. 2011; Nogueira Collazo et al. 2014). The fitness of individuals in competitive co-evolution algorithms depends on the ability of the individual to defeat an opponent in a competition, and the progress of either party in the competition will endanger the survival of the other party. This method has been used by some researchers to solve various problems. A simple, non-problem-specific framework was proposed by Sato & Arita (2009) to extend the range of CCEAs and avoid local optima by utilizing the loss of gradient. A competitive co-evolutionary multi-objective genetic algorithm (cc-MOGA) was used to approximate a Pareto front of efficient silvicultural regimes of Eucalyptus fastigiata based on maintaining a maximum growth rate for as long as possible for any one rotation (Chikumbo & Straka 2012). The fitness of individuals in a CCEA depends on the cooperation of individuals, and in a competition, there is a beneficial impact on the individual associated with cooperation. The progress of any party involved in cooperation is beneficial to both sides. The cooperative co-evolutionary algorithm has been widely used in various studies. A cooperative evolutionary approach was proposed for the solution of the instance selection problem, and the experimental results showed that the proposed method was robust and could effectively solve the problem using large data sets (García-Pedrajas et al. 2009). A new cooperative co-evolutionary algorithm for solving structural configuration and parameter optimization issues based on adaptive platform product customization (PPC) was proposed by Li et al. (2008). However, the method is slow to converge at the beginning of the evolutionary process. This initial slow convergence property improves its searching capability and ensures a high-quality solution. Moreover, cooperative co-evolutionary algorithms have been used to study the dynamic optimization problems of random migration and evolution strategy. The experimental results show that the method is effective in locating and tracking the optimal solution and more scalable than the evolution strategy in a dynamic environment (Au & Leung 2014). In addition, the competitive and cooperative co-evolutionary algorithms were applied to the design of a multi-objective particle swarm optimization algorithm, and the simulation results showed that the proposed algorithm was superior to other methods of competition and co-evolution (Goh et al. 2010). However, the fitness values of these two algorithms change for different cooperative individuals, which increases the computational time.

To solve this problem, a uniform co-evolutionary algorithm involving absolute fitness and relative fitness is adopted. The absolute fitness depends on an individual, while the relative fitness is determined by the coordination between individuals. The adaptability of individuals and their interactions based on the external environment determines the ability of the entire system to adapt to environmental change. The absolute fitness value reflects the ability of individuals to adapt to environmental change, the relative fitness value reflects the adaptability of each element in the problem domain, and the comprehensive fitness value is the comprehensive adaptability of each element based on the absolute fitness and relative fitness.

Jiansanjiang is located on the northeastern Sanjiang Plain. It belongs to the humid monsoon climate zone (cold temperate) and is home to the largest agro-ecological park in China. Its geographical coordinates are 132°31′–134°32′E longitude and 46°49′–48°12′N latitude. The annual average temperature over the entire area is 1.0 °C to 2.0 °C, the region covers an area of 1.24 × 10⁴ km², the population is 2.3 × 10⁵, and the per capita cultivated land area is 3.33 km². The region contains 15 large and medium-sized state-owned farms, and there are three major rivers in the region, including the Songhua River, Heilongjiang River, and Wusu River (see Figure 1). The water area is wide and the water quality is good. The total amount of surface water resources in this area is 2.85 × 10¹¹ m³; the surface water transit capacity is 2.74 × 10¹¹ m³, including 2.14 × 10¹¹ m³ in the Heilongjiang River and 5.99 × 10¹⁰ m³ in the Wusu River. The exploitable amount of groundwater resources in this area is 14.84 × 10⁸ m³/a, and its utilization is 13.35 × 10⁸ m³/a, indicating that the region is rich in water resources and has great potential for development and utilization. However, because the region is largely populated with domestic housing, industrial water consumption is relatively small and the utilization of surface water resources is low. The rapid development of rice planting has led to a large concentration of groundwater resources in recent years, resulting in an imbalance in the supply and demand of water resources, which has seriously affected the ability of the water security system to adapt to environmental changes (Liu 2013).

The grey system theory was proposed by Deng in 1982 (Morán et al. 2006). This theory can effectively address incomplete information and unclear problems. In the grey system, black represents the lack of system information, and white represents the complete information. A system containing incomplete and unclear information is called a grey system (Morán et al. 2006; Vinoth Kumar & Pradeep Kumar 2014). Grey correlation analysis uses the similarity degree of sequence curve geometry to determine the degree of correlation of a grey process development scenario. It is a quantitative method for analyzing the correlation degree of each factor in a grey system. The internal information in a water security system is incomplete, and the grey correlation degree uses the existing white information to reduce the associated error when evaluating the system (Lin & Lin 2002; Hasani et al. 2012). In this paper, the measured values of regional water security systems are used as comparative sequences, their ideal values are treated as reference sequences, and the grey correlation degree of each index is used as the adaptive measure value (absolute fitness).

Ehrlich and Raven proposed the concept of co-evolution in ecology in 1964 (Hillis 1990). This concept refers to the ability of several related populations to interact with each other, adapt to environmental changes and promote their ability to adapt to these changes. The co-evolutionary algorithm is a global optimization algorithm that was inspired by the co-evolution phenomena associated with the interactions between individuals in nature (Nogueira Collazo et al. 2014). According to the principle of constructing the problem domain of the co-evolutionary algorithm (Zhang et al. 2010), the adaptability of water security systems is studied based on the entire problem domain and several sub-problem domains. The factors that affect the adaptability of water security systems are considered the elements of the problem domain, and the relative fitness between individuals is calculated using the improved co-evolutionary algorithm.

In this paper, the adaptability of the water security systems in the study area is considered the research domain, and it is divided into water resource system adaptability, socioeconomic system adaptability, and eco-environmental system adaptability. The adaptability of water resources systems is based on the water resource content, water use efficiency, and human control. The influence of regional, social, and economic development on the sustainable development of water security systems is the concentrated embodiment of the adaptability of socioeconomic systems. The adaptability of eco-environment systems reflects the adaptability of water security systems to changes in environmental conditions related to water and soil resources, natural disasters, man-made factors caused by climate change, and the destruction of the water and soil environment. The evaluation elements of each sub-problem domain are selected according to the ‘International water management standards for the promotion of sustainable use of freshwater’ issued by the Global Water Management Partnership (GWP), the ‘World environmental assessment report’ issued by the United Nations Environment Program (UNEP), the ‘Annual report on water resources management’ issued by the Water Resources Department of Ministry of Water Resources in China, and the principles of being objective, systematic, dynamic, data-focused, and attentive to regional characteristics (see Table 1).

The weight of each element (index) is determined using the improved entropy weight method. The absolute fitness of each index is determined using improved Euclidean grey weighted correlation analysis, and the relative fitness of each element is obtained using the improved co-evolutionary algorithm. According to the absolute fitness and relative fitness of each element (index), a unified co-evolution model is constructed, and the comprehensive fitness of each index is obtained. Simultaneously, the influence of the sub-problem domain on the overall problem domain is analyzed based on the comprehensive fitness and coordination index of each sub-problem domain. Then, the fitness of the entire problem domain is determined according to the projected weight value of the comprehensive fitness of each index. According to an assessment of urban water security systems, the ability of regional water security systems to adapt to environmental change is analyzed. The specific process is shown in Figure 2, and the model operation procedure is as follows.

Step 1: Numerical normalization processing of evaluation indexes

Step 2: Determine the weight of the evaluation index in the sub-problem domain

The weight of each index is determined using the improved entropy weight method. This method overcomes the shortcoming that the index weight is affected by the difference coefficient and prevents an index weight of 0 from being assigned. Additionally, this approach fully considers the influence of the interactions between the indexes.

Step 3: Calculate the absolute fitness of the index in the sample information matrix using the improved Euclidean grey weighted average correlation method

Step 4: Calculate the relative fitness of each index using the improved co-evolutionary algorithm, and the comprehensive fitness is obtained by combining the relative fitness and absolute fitness

Step 5: Calculate the adaptability of each sub-problem domain, and analyze the importance of each sub-problem domain to the problem domain based on the coordination index

Step 6: Calculate the adaptability of the entire problem domain

Based on the Chinese city water security system indexes and grading standards (Liu 2011; Shao et al. 2013), project survey statistics, the relevant literature regarding index classification methods (Xiang 2011), and the regional characteristics of the study area (Li & Ma 2015), the adaptability is divided into four levels. The grade threshold of each element is shown in Table 2. According to the threshold of each element of water security systems, the adaptability criterion is obtained by the unified co-evolution model (see Table 3).

The evaluation index system for water security systems was established based on the index values between 2002 and 2011 in the study area (see Table 4). Our research data were primarily obtained from the ‘Jiansanjiang Statistical Yearbook (2002–2011)’, the ‘Heilongjiang Reclamation Area Statistical Yearbook (2002–2011)’, and a field study conducted during this research project.

In this paper, based on the data of the water security system evaluation index for the period 2002–2011 and using Matlab2012a software, the weights, absolute fitness values, relative fitness values, and comprehensive fitness values of the elements in each sub-problem domain (see Table 5) are obtained by the unified co-evolution model (steps 1–4; Equations (1)–(8)). According to the comprehensive fitness value of each element, the fitness degree and coordination index of each sub-problem domain of the water safety system in the study area (see Table 6) are obtained using operation step 5 (Equation (9)), and the fitness of the entire problem domain (see Table 7) is obtained using step 6 (Equation (10)).

According to the absolute fitness, relative fitness, and comprehensive fitness values in Table 5, the fitness bar graph of each element of the study area's water security system is obtained (see Figure 3). Based on the data in Table 6, the comprehensive fitness and coordination index change curves of each sub-problem domain are also obtained (see Figure 4). Finally, the comprehensive fitness change curve of the study area's water security system problem domain is determined (see Figure 5).

Figure 3 shows that the absolute fitness values of each element are significantly greater than their relative fitness values. This indicates that each element itself has a strong adaptability to the environment, which is directly related to the good natural foundation in the study area (Liu 2013). The ability of the elements to interact with each other to adapt to environmental change is weak, which is due to the various elements focusing on their own development; mutual interaction is caused by the effects of production. The comprehensive fitness value can fully reflect the ability of each factor to adapt to environmental changes. The result shows that the comprehensive fitness values of X₁, X₂, X₄, X₆, X₇, X₁₁, X₁₃, X₁₅, X₂₅, X₂₉, and X₃₂ all exceeded 0.5 (mean value of 0.701), which is because the absolute fitness (mean value of 0.863) and relative fitness (mean value of 0.698) of these elements are higher; these elements also have a stronger ability to recover themselves and resist external disturbances. However, the overall fitness values of the remaining factors are below 0.5 (mean value of 0.444), which is due to the absolute fitness (mean value of 0.613) and relative fitness (mean value of 0.438) of these elements being low; these elements tend to mutate when subjected to external conditions or other elements. Therefore, it is an effective measure for improving the comprehensive fitness of each element to strengthen the construction of each element and to improve the coordinated development relationship among the various factors.

For the period 2002–2011, Figure 4(a) shows that the average annual comprehensive fitness values of the water resources, socioeconomic, and eco-environmental system in the study area are 0.795, 0.345, and 0.619, respectively, indicating that the water resources system has good adaptability. The adaptability of the ecological environment system at the medium level during this period, and the adaptability of the socioeconomic system is low. The comprehensive fitness of the studied water resources system shows a rising trend, with an average annual increase of 5.03%, which is mainly due to the abundant water resources (average annual water resources amount of 4.35 × 10⁹ m³) in the study area. Moreover, over the studied period, the comprehensive supply of groundwater increases (maximum increase of 39.64%), the processing capacity of wastewater treatment facilities increases (average annual growth rate of 85%), and the cost of wastewater treatment facilities increases (average annual increase was 13.71%), improving the adaptability of the water resources system. The comprehensive fitness of the socioeconomic system shows an upward trend, with an average annual increase of 6.94%; this is due to the decrease in the natural growth rate of the population (an average annual decrease of 5.33%), which reduces the pressure on the social and economic development of the study area. Moreover, the proportion of investments in environmental protection accounted for by the GDP increases with an average annual growth rate of 2.02%, which reduces the pollution level of the enterprises in the study area. The grain yield per unit area and regional agricultural production density increases with an average annual growth rate of 3.26% and 3.81%, respectively, which improves the efficiency of agricultural economic development. However, due to the small change in each element and their low comprehensive fitness values, the adaptability of the sub-problem domain is low. The comprehensive fitness of the eco-environmental system fluctuates upward and downward. In 2002–2003, the comprehensive fitness of the system shows a rising trend due to a decrease in the extent of flood damage (decrease of 26.08%) and an increase in vegetation coverage (increase of 0.66%), which reduces the amount of soil erosion in the study area. In 2004–2005, the comprehensive fitness of the system shows a downward trend due to the increase of cultivated land area (increase of 37.25%), which leads to an increase in the fertilizer application rate (increasing range of 7.75%) and an increase in the content of soil toxic substances in the study area; the number of local livestock increases (increase of 4.98%); and the afforestation area decreases (decrease of 49.44%), aggravating the degree of desertification in the study area. In 2006–2011, the comprehensive fitness of the system increases with a maximum increase of 40.65%; the effective irrigation area and the actual irrigation area in the study area increases (average annual increases of 12.60% and 12.85%, respectively), reducing the ecological environment carrying capacity; the local drought and flood disaster degree decreases (average annual decreases of 14.12% and 15.81%, respectively); and the number of livestock grazing decreases (average annual decrease of 2.28%), improving the ability of the eco-environmental system to protect itself against natural disasters.

Figure 4(b) shows that in 2002–2011, the contribution degree of water resources system to the study area's water security system adaptability increases (average annual increase of 9.58%), and the average annual coordination index value is 0.567. The contribution degree of the socioeconomic system to the water security system adaptability decreases (average annual decrease of 7.06%), and the average annual coordination index value is 0.285. The contribution degree of the eco-environmental system to the water security system adaptability exhibits a fluctuating downward trend (maximum decrease of 37.62%), and the average coordination index value is 0.403. The results show that the water resources system enhances the ability of the study area's water security system to adapt to the environmental changes, while the socioeconomic system and the eco-environmental system decrease annually.

Figure 5 shows that in 2002–2011, the comprehensive fitness of water security system in the study area fluctuates upward (maximum increase of 39.96%), and the annual comprehensive fitness is 0.556, which indicates the system adaptability is at level II. The system is barely able to adapt to changes in the environment. Despite the comprehensive fitness of the water resources system and the contribution degree to the problem domain being high, the comprehensive fitness of the socioeconomic and the eco-environmental system (especially the socioeconomic system) and their contribution degree to the problem domain are low; and their contribution to the problem domain decreases each year, which further decreases the comprehensive fitness of the water security system in the study area. Therefore, to improve the water security system adaptability, the healthy development of the water resources system should be promoted. Moreover, vigorous improvements in the sustainable development of the society and economy and the protection and improvement of the quality of the ecological environment are needed.

This study shows that the main reason for the reduced adaptability of the water security system to the changing environment is the low comprehensive fitness of the socioeconomic and the eco-environmental system, and the two systems' contributions to the sustainable development of the water safety system decrease every year. Therefore, effective measures should be taken to improve the fitness and contribution of these two systems; the specific suggested measures are as follows:

1. Based on the low comprehensive adaptability of the socioeconomic system and the low contribution of the system to the problem domain, the study area should adjust the three major industrial structures and diversify the production methods, which can increase the per capita GDP and reduce the pressure on the water security system caused by the rapid socioeconomic development. The study area also needs to mobilize all social forces to enhance environmental protection and water conservancy construction funds for diversified, multi-channel, and multi-level financing mechanisms related to environmental protection and water conservancy investments. Moreover, the area should improve the relationship between economic development and the use of water resources and the protection of the ecological environment in the study area.

2. According to the relatively low comprehensive adaptability of the eco-environmental system and the relatively low contribution of the system to the problem domain, the local government should carry out practical farmer fertilizer technical guidance and scientific breeding training, improve farmer fertilizer application technology and grain pest disaster prevention level, and promote farmers to use pollution-free organic fertilizer on farmland, improve soil organic matter content, and increase the effective area of cultivated land. In the fenced grazing areas, controlling livestock grazing quantity, increasing afforestation efforts, continuing to reclaim wasteland, reducing land desertification degree, and reducing the loss of water and soil are all needed.

3. Although the comprehensive adaptation degree of the study area's water resources system is high in the study period, if we ignore the development scenario of the water resources system, the ability of the water security system to adapt to the changing environment will be seriously hindered. Therefore, to strengthen the social and economic development and ecological environmental protection at the same time, the study area needs to rely on scientific and reasonable development and utilization of water resources, make full use of rainwater resources to replace groundwater surface water, improve the quality and yield of rice using surface water irrigation, and store surface runoff decreased by groundwater exploitation (the groundwater to vertical replenishment effect can also improve the local ecological environment). Moreover, the way in which wastewater is discharged should be addressed, and the construction of farm sewage treatment facilities should be strengthened. Centralized wastewater treatment emissions act to scatter emissions; strictly controlling new pollution sources of water and a finite period of governance are needed.

Based on the complex adaptive features in water security systems, the co-evolution theory has been introduced. The adaptability of water security systems is defined as the problem domain, and 33 elements (indicators) and sub-problem domains based on water resources, the social economy, and ecological environment are used. An evaluation index system of water security systems is established. Based on reliable survey data, the unified co-evolution model is used to study the adaptability conditions of a water security system. The results show that the adaptability of the water security system in the study area is low, and the comprehensive fitness shows an upward trend. In the sub-problem domains, the adaptability of the water resources system is high, and the comprehensive adaptability of the system increases every year. Moreover, the adaptability of the socioeconomic and the eco-environmental system is low, the comprehensive fitness of the socioeconomic system exhibits an increasing trend, and the comprehensive fitness of the eco-environmental system fluctuates (average increasing trend). The Euclidean grey weighted correlation method is used to calculate the absolute fitness of each element; this method considers the importance of each element in the system and the fluctuation coefficient, which is the fluctuation in each point correlation coefficient based on its average value. The method fully reflects the influence of the correlation degree between the reference sequence and comparison sequence on the overall correlation degree. The relative fitness of each element is used in the improved co-evolution method, and the method is based on the individual variation in each element in the system based on the principles of competitive exclusion and feature substitution (Shang 2002).

In summary, the unified co-evolutionary model proposed in this paper has good practical significance for studying the adaptability of regional water security systems. Moreover, it provides a reliable basis for improving the adaptability of water security systems.

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grant no. 51479032 and 51579044) and the Natural Science Foundation of Heilongjiang Province, China (Grant no. E201321).