# Practical Efficient Regional Land-Use Planning Using Constrained Multi-Objective Genetic Algorithm Optimization

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Resource

^{2}. More than 45,000 people live and work in this area (up to 2018). To facilitate the optimization computation, the whole region is rasterized into 1878 × 1418 = 2,663,004 cells, with each cell being 10 × 10 m in size (Figure 1). This number of cells is a substantial increase over past models and an indication of our progress to more realistic models than past simulations; for example, 16,779 cells were used by Cao, Huang, Wang, and Lin [10] and 1600 cells were used in the early model by Stewart, Janssen, and Herwijnen [32].

#### 2.2. Model for Land-Use Optimization: LIr-MSO

#### 2.2.1. Objectives

- Objective 1: Minimization of Conversion Cost

_{st}represents the transfer coefficient from existing land-use type s to type t; TA

_{st}denotes the transfer area from land-use type s to type t; $K$ is the number of land-use types.

- Objective 2: Maximization of GDP

_{k}is unit GDP value for land-use type k; A

_{k}is total changed area of land-use type k; $K$ is the number of land-use types.

- Objective 3: Maximization of ESV

_{k}represents the ESV of the land-use type k per unit area; A

_{k}represents the total changed area of land-use type k; $K$ is the number of land-use types.

- Objective 4: Maximization of Compactness

_{hk}is perimeter of the h-th patch in land-use type k; A

_{hk}is area of the h-th patch in land-use type k; H

_{k}is number of patches of land-use type k; $K$ is the number of land-use types.

- Objective 5: Minimization of Conflict Degree

_{ik}is a binary variable. X

_{ik}= 1 when cell i is developed into land-use type k, otherwise X

_{ik}= 0; C

_{kl}is the conflict degree between two adjacent cells with land-use type k and l in the changed area; $K$ is the number of land-use types.

#### 2.2.2. Constraints

#### 2.2.3. Procedures of the LIr-MSO Model

**Step 1: Initialization**

^{2}), and for commercial land, industrial land, and public land, the minimum area is 0.5 ha (50 cells), respectively. As demonstrated in the following experiments, such initiation will help avoid fragmentation and the phenomenon of large patches engulfing small patches in the following operators (e.g., crossover and mutation) whereby some initially generated patches might be merged in the final solution, and also some isolated cells of impractical size might still exist.

_{tk}is the conversion probability from land-use type t to land-use type k; A

_{tk}is the total changed area from land-use type t to type k; $K$ is the number of land-use types.

**Step 2: Fitness Calculation**

_{i}represents the weight of objective i. The sum of weights is 1.

**Step 3: Selection**

_{i}:

_{i}will be admitted to participate in the next step; otherwise, it will enter into the next selection to determine s; where the other possibility is that it will not be selected (s = 0).

**Step 4: Crossover**

**Step 5: Mutation**

**Step 6: Elite Strategy**

**Step 7: Terminate the algorithm**

## 3. Results

#### 3.1. Objective Quantification and Constraints

#### 3.2. Implementation and Evaluation

^{7}) between the highest value and lowest values (30,467 for Residential to 0.001 for Forest respectively). In preliminary experiments, we tested the nominalization of Equation (8) and found that the nominal GDP fitness value of the optimal pattern was not much more than 0.08 compared to, for example, compactness at over 0.9, leading to GDP playing a very minor role in the overall fitness contribution. With such a large disparity in GDP values, we resorted to taking log

_{10}of the numerator and the denominator of Equation (8) to raise the nominal value of GDP (to more than 0.8).

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Land-use map of Dapeng Community in 2017 (map to the right), located within the Greater Bay Area (lower left map) of China (upper left map). For modeling purposes, the land-use map is divided into 1878 × 1418 cells, with each cell being 10 × 10 m in size. Color codings show different land-use types as listed in the legend.

**Figure 2.**Workflow procedure of the Land use Intensity-restricted Multi-objective Spatial Optimization (LIr-MSO) model for iteratively deriving the fittest optimal land-use pattern from an initial pattern.

**Figure 3.**Illustration of the 3 × 3 matrix arrangement where the degree of conflict around a cell (i = 1 to N, where N is the total number of cells) is calculated with respect to each of its neighbors (j = 1 to 8).

**Figure 4.**Schematic illustration of the procedure for crossover from two viable parents (Parent1 and Parent2) with two different land uses (a and b respectively) in the center cells. Crossover to form an Offspring is performed by replacing the center cell in Parent1 if the new center cell type outnumbers the old.

**Figure 5.**Procedure of Point-based Mutation (PM) where the center cell within a 3 × 3 window in the parent is replaced by the most numerous type.

**Figure 6.**Replacement mode in the elite strategy applied to a current and future generation (A(n) and A(n + 1) respectively) for the three cases of relative fitness comparison.

**Figure 7.**Constraints in Dapeng Community in relation to (

**a**) changeable and unchangeable land, and (

**b**) areas of allowable development where the land slope does not exceed 25 degrees.

**Figure 8.**Change in fitness score of the comprehensive model with the number of iterations showing a relatively rapid change up to about 21 iterations followed by a transition toward a much slower phase of increase, punctuated by periods of static fitness. Shorter periods of relatively static change are also noticeable in the rapid phase. The different Conditions refer to the contrast experiments described in the main text: (1) without initialization revision; (2) without mutation revision; (3) without initialization and mutation. LIr-MSO refers to the comprehensive model that includes both initialization and mutation revision.

**Figure 9.**The final optimal pattern of land use showing different land uses (colored as per the Legend) with example zoomed in comparisons. Changes in land use in the numbered regions from 1 to 5 are referred to in the main text.

**Figure 10.**The pattern of areas of changed land use (regardless of type) in the developable area between the original and the optimal land-use pattern. No changed areas occur within the ecological reserve area.

**Figure 11.**Comparison, including zoomed inserts, of final land-use patterns across three contrast experiments (

**a**–

**c**): 1. without initialization revision; 2. without mutation revision; 3. without initialization and mutation revision. In (

**d**), the normalized values are listed for each experiment/condition and compared to the optimal solution obtained with the LIr-MSO model.

**Table 1.**Transfer coefficient, from a scale of 0 (change not possible) to 1 (no restrictions in swapping over) for changing land-use types. Abbreviations are as follows for the land-use type: Residential land (R), Commercial land (C), Industrial land (I), Arable land (Ar), Aquaculture land (Aq), Forest land (F), Other land (O), Beach (B), Public land (P), and Water (W). Columns are the source land use and rows are the changed land use.

Change to\Change from | R | C | I | O | F | Ar | P |
---|---|---|---|---|---|---|---|

R | 0 | 0.44 | 0.32 | 0.18 | 0.22 | 1 | 0.24 |

C | 0.23 | 0 | 0.31 | 0.18 | 0.22 | 1 | 0.27 |

I | 0.29 | 0.37 | 0 | 0.18 | 0.22 | 1 | 0.45 |

O | 1 | 1 | 1 | 0 | 1 | 1 | 1 |

F | 0.89 | 0.92 | 0.89 | 0.7 | 0 | 0.3 | 0.85 |

Ar | 0.83 | 0.85 | 0.82 | 0.7 | 0.4 | 0 | 0.81 |

P | 0.35 | 0.51 | 0.33 | 0.34 | 0.18 | 1 | 0 |

**Table 2.**GDP (Gross Domestic Product) and ESV (Ecological Service Value) per unit area for different land-use types. Land-use type abbreviations are as per Table 1.

Land-Use Type | GDP per Unit Area (RMB/m^{2}) | ESV per Unit Area |
---|---|---|

R | 30,467 | 0 |

C | 699 | 0 |

I | 4508 | 0 |

P | 0 | 0 |

Ar | 0 | 7.9 |

Aq | 4.9 | 7.9 |

F | 0.001 | 28.12 |

O | 0 | 1.39 |

B | 0 | 28.12 |

W | 0 | 45.35 |

**Table 3.**Conflict degree between different land uses. The matrix is symmetrical so that conflict degree does not depend on the horizontal directionality of the spatial juxtaposition. Land-use type abbreviations are as per Table 1.

R | C | I | O | F | Ar | P | |
---|---|---|---|---|---|---|---|

R | 0 | 4 | 8 | 5 | 7 | 8 | 0 |

C | 4 | 0 | 6 | 5 | 7 | 8 | 2 |

I | 8 | 6 | 0 | 5 | 7 | 8 | 7 |

O | 5 | 5 | 5 | 0 | 1 | 1 | 5 |

F | 7 | 7 | 7 | 1 | 0 | 2 | 6 |

Ar | 8 | 8 | 8 | 1 | 2 | 0 | 8 |

P | 0 | 2 | 7 | 5 | 6 | 8 | 0 |

Land Use Type | Lower Area Limits (ha) | Upper Area Limits (ha) |
---|---|---|

Residential land | No less than 410 | No more than 660 |

Industrial land | No less than 250 | No more than 500 |

**Table 5.**Comparison of the change in area (km

^{2}) between initial pattern and optimal multi-objective optimal pattern for the different land uses. Abbreviations are described in Table 1.

Objs\Land Use (km^{2}) | C | I | O | F | Ar |

Initial | 2.3894 | 6.5216 | 2.0319 | 67.2372 | 1.7036 |

LIr-MSO | 4.9478 | 8.1120 | 1.8262 | 62.8576 | 1.6818 |

Changed (%) | 107.07% | 24.39% | −10.12% | −6.51% | −1.28% |

Objs\Land Use (km^{2}) | Aq | W | B | R | P |

Initial | 1.2413 | 1.3628 | 0.2270 | 4.8931 | 0.6966 |

LIr-MSO | 1.2413 | 1.3628 | 0.2270 | 5.2754 | 0.7726 |

Changed (%) | - | - | - | 7.81% | 10.91% |

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**MDPI and ACS Style**

Pan, T.; Zhang, Y.; Su, F.; Lyne, V.; Cheng, F.; Xiao, H.
Practical Efficient Regional Land-Use Planning Using Constrained Multi-Objective Genetic Algorithm Optimization. *ISPRS Int. J. Geo-Inf.* **2021**, *10*, 100.
https://doi.org/10.3390/ijgi10020100

**AMA Style**

Pan T, Zhang Y, Su F, Lyne V, Cheng F, Xiao H.
Practical Efficient Regional Land-Use Planning Using Constrained Multi-Objective Genetic Algorithm Optimization. *ISPRS International Journal of Geo-Information*. 2021; 10(2):100.
https://doi.org/10.3390/ijgi10020100

**Chicago/Turabian Style**

Pan, Tingting, Yu Zhang, Fenzhen Su, Vincent Lyne, Fei Cheng, and Han Xiao.
2021. "Practical Efficient Regional Land-Use Planning Using Constrained Multi-Objective Genetic Algorithm Optimization" *ISPRS International Journal of Geo-Information* 10, no. 2: 100.
https://doi.org/10.3390/ijgi10020100