Harmonious development of 3Es (economy-energy-environment) system is the key to realize regional sustainable development. The structure and components of 3Es system are analyzed. Based on the analysis of causality diagram, GDP and industrial structure are selected as the target parameters of economy subsystem, energy consumption intensity is selected as the target parameter of energy subsystem, and the emissions of COD, ammonia nitrogen, SO_{2}, and _{2} emission intensity are selected as the target parameters of environment system. Fixed assets investment of three industries, total energy consumption, and investment in environmental pollution control are selected as the decision variables. By regarding the parameters of 3Es system optimization as fuzzy numbers, a fuzzy chance-constrained goal programming (FCCGP) model is constructed, and a hybrid intelligent algorithm including fuzzy simulation and genetic algorithm is proposed for solving it. The results of empirical analysis on Shandong province of China show that the FCCGP model can reflect the inherent relationship and evolution law of 3Es system and provide the effective decision-making support for 3Es system optimization.

How to balance the economic development, energy security, and environmental protection to achieve sustainable development has been one of the greatest challenges of the 21st century. Referred to as the 3Es (economy-energy-environment) issues, they often involve simultaneous consideration of the speed and quality of economic development, energy consumption, and pollutants and GHGs (greenhouse gases) emissions. Therefore, it is imperative to optimize 3Es system in order to achieve coordinated development. The coordination is not only the basic assurance for the energy security and sustainable development of economy, but also an effective way to reduce environmental pollution.

There are some researches on the optimization of 3Es system, and a number of optimization models have been proposed. According to the modelling method, 3Es models can be divided into three categories, that is, top-down model, bottom-up model, and mixed model [

In summary, 3Es system optimization is one of the significant ways to achieve the regional sustainable development. Extensive mathematical programming models have been put forward to demonstrate the relationships of 3Es system and obtain the optimal decision scheme. From the perspective of reality, uncertain models including interval, stochastic, and fuzzy programming models are better than deterministic models. Since plenty of statistical data is needed in the stochastic programming model to determine the probability distributions of variables, it is rarely used for 3Es optimization directly. Many interval and fuzzy programming models were constructed and applied for micro energy systems optimization, which were transformed into deterministic models with interaction parameters. Few studies constructed specifically the uncertain models of regional 3Es system considering targets of economy, energy, and environment subsystems simultaneously. In this paper, a fuzzy chance-constrained goal programming model (FCCGP) and its hybrid intelligent algorithm are put forward for optimization of 3Es system, and an empirical analysis on Shandong province is conducted for application of the above model and algorithm.

This paper is organized as follows: Section

3Es system consists of three subsystems, namely, energy subsystem, economy subsystem, and environment subsystem, which interrelate with and influence each other. The development of each subsystem not only depends on its own structure but also depends on the other subsystems. The elements and composition structure of 3Es system are shown in Figure

Elements and composition structure of 3Es system.

Due to the fact that the impact value of energy investment and environmental pollution on the economic output is difficult to be estimated, the backward effects from energy of environment subsystem to economy subsystem are generally not considered into 3Es system optimization models. Referring to the literatures [

Investments in fixed assets _{2} emissions _{2} emissions intensity.

GDP

GDP proportion of tertiary

Investment in environmental pollution control

Causality diagram of 3Es system in Shandong province.

Each subsystem of 3Es system has the corresponding targets. Generally, economy subsystem pursues high GDP growth rate and scientific industrial structure. GDP and three industry structures are selected as the target parameters of economic subsystem:

Energy subsystem pursues lower growth rate of energy consumption and lower energy consumption intensity. Based on the target reduction ratio, the energy consumption intensity of the target year can be obtained by

Environment subsystem pursues fewer emissions of pollutants and GHGs. The pollutants and GHGs usually include chemical oxygen demand (COD), ammonia nitrogen, sulphur dioxide (SO_{2}), nitrogen oxides (_{2}). Based on the reduction ratios, they can be computed by the following formula:_{2}, and _{2}.

According to the principles of controllability and exogenesis, the decision variables of the 3Es system include the investments in fixed assets of the three industries, total energy consumption, and total investment in environmental pollution control.

3Es system is a complex system and contains multiple optimization objectives. Generally, the target of economy subsystem includes two aspects: GDP of the target year is not lower than the planning value; industrial structure achieves the planning target; that is, the GDP proportions of primary industry and secondary industry are not higher than their target values and that of tertiary industry is not lower than its target value. The target of energy subsystem is that the energy consumption intensity is not higher than the planning value. The target of environment subsystem includes two aspects: the emissions of pollutants including COD, ammonia nitrogen, SO_{2}, and _{2} emissions intensity is not higher than its planning value.

Due to the small sample of historical data and the uncertainty of forecasting, many parameters of 3Es system can be seen as fuzzy parameters. In this paper, a fuzzy chance-constrained goal programming model (FCCGP) is constructed for optimizing 3Es system. According to the above targets of 3Es system, the constraints consist of two types: (a) the uncertain constraint that each subsystem achieves its targets holding with a certain confidence level; (b) technical constraints. The uncertain constraints are as follows.

GDP of the target year equals the sum of the added values of three industries:

The fuzzy chance constraints that three industry structures of the target year should achieve the desired structure are satisfied with certain confidence levels:

The constraint that GDP of the target year is not lower than the planning value is satisfied with a certain confidence level:

The constraint that energy consumption intensity of the target year is not higher than the planning value is satisfied with a certain confidence level:

The constraints that the emissions of COD, ammonia nitrogen, SO_{2}, _{2} are not higher than their planning values are satisfied with certain confidence levels:

_{2}, and

_{2}, and

_{2}, and

_{2}, and

_{2}emission coefficient, that is, CO

_{2}emissions per unit of energy consumption,

_{2}, and

_{2}emission intensity,

The technical constraints include the following.

Each decision variable should be within a certain range:

The sum of investments in fixed assets of three industries should be within a certain range:

All the deviation variables are nonnegative:

The objective of the model is to minimize the total deviations according to the priority structure and target levels set by the decision-maker:

Fuzzy simulation is a technology of sampling test for the fuzzy system model. If

Generate

Find the maximal value

Return

A hybrid intelligent algorithm can be employed for solving the fuzzy chance-constrained goal programming model, which integrates fuzzy simulation and genetic algorithm. The procedure of this algorithm is as follows [

Initialize a population with

According to the credibility distributions of all the fuzzy variables including

Calculate the values of deviation variables of each chromosome:

Compare all the objective values of

Select chromosomes by spinning the roulette wheel; that is, repeat the following process

Set a parameter

Set a parameter

Repeat the second to seventh steps for

As a major economic province of China, Shandong province has achieved significant economic growth, and since 2007, its economic output has been ranked third in 31 provinces. Although many efforts have been made for energy saving and pollutants reduction, the energy efficiency level of Shandong province still falls behind the national average level [

The data of the fixed assets investments of three industries at 2000 price index, total energy consumptions, and investment in environmental pollution control from 2000 to 2014 are shown in Table

Data of the fixed assets investments, energy consumptions, and investment in environmental pollution control of Shandong province from 2000 to 2014.

Year | Fixed assets investment (10^{8} Yuan) | Total energy consumption (10^{4} tce) | Investment in environmental pollution control (10^{8} Yuan) | ||
---|---|---|---|---|---|

Primary industry | Secondary industry | Tertiary industry | |||

2000 | 77.1 | 1176.7 | 1288.8 | 11361.9 | 76.2 |

2001 | 78.2 | 1193.1 | 1306.9 | 9955.0 | 89.8 |

2002 | 79.1 | 1206.3 | 1321.3 | 14599.0 | 144.6 |

2003 | 81.4 | 1241.2 | 1359.6 | 16624.8 | 156.4 |

2004 | 87.4 | 1333.1 | 1460.2 | 19623.7 | 191.9 |

2005 | 89.9 | 1371.1 | 1501.8 | 24162.0 | 238.8 |

2006 | 91.5 | 1395.8 | 1528.8 | 26759.3 | 258.1 |

2007 | 95.2 | 1452.2 | 1590.6 | 29176.6 | 320.8 |

2008 | 102.5 | 1564.0 | 1713.1 | 30570.0 | 432.2 |

2009 | 99.4 | 1515.5 | 1660.0 | 32420.2 | 459.5 |

2010 | 103.0 | 1570.7 | 1720.4 | 34807.8 | 483.9 |

2011 | 110.0 | 1678.1 | 1838.1 | 37132.0 | 614.1 |

2012 | 110.9 | 1692.2 | 1853.5 | 38899.3 | 739.1 |

2013 | 111.4 | 1698.8 | 1860.7 | 35358.0 | 848.0 |

2014 | 111.7 | 1703.9 | 1866.3 | 36511.0 | 823.8 |

Sources:

Note: — indicates the lack of data.

The forecast of the fixed assets investment in primary industry is taken as an example to illustrate the application of various methods. Using the annual sequence number as independent variable, the linear regression (LR) equation of the fixed assets investment in primary industry can be obtained as follows:

Note: data in the parentheses denote

By first-order accumulating operation on the raw data, the accumulated values of the fixed assets investment in primary industry can be represented as a row vector

Comparison of grey forecast results and actual values.

The results of residual test and posterior variance test are as follows. The maximum relative error is 5.10%, the average relative error is 1.89%, the forecast accuracy is 98.11%, the posterior error ratio is 0.1945, and the small error frequency is 1. The test results show that grey forecast model has high precision and can be used for short-term forecasting. Inputting

In addition to the above forecasting methods, exponential regression (ER), power function regression (PR), quadratic regression (QR), and cubic curve regression (CR) can also be applied to fit the relation between the fixed assets investment in primary industry and the annual sequence number. The regression results are obtained as follows:

All the correlation coefficient square values are greater than 0.8, so the above regression equations are significant. Inputting

Forecast results of decision variables in 2015.

Forecast method | Fixed assets investment (10^{8} Yuan) | Total energy consumption (10^{4} tce) | Investment in environmental pollution control (10^{8} Yuan) | ||
---|---|---|---|---|---|

Primary industry | Secondary industry | Tertiary industry | |||

LR | 117.9 | 1797.7 | 1969.1 | 43613.5 | 851.2 |

GF | 119.6 | 1824.8 | 1998.7 | 45597.1 | 1112.7 |

ER | 120.2 | 1833.1 | 2008.0 | 51777.5 | 1211.8 |

PR | 109.6 | 1672.5 | 1831.9 | 40551.8 | 735.2 |

QR | 130.7 | 1778.8 | 1948.3 | 38334.4 | 984.6 |

CR | 111.9 | 1707.3 | 1870.3 | 33948.2 | 970.3 |

Lower bound | 109.6 | 1672.5 | 1831.9 | 33948.2 | 735.2 |

Upper bound | 130.7 | 1833.1 | 2008.0 | 51777.5 | 1211.8 |

The added values per unit investment of three industries from 2000 to 2014 are shown in Figure

Forecast results of the added values per unit investment of three industries in 2015 (unit: Yuan/Yuan).

Forecast method | The added values per unit investment | ||
---|---|---|---|

Primary industry | Secondary industry | Tertiary industry | |

LR | 20.57 | 14.77 | 7.48 |

GF | 20.64 | 16.68 | 8.31 |

ER | 20.66 | 17.31 | 8.37 |

PR | 19.74 | 12.72 | 6.38 |

QR | 20.80 | 15.83 | 8.14 |

CR | 21.21 | 15.62 | 8.01 |

The added values per unit investment of three industries from 2000 to 2014.

The production coefficients of four pollutants and CO_{2} emission coefficients from 2000 to 2014 are shown in Table _{2} emission coefficients are forecasted based on the samples of 2005–2014.

The production coefficients of pollutants and CO_{2} emission coefficients from 2000 to 2014.

Year | The production coefficients of pollutants (t/10^{8} Yuan) | CO_{2} emission coefficients (t/10^{4} Yuan) | |||
---|---|---|---|---|---|

COD | Ammonia nitrogen | SO_{2} | | ||

2000 | 531.08 | — | 427.73 | — | 1.5588 |

2001 | 473.72 | 13.63 | 383.51 | — | 1.5956 |

2002 | 385.00 | 12.52 | 340.54 | — | 1.2807 |

2003 | 338.53 | 10.41 | 339.03 | — | 1.5982 |

2004 | 280.36 | 9.58 | 293.57 | — | 1.6750 |

2005 | 247.16 | 9.03 | 284.08 | — | 2.2665 |

2006 | 199.37 | 13.91 | 311.22 | 121.74 | 2.0849 |

2007 | 180.69 | 7.29 | 251.87 | 89.25 | 1.9663 |

2008 | 182.83 | 8.00 | 280.38 | 77.03 | 1.9407 |

2009 | 165.39 | 9.27 | 273.67 | 73.96 | 1.7856 |

2010 | 154.63 | 11.32 | 268.44 | 69.16 | 1.6662 |

2011 | 150.94 | 7.00 | 314.13 | 68.12 | 1.5793 |

2012 | 134.31 | 5.69 | 239.98 | 62.21 | 1.5230 |

2013 | 98.60 | 4.26 | 247.97 | 59.57 | 1.2420 |

2014 | 86.96 | 3.42 | 268.11 | 61.15 | 1.2194 |

Note: — indicates the lack of data.

Forecast results of the production coefficients of four pollutants and CO_{2} emissions coefficients in 2015.

Forecast method | The production coefficients of pollutants (t/10^{8} Yuan) | CO_{2} emissions coefficient (t/t) | |||
---|---|---|---|---|---|

COD | Ammonia nitrogen | SO_{2} | | ||

LR | 14.33 | 4.24 | 225.62 | 45.22 | 1.1026 |

GF | 74.65 | 5.32 | 237.77 | 53.96 | 1.1842 |

ER | 80.78 | 4.51 | 234.10 | 50.72 | 1.1640 |

PR | 114.70 | 5.84 | 250.08 | 56.27 | 1.3464 |

QR | 127.19 | 2.91 | 282.99 | 70.03 | 1.0765 |

CR | 57.94 | −0.27 | 239.55 | 48.1 | 0.9863 |

Note:

The removal coefficients of COD, ammonia nitrogen, SO_{2}, and

The removal coefficients of four pollutants from 2000 to 2014 (unit: t/10^{8} Yuan).

Year | The removal coefficients of pollutants | |||
---|---|---|---|---|

COD | Ammonia nitrogen | SO_{2} | | |

2000 | 22312.87 | — | 4204.09 | — |

2001 | 19102.87 | 386.51 | 4054.03 | — |

2002 | 11278.36 | 248.46 | 2884.60 | — |

2003 | 10841.76 | 247.79 | 3612.67 | — |

2004 | 9002.71 | 224.17 | 3286.14 | — |

2005 | 7506.24 | 195.67 | 3160.82 | — |

2006 | 6529.95 | 449.66 | 5691.74 | 13.98 |

2007 | 5667.44 | 204.30 | 4286.80 | 11.91 |

2008 | 4968.03 | 206.52 | 5140.90 | 18.51 |

2009 | 4824.66 | 272.07 | 5948.39 | 50.10 |

2010 | 4789.07 | 363.43 | 6514.73 | 27.20 |

2011 | 4409.67 | 195.86 | 7002.29 | 29.71 |

2012 | 3601.40 | 145.61 | 4683.00 | 60.08 |

2013 | 2523.13 | 103.74 | 5034.74 | 77.42 |

2014 | 2498.19 | 92.75 | 6540.74 | 84.55 |

Note: — indicates the lack of data.

Forecast results of the removal coefficients of pollutants in 2015 (unit: t/10^{8} Yuan).

Forecast method | The removal coefficients of pollutants | |||
---|---|---|---|---|

COD | Ammonia nitrogen | SO_{2} | | |

LR | −1206.00 | 135.80 | 6503.00 | 86.63 |

GF | 1741.53 | × | × | 110.45 |

ER | 2085.52 | 127.80 | 6655.57 | 112.52 |

PR | 3099.84 | 161.19 | 5659.68 | 72.30 |

QR | 4924.04 | 67.34 | 6539.95 | 103.59 |

CR | 72.02 | −66.19 | 4731.15 | 113.16 |

Note:

All the forecast methods are applied according to their premises, so the above results are reasonable theoretically. Due to less effective forecast results, the above indicators can be seen as interval or fuzzy variables. In order to make full use of the forecast results, all the indicators are considered to obey the triangular fuzzy distributions. The triangular fuzzy variable

The values of the parameters in triangular fuzzy variables of FCCGP model.

Variable | | | |
---|---|---|---|

| 19.74 | 20.60 | 21.21 |

| 12.72 | 15.49 | 17.31 |

| 6.38 | 7.78 | 8.37 |

| 57.94 | 91.05 | 127.19 |

| 2.91 | 4.56 | 5.84 |

| 225.62 | 245.02 | 282.99 |

| 45.22 | 54.05 | 70.03 |

| 0.9863 | 1.1433 | 1.3464 |

| 1741.53 | 2962.73 | 4924.04 |

| 67.34 | 123.03 | 161.19 |

| 4731.15 | 6017.87 | 6655.57 |

| 72.30 | 99.78 | 113.16 |

According to the 12th five-year plan of Shandong province, the annual average growth rate of GDP is 9%, the industrial structure in 2015 is 7: 48: 45, the annual average growth rate of fixed assets investment is set about 15%, energy consumption intensity and carbon emission intensity should drop by 17% and 18% from 2010, the emissions of COD, ammonia nitrogen, SO_{2}, and _{2}, and

According to the requirements of new normal economy that emphasize structural adjustment, the elimination of energy bottleneck and green low-carbon development, and the effects that Shandong province has achieved at the early time, the GDP proportion of tertiary industry, energy consumption intensity, and CO_{2} emission intensity should be paid more attention in 2015. Assuming the predetermined confidence levels of all the targets are

According to the above hybrid intelligent algorithm, the population size _{2} and _{2} emission intensity is 139.22 tons per million Yuan.

Solution results of FCCGP model of Shandong province in economic priority scenario.

Variable | Solution |
---|---|

| 130.7 |

| 1784.5 |

| 2008 |

| 37470.8 |

| 879.9 |

| 0 |

| 0 |

| 0 |

| 0 |

| 0.0787 |

| 0 |

| 0 |

| 390074.21 |

| 29.57 |

| 0.0262 |

In economic priority scenario, there are greater differences between the optimized results and the targets in energy and environment subsystems. Considering the importance of environment subsystem for sustainable development, environment priority scenario is defined with the priority orders of three subsystems that are environment

Solution results of FCCGP model of Shandong province in environment priority scenario.

Variable | Solution |
---|---|

| 130.7 |

| 1716.2 |

| 2008 |

| 37080.1 |

| 1307.6 |

| 0.0101 |

| 0.0204 |

| 0.0103 |

| 610.71 |

| 0 |

| 0 |

| 0 |

| 0 |

| 0 |

| 0 |

A scenario endowing the equivalent status for three subsystems is put forward to compare with the first two scenarios. The optimal solutions are shown in Table _{2} are 1340146 t.

Solution results of FCCGP model of Shandong province in the scenario of equivalent status.

Variable | Solution |
---|---|

| 130.7 |

| 1749.6 |

| 2008 |

| 44278.8 |

| 1103.5 |

| 0.0007 |

| 0.0186 |

| 0.0293 |

| 549.72 |

| 0.0949 |

| 0 |

| 0 |

| 163320 |

| 0 |

| 0 |

It can be known from the comparison of three scenarios that the results of the scenario of equivalent status are not improved better than those of environment priority scenario, while environment priority scenario is better than economic priority scenario. Therefore, the optimization results of environment priority scenario can be applied to guide practice of 3Es system optimization of Shandong province. In 2015, 13.07, 171.62, and 200.8 ten billion Yuan can be invested into the primary, secondary, and tertiary industries, respectively, total energy consumption should be controlled below 370.801 million tce, and 130.76 ten billion Yuan can be invested into environmental pollution control.

The optimization results show that Shandong province should increase the investments in fixed assets of three industries and environmental pollution control in 2015. The investments in fixed assets of the primary, secondary, and tertiary industries in 2015 can be 17%, 4.73%, and 7.59% higher than those in 2014, respectively. The total investments in fixed assets and environmental pollution control in 2015 can be 6.55% and 6.81% higher than those in 2014. Meanwhile, the total energy consumption in 2015 can be merely 2.63% more than that in 2014, which means the growth should be slowed. Practically, Shandong province is undergoing a critical period of structural adjustment at present. The secondary industry consumes considerable amount of energy and causes environmental pollutions and carbon emissions; therefore, it is reasonable to reduce the investment growth of the secondary industry. On the contrary, increasing the investment in the tertiary industry and speeding up its development can reduce energy consumption and environmental pollutions. In addition, the carrying capacity of energy resources in Shandong province has been continuously improving, so it is necessary to reduce the growth of energy consumption while ensuring economic development, which means that Shandong province should strengthen energy conservation, improve energy efficiency, and develop alternative energy sources.

In this study, we have analyzed the structure of 3Es system and selected the typical indicators to demonstrate the main causal relationships. The target parameters and decision variables are set and a FCCGP model is put forward for 3Es system optimization. In the FCCGP model, uncertain parameters are fuzzy variables, and fuzzy chance constraints are satisfied with certain confidence levels. The proposed model is essentially flexible, and any number and form of fuzzy goals and constraints can be contained into it. A hybrid intelligent algorithm including fuzzy simulation and genetic algorithm is put forward for solving the uncertain model. Depending upon the nature of the study region, the user can modify the model and algorithm inputs to get desired outputs. After the empirical analysis on Shandong province, we can conclude that the parameters of 3Es system optimization can be regarded as triangular fuzzy numbers, and FCCGP models with fuzzy variables can demonstrate the relations of interaction among three subsystems. The results of 3Es system optimization of Shandong province testify the feasibility of FCCGP models, which can be applied to guide the practice of 3Es system optimization so as to realize their harmonious development. According to the optimization results, Shandong province should obey the rule of environment priority. In this scenario, 3Es system can realize relatively more scientific development, although it may lower the economic development to a certain extent.

Limited by the definition of research object and availability of data, in this paper, we neither include imports and exports, household consumption and other contents into economic subsystem, nor take into consideration land, forest, mineral, water resources, population, science and technology, and other subsystems. This weakened the complex relationship between each subsystem in some certain extent and might affect the objectivity of the programming results, which should be improved in the future studies.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by Natural Science Foundation of Shandong Province (ZR2015GM008), MOE (Ministry of Education in China) Project of Humanities and Social Sciences (16YJAZH054), and the Fundamental Research Funds for the Central Universities (15CX04101B).

_{2}emissions: a technical manual