# A Hybrid Inexact Optimization Method for Land-Use Allocation in Association with Environmental/Ecological Requirements at a Watershed Level

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## Abstract

**:**

^{12}yuan under the minimum violating probabilities; the optimized areas of commercial land, industrial land, agricultural land, transportation land, residential land, water land, green land, landfill land and unused land will be optimized cultivated land, forest land, grass land, water land, urban land, unused land and landfill will be [228234, 237844] ha, [47228, 58451] ha, [20982, 23718] ha, [33897, 35280] ha, [15215, 15907] ha, [528, 879] ha and [1023, 1260] ha. These data can be used for generating decision alternatives under different scenarios and thus help decision makers identify desired policies under various system-reliability constraints of ecological requirement and environmental capacity. Tradeoffs between system benefits and constraint-violation risks can be tackled. They are helpful for supporting (a) decision of land-use allocation and government investment; (b) formulation of local policies regarding ecological protection, environment protection and economic development; (c) analysis of interactions among economic benefits, system reliability and ecological requirements.

## 1. Introduction

## 2. Inexact Stochastic Fuzzy Programming (ISFP) Model

_{i}is a m × n matrix of coefficients of constraints and b

_{i}is a m × 1 matrix; ${b}_{opt}^{\pm}$ is the aspiration level of the objective values which is set beforehand; p

_{s}denotes the probability that the constraints s are violated. $\text{\hspace{0.17em}}{b}_{s}^{({p}_{s})}$ represents corresponding values given the cumulative distribution function of ${b}_{s}$ and the probability of violating constraint s (p

_{s}). The solution method of model (1) is expressed as follows: on the basis of the principle of fuzzy flexible programming [40], we let λ

^{±}value correspond to the membership grade of satisfaction for a fuzzy decision; specifically, the flexibility in the constraints and fuzziness in the system objective (which are represented by fuzzy sets and denoted as “fuzzy constraints” and a “fuzzy goal”) are expressed as membership grades λ

^{±}. The λ

^{±}corresponds to the degrees of overall satisfaction for the constraints/objective. Model (1) can be converted to:

_{1}) and ${x}_{j\text{\hspace{0.17em}}opt}^{-}$ (j = k

_{1}+ 1, k

_{1}+ 2, …, n) be solutions of sub-model (3). Then, the second sub-model corresponding to ${\lambda}^{+}$ can be formulated supported by the solution of sub-model (4):

_{1}) and ${x}_{j\text{\hspace{0.17em}}opt}^{+}$ (j = k

_{1}+ 1, k

_{1}+ 2, …, n) be solutions of sub-model (4). Thus, we can obtain the interval solutions as follows:

## 3. ISFP Model for Land-Use Planning of Poyang Lake Watershed

#### 3.1. The Study Area

^{3}km

^{2}, accounting for 9% of the Yangtze River basin. The Poyang Lake watershed is one of the most important flood control libraries in the middle reaches of Yangtze River basin, and the water storage capacity can reach 19.2 × 10

^{9}–20.9 × 10

^{9}m

^{3}. Poyang Lake is the biggest freshwater lake in China. The watershed contains 11 districts and the population is approximately 44,228,000 (2012). The watershed’s gross domestic product (GDP) increased rapidly from 0.32 × 10

^{12}RMB in 2003 to 6.45× 10

^{12}RMB in 2012, in concert with a population increase from 38,729,000 million to 44,228,000 million.

^{9}ton, accounting for 6.59% of China. The discharge quantity of chemical oxygen demand (COD) and ammonia nitrogen (NH

_{3}-N) were 445.3 × 10

^{3}ton and 34.3 × 10

^{3}ton. The discharge quantity of living sewage was 3.56 billion ton, which increased by 9.31% over 2011. Field investigations and monitoring data indicated that water pollution was mostly discharged from both point sources and non-point sources. In addition, pollution from solid wastes was also serious. In 2012, the output quantity of solid wastes in the Poyang Lake watershed was 128.39 million ton, increasing 18.7% comparing with 2011. Specially, the output quantity of hazardous solid wastes was 2.69 million ton, increasing 20.64% comparing with 2011. These wastewater and solid wastes hadn’t been disposed properly and posed a threat to the safety of residents’ healthy.

#### 3.2. Modeling Framework

- (i)
- Multiple processes. A number of processes (e.g., environment protection and ecosystem service), as well as their interactions, are contained in Wuhan’s land-use system. Competitions and interactions may exist not only in each individual process but also between each other. For example, more allocation to industry land will result in more system benefit but lead to more pollutant, thus demand more landfill to tackle the solid wastes; more allocation to green land will be propitious to ecological stability but will obtain less system benefit. These competitions are further intensified by varying social-economic, geographical, ecological and environmental conditions, as well as spatial and temporal distributions of land sources.
- (ii)
- Complexities and uncertainties. Normally, land market, environment capacity and government policies of Wuhan are unstable and variable, which are subject to spatial and/or temporal fluctuations. For example, investment to build incinerators and waste water treatment plants are statistically uncertain, which can be expressed as probabilistic distributions. In addition, these uncertainties are further complicated by a variety of imprecise information such as land-quality characteristics, land prices, and demand projections. Thus, uncertainties may exist in multiple formats, leading to complexities in the relevant decision-making process.
- (iii)
- Dynamic. For the planning horizon, social, economic, legislational and resources conditions will vary with time. Reflection of such variations would be important for generating effective planning alternatives.

- constraint 1: economic constraints
- constraint 2: social constraints
- constraint 3: land suitability constraints
- constraint 4: environmental constraints
- constraint 5: ecological constraints
- constraint 6: technical constraints

- constraint 1: government investment constraint
- constraint 2: agricultural production input-output constraint
- constraint 3: water production input-output constraint
- constraint 4: available water consumption constraint
- constraint 5: available electricity power consumption constraint
- constraint 6: maximum people in a unit land area constraint
- constraint 7: available labor constraint
- constraint 8: land suitability constraints
- constraint 9: wastewater treatment capacity constraint
- constraint 10: solid-waste treatment capacity constraint
- constraint 11: available soil erosion constraint
- constraint 12: forest and grass cover rate constraints
- constraint 13: fertilizer consumption constraints
- constraint 14: total land areas constraint
- constraint 15: non-negative constraints

#### 3.2.1. Economic Objective

^{2}); $W{P}_{i,j=4,k}^{\pm}$ = unit benefit of water land (yuan/km

^{2}); $U{P}_{i,j=5,k}^{\pm}$ = unit benefit of urban land (yuan/km

^{2}); $NW{C}_{i,j=1,k}^{\pm}$ = unit wastewater-tackling cost of agricultural land (yuan/km

^{2}); $NS{C}_{i,j=1,k}^{\pm}$ = unit solid-waste-tackling cost of agricultural land (yuan/km

^{2}); $NE{C}_{i,j=1,k}^{\pm}$ = unit electricity cost of agricultural land (yuan/km

^{2}); $NW{C}_{i,j=5,k}^{\pm}$ = unit wastewater-tackling cost of urban land (yuan/km

^{2}); $NS{C}_{i,j=5,k}^{\pm}$ = unit solid-waste-tackling cost of urban land (yuan/km

^{2}); $NE{C}_{i,j=5,k}^{\pm}$ = unit electricity cost of urban land (yuan/km

^{2}); $FM{C}_{i,j=2,k}^{\pm}$ = unit maintenance costs of forest land (yuan/km

^{2}); $GM{C}_{i,j=3,k}^{\pm}$ = unit maintenance costs of grass land (yuan/km

^{2}); $WM{C}_{i,j=4,k}^{\pm}$ = unit maintenance costs of water land (yuan/km

^{2}); $UD{C}_{i,j=6,k}^{\pm}$ = unit developing costs of unused land (yuan/km

^{2}); $UL{C}_{i,j=7,k}^{\pm}$ = unit maintenance costs of landfill (yuan/km

^{2}).

#### 3.2.2. Economic Constraints

#### (i) Government investment constraint

#### (ii) Agricultural production input-output constraint

^{2}); $DA{B}^{\pm}$ = demand agricultural production (ton). “$\gtrsim $”means fuzzy greater than.

#### (iii) Water production input-output constraint

^{2}); $DW{P}^{\pm}$ = demand aquatic production(ton).

#### (iv) Available water consumption constraint

^{2}); $A{W}^{\pm}$ = available water (ton).

#### (v) Available electricity power consumption constraint

^{2}, KWH/ km

^{2}); $E{W}^{\pm}$ = available electric power (kilowatt hour, KWH).

#### 3.2.3. Social Constraints

#### (i) Maximum people in a unit land area constraint

^{2}).

#### (ii) Available labor constraint

^{2}); $A{L}^{\pm}$ = available labors(person).

#### 3.2.4. Land Suitability Constraints

^{2}).

#### 3.2.5. Environmental Constraints

#### (i) Wastewater treatment capacity constraint

^{2}); $UW{F}_{i,j\text{\hspace{0.17em}}=\text{\hspace{0.17em}}5,k}^{\pm}$ = wastewater discharging factor of urban land (ton/km

^{2}); $AWD$ = wastewater treatment plant capacity (ton); p = probability of violating the constraints of environmental capacities, and p ∈ [0,1].

#### (ii) Solid-waste treatment capacity constraint

^{2}); $US{F}_{i,j\text{\hspace{0.17em}}=\text{\hspace{0.17em}}5,k}^{\pm}$ = solid-waste discharging factor of urban land (ton/km

^{2}); $ASD$ = solid-waste treatment plant capacity (except landfill) (ton); $LH{P}_{i}^{\pm}$ = solid-waste discharging factor (landfill) (ton). The environmental impacts are mainly caused by industrial activities in the land-use system. Otherwise, environmental impacts are also caused by domestic wastewater/solid waste.

#### 3.2.6. Ecological Constraints

#### (i) Available soil erosion constraint

^{2}).

#### (ii) Forest and grass cover rate constraints

#### (iii) Fertilizer consumption constraints

^{2}); $M{P}^{\pm}$ = maximum fertilizer consumption (ton)

#### 3.2.7. Technical Constraints

#### (i) Total land areas constraint

^{2}).

#### (ii) Non-negative constraints

#### 3.3. Data Collection

#### 3.4. The Solution of a General ISFP Land-use Planning Model at a Watershed Level

- Step 1: Analyze the land-use system in the watershed and formulate the conceptual model;
- Step 2: Transform the conceptual model to mathematical model through ISFP method;
- Step 3: Get economic, beneficial, and cost parameters through forecasting models and land evaluation methods;
- Step 4: Obtain land suitability parameters through GIS technology;
- Step 5: Obtain ecological parameters through ecological models;
- Step 6: Obtain environmental parameters under different p levels through stochastic fitting methods;
- Step 7: Transform the ISFP-LUAM into two sub-models corresponding to the up bound and low bound objective- function values;
- Step 8: Solve two sub-models and obtain their solutions;
- Step 9: Obtain the solutions of the ISFP-LUAM and get the optimal land areas for each user;
- Step 10: Analyze the results and generate decision alternatives.

Symbol | Lower Bound | Upper Bound | Symbol | Lower Bound | Upper Bound |
---|---|---|---|---|---|

MGI (10^{12} yuan) | 92.15 | 103.99 | LC_{i=}_{1,k=1} (people/km^{2}) | 312.58 | 442.19 |

UAB_{i=}_{1,k=1} (ton/km^{2}) | 2.84 | 3.91 | AL (10^{3} people) | 4498.00 | 5643.00 |

DAB (10^{6} ton) | 5.34 | 6.97 | AWF_{i=}_{1,j=1,k=1} (10^{3} ton/km^{2}) | 5.67 | 7.28 |

UWP_{i=}_{1,k=1} (ton/km^{2}) | 2.25 | 6.51 | UWF_{i=}_{1,l=5,k=1} (10^{6} ton/km^{2}) | 15.64 | 22.18 |

DWP (10^{6} ton) | 1.14 | 2.58 | ASF_{i=}_{1,j=1,k=1} (ton/km^{2}) | 42.18 | 55.47 |

WC_{i=}_{1,k=1} (10^{3} m^{3}/km^{2}) | 221.38 | 256.47 | USF_{i=}_{1,l=5,k=1} (10^{3} ton/km^{2}) | 105.24 | 226.37 |

AW (10^{9} m^{3}) | 2.69 | 4.32 | LHP_{i=}_{1} (ton) | 1865.27 | 2021.34 |

EC_{i=}_{1,k=1} (10^{6} kwh/km^{2}) | 5.12 | 7.58 | OP_{i=}_{1,k=1} | 2% | 2.5% |

EW (10^{9} kwh) | 39.54 | 72.19 | AO (km^{2}) | 2564.27 | 3302.18 |

TP (10^{6} people) | 42.19 | 59.27 | FP_{i=}_{1,k=1} (ton) | 12.34 | 13.27 |

MIP (people/km^{2}) | 789.00 | 854.00 | TUL (10^{3} km^{2}) | 162.00 | 195.00 |

Land-use Type | Symbol | Lower Bound | Upper Bound |
---|---|---|---|

Benefits of land use | AP_{i=}_{1,j=1,k=1} (10^{6}) | 0.13 | 0.15 |

AP_{i=}_{2,j=1,k=1} (10^{6}) | 0.09 | 0.11 | |

AP_{i=}_{3,j=1,k=1} (10^{6}) | 0.25 | 0.34 | |

WP_{i=}_{1,j=4,k=1} (10^{3}) | 25.69 | 36.98 | |

WP_{i=}_{2,j=4,k=1} (10^{3}) | 18.21 | 20.12 | |

WP_{i=}_{3,j=4,k=1} (10^{3}) | 78.91 | 105.21 | |

UP_{i=}_{1,j=5,k=1} (10^{6}) | 54.32 | 66.87 | |

UP_{i=}_{2,j=5,k=1} (10^{6}) | 27.35 | 35.64 | |

UP_{i=}_{3,j=5,k=1} (10^{6}) | 158.98 | 225.21 | |

Costs of land use | NWC_{i=}_{1,j=1,k=1} (10^{3}) | 115.32 | 126.31 |

NSC_{i=}_{1,j=1,k=1} (10^{3}) | 261.32 | 298.54 | |

NEC_{i=}_{1,j=1,k=1} (10^{3}) | 98.35 | 115.21 | |

NWC_{i=}_{1,j=5,k=1} (10^{3}) | 2132.12 | 2564.89 | |

NSC_{i=}_{1,j=5,k=1} (10^{3}) | 5698.25 | 7789.24 | |

NEC_{i=}_{1,j=5,k=1} (10^{3}) | 229.65 | 339.17 | |

FMC_{i=}_{1,j=2,k=1} (10^{3}) | 112.31 | 152.13 | |

GMC_{i=}_{1,j=3,k=1} (10^{3}) | 258.14 | 265.38 | |

WMC_{i=}_{1,j=4,k=1} (10^{3}) | 118.25 | 156.38 | |

UDC_{i=}_{1,j=6,k=1} (10^{3}) | 196.35 | 256.28 | |

ULC_{i=}_{1,j=7,k=1} (10^{3}) | 95.23 | 98.25 |

Symbol | Lower Bound | Upper Bound |
---|---|---|

MIL_{j}_{=1} (10^{6}) | 53.58 | 55.45 |

MIL_{j}_{=2} (10^{6}) | 31.77 | 33.64 |

MIL_{j}_{=3} (10^{6}) | 0.12 | 0.15 |

MIL_{j}_{=4} (10^{6}) | 21.18 | 22.43 |

MIL_{j}_{=5} (10^{6}) | 8.10 | 11.21 |

MIL_{j}_{=6} (10^{3}) | 93.45 | 105.91 |

MIL_{j}_{=7} (10^{3}) | 79.74 | 83.48 |

Eco-environmental Capacity | p level | |||
---|---|---|---|---|

p = 0.01 | p = 0.05 | p = 0.10 | p = 0.15 | |

AWD(10^{9} ton) | 17.72 | 19.25 | 29.34 | 42.68 |

ASD(10^{6} ton) | 146.79 | 168.95 | 198.25 | 249.67 |

AO (km^{2}) | 2932.15 | 3269.31 | 3965.24 | 4458.21 |

MR | 44% | 36% | 32% | 29% |

MP (10^{3}) | 559.68 | 665.32 | 778.98 | 998.28 |

## 4. Results Analysis

#### 4.1. Optimized Land-use Patterns under Different p Levels and Land Use Policy Analysis

**Figure 3.**Optimized land-use allocation in Lake Controlling Development Zone under different p levels.

^{12}yuan, which means the expected system benefit would change between 15.17 × 10

^{12}yuan and 18.29 × 10

^{12}yuan with varied reliability levels, implying the actual value of each continuous variable varies within its lower and upper bounds. In general, planning with a lower system benefit will be associated with a lower risk of violating the system constraints. Conversely, a plan targeting a higher system benefit may be associated with a higher risk of violating system constraints.

#### 4.2. Optimized Environmental Pollutants Emissions and Ecological Patterns under Different p Levels and Eco-Environmental Policy Analysis

#### 4.3. Tradeoff between Economic Objective and Eco-Environmental Constraints

^{12}yuan. In comparison, when p = 0.05, the values change to [23.18, 36.94] × 10

^{12}yuan. Similar characteristics exist in solutions under the other significance levels (p = 0.05 and 0.10). The relationship between p and system benefit is shown in Figure 8.

#### 4.4. Tradeoff between Constraints and System Benefit and Economic Policy Analysis

^{12}yuan, while under λ = 0.98 (p = 0), the system benefit will be [68.31, 72.19] × 10

^{12}yuan. The λ values indicate the tradeoff between system benefit and all the constraints (including eco-environmental constraints). Lower λ values would guarantee all the requirements are met, result in a more strict constraints and a lower system benefit; in comparison, a higher λ values lead to a more flexible constraints and a higher system benefit. For example, a higher available electricity power, water and soil erosion corresponding to a higher λ values and give a higher system benefit.

#### 4.5. Summary

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Qiu, B.; Lu, S.; Zhou, M.; Zhang, L.; Deng, Y.; Song, C.; Zhang, Z.
A Hybrid Inexact Optimization Method for Land-Use Allocation in Association with Environmental/Ecological Requirements at a Watershed Level. *Sustainability* **2015**, *7*, 4643-4667.
https://doi.org/10.3390/su7044643

**AMA Style**

Qiu B, Lu S, Zhou M, Zhang L, Deng Y, Song C, Zhang Z.
A Hybrid Inexact Optimization Method for Land-Use Allocation in Association with Environmental/Ecological Requirements at a Watershed Level. *Sustainability*. 2015; 7(4):4643-4667.
https://doi.org/10.3390/su7044643

**Chicago/Turabian Style**

Qiu, Bingkui, Shasha Lu, Min Zhou, Lu Zhang, Yu Deng, Ci Song, and Zuo Zhang.
2015. "A Hybrid Inexact Optimization Method for Land-Use Allocation in Association with Environmental/Ecological Requirements at a Watershed Level" *Sustainability* 7, no. 4: 4643-4667.
https://doi.org/10.3390/su7044643