Spatially contiguous block crossover operator generation and land use planning scheme optimization method

Abstract

This application provides a method for generating spatial adjacency block crossover operators and optimizing land spatial planning schemes, relating to the field of land spatial planning technology. From a population of land spatial planning schemes that meet hard planning constraints, a first-generation individual and a second-generation individual are selected. Starting from the seed unit of the parent individual, and according to a preset growth scale, a spatial region growth method is used to generate geographically continuous spatial contiguous blocks with homogeneous internal attributes. All usage codes corresponding to the spatial contiguous blocks in the first-generation individual are extracted as the first gene segment, which is then copied and applied to the corresponding gene loci of the second-generation individual to generate the first-generation individual. Similarly, all usage codes corresponding to the spatial contiguous blocks in the second-generation individual are extracted as the second gene segment, which is then copied and applied to the corresponding gene loci of the first-generation individual to generate the second-generation individual. The scheme provided in this application has the advantages of better spatial integrity and efficient inheritance of high-quality spatial characteristics from the parent generation.

Description

Technical Field

[0001] This application relates to the field of land spatial planning technology, and more specifically, to a method for generating spatial adjacency block cross operators and optimizing land spatial planning schemes. Background Technology

[0002] Territorial spatial planning needs to balance multiple objectives such as ecological security, economic development, and food security, and has rigid requirements for the continuity and functional integrity of spatial layout. Currently, genetic algorithms are a commonly used technique for solving multi-objective territorial spatial planning optimization problems; however, traditional genetic algorithm crossover operators (such as single-point crossover and two-point crossover) have significant drawbacks: 1. Traditional crossover operators exchange genes by randomly splitting chromosome gene sequences, without considering the geographical relevance of land spatial planning. This results in the fragmentation of continuous spatial areas in offspring planning schemes, leading to unreasonable layouts such as fragmented ecological protection units, isolated urban construction land, and scattered permanent basic farmland, which violate the spatial morphology rules of land spatial planning. 2. The gene exchange process disrupts the locally rational spatial functional structure of the parent generation scheme, which greatly reduces the feasibility of the offspring scheme. A large amount of additional computing power is required for subsequent correction, resulting in low optimization efficiency. 3. The general cross operator cannot adapt to the specific needs in areas such as "geographical feature constraints" and "spatial morphology requirements" in land spatial planning, making it difficult to balance mathematical optimality and practical feasibility in the optimization results.

[0003] Therefore, there is an urgent need for a cross operator that can ensure spatial continuity and preserve the high-quality spatial structure of the parent generation, in order to solve the technical problems of spatial fragmentation and functional separation in the optimization of land spatial planning by traditional cross operators. Summary of the Invention

[0004] The purpose of this application is to provide a method for generating spatial adjacency block cross operators and optimizing land spatial planning schemes, so as to solve the problems of spatial fragmentation and functional separation in existing land spatial planning optimization technologies.

[0005] To achieve the above objectives, the technical solutions adopted in the embodiments of this application are as follows: On one hand, embodiments of this application provide a method for generating spatial adjacency block crossover operators, the method comprising: First and second parent individuals are selected from the population of land spatial planning schemes that meet the hard constraints of planning. Both the first and second parent individuals are one-dimensional integer chromosomes with a length equal to the total number of planning units M. Each element in the chromosome corresponds to the use code of a planning unit. The planning units include rigid constraint units and non-rigid constraint units. One planning unit is randomly selected from the non-rigid constraint units as a seed unit. Starting from the seed unit, a spatially continuous block with geographically continuous and internally homogeneous properties is generated using a spatial region growth method according to a preset growth scale. The growth scale is determined based on the planning area scale. Extract all the usage codes corresponding to the spatial contiguous block in the first parent individual as the first gene fragment, copy it as a whole and cover the corresponding gene loci in the second parent individual, while keeping the other gene loci of the second parent individual unchanged, to generate the first offspring individual; Extract all the usage codes corresponding to the spatial contiguous block in the second parent individual as the second gene fragment, copy it as a whole and overwrite the corresponding gene loci in the first parent individual, while keeping the other gene loci of the first parent individual unchanged, to generate the second offspring individual.

[0006] On the other hand, embodiments of this application also provide a method for optimizing land spatial planning schemes, the method comprising: Using superpixel segmentation technology, the planning area is divided into several planning units with homogeneous internal attributes, and the geographical attributes and constraint types of each planning unit are labeled. Among them, planning units located within the ecological protection red line or permanent basic farmland boundary are labeled as rigid constraint units, and the rest are labeled as unconstrained units. Generate an initial population consisting of N initial planning schemes; the number of initial planning schemes is determined based on the total number of planning units; The suitability of each initial planning scheme is evaluated; Based on the evaluation results, a combined strategy of binary tournament selection method and non-dominated ranking and crowding calculation was adopted to select N / 2 individuals from the current population to form a mating pool. Pair individuals in the mating pool into two pairs, and apply the spatial adjacency block crossover operator generation method described above to each pair of parent individuals to generate two offspring individuals; then perform mutation operations and feasibility verification on the offspring individuals; The parent and offspring populations are merged, and N individuals are selected based on non-dominated sorting and crowding to form a new generation population. The fitness of each planning scheme in the population is evaluated repeatedly, and individuals in the mating pool are paired to generate new offspring individuals. The offspring individuals are then subjected to mutation operations and feasibility verification until the preset iteration termination condition is met. Extract the Pareto optimal frontier individuals from the final population, decode them into a spatial planning layout map, and output it.

[0007] Compared with the prior art, this application has the following advantages: First, this application uses spatially contiguous blocks as the basic unit of genetic exchange, replacing the random cutting of one-dimensional gene sequences by traditional operators. The contiguous blocks generated through spatial region growing ensure that the exchanged gene fragments are adjacent and complete in real geographical space. This allows offspring schemes to fully inherit continuous functional zones from their parents, ensuring the spatial continuity and integrity of ecological protection zones, urban construction zones, and farmland protection zones. The generated schemes strictly conform to the spatial morphology rules of national land spatial planning, thus fundamentally solving the spatial fragmentation problem of traditional crossover operators.

[0008] Secondly, through a combination of holistic replication and precise coverage in the exchange model, the rational local spatial structures validated by natural selection in the parent generation's scheme can be directly and completely passed on to the offspring. This inheritance is not a fragmented splicing of gene segments, but a complete transplantation of spatial functional areas, which greatly improves the initial quality of individual offspring and achieves the efficient inheritance of the parent generation's superior spatial characteristics.

[0009] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0010] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 An exemplary flowchart of a spatial adjacency block crossover operator generation method provided in an embodiment of this application.

[0012] Figure 2 Provided for the embodiments of this application Figure 1 An exemplary flowchart of the sub-step S104.

[0013] Figure 3 Provided for the embodiments of this application Figure 2 An exemplary flowchart of the sub-step S1042.

[0014] Figure 4 An exemplary flowchart of the land spatial planning scheme optimization method provided in the embodiments of this application.

[0015] Figure 5 Another exemplary flowchart of the land spatial planning scheme optimization method provided in the embodiments of this application. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0017] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0018] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this application, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0019] It should be noted that in this paper, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0020] The following detailed description of some embodiments of this application is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0021] As one implementation, this application provides a method for generating spatial adjacency block crossover operators. Please refer to [link to relevant documentation]. Figure 1 The method includes: S102, select the first parent individual and the second parent individual from the population of land space planning schemes that meet the hard constraints of planning. The first parent individual and the second parent individual are both one-dimensional integer chromosomes with a length equal to the total number of planning units M. Each element in the chromosome corresponds to the use code of a planning unit. The planning units include rigid constraint units and non-rigid constraint units. Randomly select a planning unit from the non-rigid constraint units as the seed unit.

[0022] S104, starting from the seed unit, uses the spatial region growth method to generate geographically continuous and internally homogeneous spatial continuous blocks according to the preset growth scale. The growth scale is determined based on the planning area scale.

[0023] S106, extract all the usage codes corresponding to the spatially contiguous blocks in the first parent individual as the first gene fragment, copy it as a whole and cover the corresponding gene loci in the second parent individual, while the remaining gene loci in the second parent individual remain unchanged, and generate the first offspring individual.

[0024] S108: Extract all usage codes corresponding to the spatially contiguous blocks in the second parent individual as the second gene fragment, copy it as a whole and cover the corresponding gene loci in the first parent individual, while keeping the remaining gene loci of the first parent individual unchanged, and generate the second offspring individual.

[0025] Understandably, this application transforms the gene exchange unit in the genetic algorithm from traditional random gene fragments into spatially continuous blocks defined by actual plot contiguous relationships based on geographical spatial continuity. This allows locally spatial structures that were originally rationally laid out and functionally complete in the parent generation, such as contiguous ecological protection areas, interconnected construction clusters adjacent to town centers, and concentrated high-standard farmland, to be replicated and migrated as a whole during the crossover process. This avoids the problem of spatial fragmentation and achieves efficient inheritance of the high-quality spatial characteristics of the parent generation.

[0026] In the specific implementation process, it is necessary to select two high-quality parent individuals from the population of land spatial planning schemes that meet the hard constraints of planning, and randomly select one of them as the starting point from the plots that can be flexibly adjusted, so as to ensure that the cross-operation is carried out on a legal, feasible and realistic spatial basis from the beginning.

[0027] It should be understood that the population of land spatial planning schemes mentioned in this application refers to a set of multiple planning schemes, each of which is different. However, land spatial planning must have certain hard constraints. For example, planning units located within the ecological protection red line have their use codes fixed as ecological protection uses; planning units located within the permanent basic farmland boundary have their use codes fixed as agricultural planting uses; the codes of rigidly constrained units remain unchanged during genetic operations. In this application, each planning scheme is a one-dimensional array with a length equal to the total number of planning units, and each element in this one-dimensional array corresponds to the use code of a planning unit. For example, the coding rules are explicitly stated as follows: 1 represents ecological protection, 2 represents permanent basic farmland, 3 represents urban construction, and 4 represents general agriculture, and the code value strictly matches the set of permitted uses of the planning unit.

[0028] Furthermore, planning units include rigidly constrained units and non-rigidly constrained units. A rigid planning unit is one that must be used for a specific purpose, while a non-rigidly constrained unit is one whose purpose can be adjusted. For example, if an area is rigidly designated as an ecological protection zone, the corresponding planning unit is a rigidly constrained unit, and its code must be 1. Alternatively, if the function of an area is not limited, the corresponding planning unit is a non-rigidly constrained unit, and its code can be changed according to the plan. For example, setting its code to 1 means the area is designated as an ecological protection zone, setting it to 4 means the area is designated as an agricultural zone; of course, it can also be set to 5 or 6, etc., so that the area is designated as other functional zones, which is not limited here.

[0029] Based on this, the one-dimensional integer chromosome described in this application represents a one-dimensional array. Furthermore, for the population of land spatial planning schemes, the positions of 1 and 2 in the included planning schemes are fixed and identical, while the encodings of the remaining non-rigid constraint units differ. For example, the one-dimensional integer chromosome of planning scheme 1 is represented as 11223344…, and the one-dimensional integer chromosome of planning scheme 2 is represented as 11224343….

[0030] Furthermore, the population of land and space planning schemes includes multiple planning schemes, such as 200 planning schemes. It is necessary to select the first parent individual and the second parent individual from among them. The first parent individual and the second parent individual represent two of the 200 planning schemes.

[0031] Furthermore, in selecting the first and second parent individuals, this application does not use random selection. Instead, it first conducts a fitness assessment of the entire population to eliminate all schemes that do not meet the hard constraints. Then, it uses a binary tournament selection method, that is, it randomly selects two individuals each time for comparison, and keeps the one that is better. This process is repeated until a pair of first and second parent individuals that both meet the requirements of fixed unit use of 1 within the ecological protection red line and fixed unit use of 2 within the permanent basic farmland boundary are selected.

[0032] Next, the system generates offspring individuals through the first and second parent individuals. During this process, the system excludes rigidly constrained units (units within ecological protection red lines and permanent basic farmland) from all planning units, and selects a non-rigidly constrained unit as the seed unit using uniform random sampling. The sampling range covers all non-rigidly constrained units, ensuring sampling randomness and representativeness. That is, the uniform random sampling described in this application ensures that each non-rigidly constrained unit has an equal chance of being selected, without bias towards urban peripheries or remote mountain areas, ensuring that the subsequently generated spatial contiguous blocks are geographically representative and do not systematically omit certain regional types.

[0033] It should be noted that the combined action of selecting parent and seed units provided in this application essentially defines a double safety zone for subsequent spatial block growth: the first layer of safety comes from the parents themselves, which have undergone rigorous constraint verification to ensure that the purpose of each rigidly constrained unit is unbreakable. The second layer of safety comes from the seed location, which can only fall within non-rigidly constrained units. Starting from the seed unit, it naturally avoids all untouchable red lines and farmland boundaries, and will not be forced to cross lines, exceed boundaries, or forcibly cut functional areas during the growth process. Through this implementation method, the entire intersection process always operates on a real and feasible land management logic, rather than being a pure algorithmic deduction.

[0034] It is evident that this application embeds the rigid bottom-line requirements of planning management into the operation entry point of the genetic algorithm in advance, so that the generation and exchange of all subsequent spatial structures automatically inherit the legitimacy and rationality of the real world.

[0035] When determining spatially contiguous blocks, starting from a seed unit, a spatial region growing method is used to generate geographically contiguous blocks with homogeneous internal attributes, based on a preset growth scale. For one implementation method, please refer to [link / reference needed]. Figure 2 S104 includes: S1041, Determine the target number of planning units contained in a spatially continuous block based on the scale of the planning area.

[0036] S1042, starting from the seed unit, iteratively incorporates adjacent units that share the same edge or angle with the current spatial block through the spatial region growth method until the number of planning units contained in the spatial contiguous block reaches the target number; wherein, the comprehensive attribute similarity between each adjacent unit to be incorporated and the current spatial contiguous block is greater than a threshold.

[0037] And, please see Figure 3 The steps in S1042 include: S1042-1, for each adjacent unit to be included, normalization is performed based on topographic slope, soil type, and current land use indicators.

[0038] S1042-2 uses the absolute value method to calculate the similarity of each indicator.

[0039] S1042-3, determine the comprehensive attribute similarity based on the set weights and the similarity of each indicator.

[0040] S1042-4, neighboring units with a comprehensive attribute similarity greater than a threshold are included in the current spatial contiguous block until the number of planning units contained in the spatial contiguous block reaches the target number; wherein, when the number of planning units contained in the spatial contiguous block is insufficient, the threshold is reduced.

[0041] This application can be understood as starting with a selected planning unit and gradually incorporating other geographically adjacent planning units (including those sharing the same side or corner) into the surrounding area. As it grows, it is also selected based on conditions, ultimately forming a continuous area that is geographically connected and has similar internal natural conditions and land use characteristics.

[0042] It should be understood that this process is not arbitrary expansion, but rather has clear objectives and selection rules. First, the size of this spatial contiguous block needs to be determined, that is, how many planning units it should contain; this number is determined based on the size of the entire planning area. For example, if the planning area does not exceed 500 square kilometers, the spatial contiguous block should contain 10% to 15% of the total number of planning units; if the area is between 500 and 2000 square kilometers, it should be 7% to 12%; and if it exceeds 2000 square kilometers, it should be 5% to 10%. The purpose of this is to ensure that the generated spatial contiguous block is neither too large and distorted in small areas, nor too small and unrepresentative in large areas.

[0043] After determining the target number, growth begins from the seed unit. Initially, there is only one seed unit in the spatially contiguous block; then the system automatically searches for all adjacent units sharing edges or corners, forming the first batch of candidates. For each candidate adjacent unit, its performance in three aspects is examined: terrain slope, soil type, and current land cover. These three indicators are first normalized and mapped to a uniform value between 0 and 1. The terrain slope is stretched linearly; the soil type is artificially quantified into a value between 0 and 1 according to its agricultural or ecological suitability level; and the current land cover is assigned a higher score and a value between 0 and 1 based on its functional relevance, such as all being residential land or all being ecological forest land.

[0044] In this process, the similarity is calculated separately for each indicator. The indicator value of the adjacent unit is taken as the difference between the average value of all existing units in the current spatial block for that item, and the absolute value is taken. Then, this difference is subtracted from 1. The result is the similarity of that item, expressed as: Single indicator similarity = 1 - |Indicator value of the unit to be evaluated - Average indicator value of units in the spatial block|. Therefore, the closer the indicator value is to the average value, the closer the calculated similarity is to 1, indicating a greater similarity; the greater the deviation, the lower the similarity. Next, the similarity of the three indicators is multiplied by their corresponding weights. For example, the weight of terrain slope is 0.3, the weight of soil type is 0.3, and the weight of existing land cover is 0.4. These are added together to obtain a comprehensive attribute similarity, which also ranges from 0 to 1, i.e., Comprehensive similarity = (Slope similarity × 0.3) + (Soil type similarity × 0.3) + (Existing land cover similarity × 0.4).

[0045] Finally, adjacent units with a comprehensive attribute similarity greater than a threshold are included in the current spatial contiguous block until the number of planning units contained in the spatial contiguous block reaches the target number. By determining the comprehensive attribute similarity, it can be ensured that the adjacent units included in the current spatial contiguous block are a completely connected whole with the seed unit, and that their internal attributes are relatively uniform.

[0046] Specifically, when incorporating adjacent units with a comprehensive attribute similarity greater than a threshold into the current spatial contiguous block, priority is given to including adjacent units with a comprehensive attribute similarity greater than or equal to the first threshold. If the number of adjacent units meeting the conditions is insufficient, then adjacent units with a similarity lower than the first threshold but greater than or equal to the second threshold, as well as adjacent units with a similarity lower than the second threshold, are included in sequence until the number of planning units contained in the spatial contiguous block reaches the target number. The first threshold is greater than the second threshold.

[0047] For example, if the first threshold is set to 0.7 and the second threshold is set to 0.5, then adjacent units with a comprehensive attribute similarity greater than or equal to 0.7 will be prioritized for inclusion in the spatially contiguous block. If the target number is still insufficient, the criteria will be relaxed, and units with similarity between 0.5 and 0.7, or even below 0.5, will be included until the total number of units in the block reaches the predetermined target number. It should be noted that the entire growth process is always subject to two hard constraints: first, it cannot cross the boundaries of rigid constraint units that are not allowed to be cut, such as the basic farmland protection boundary or important ecological corridors; second, it must ensure that the final block is a complete and connected whole on the map, without any breaks, enclaves, or isolated islands.

[0048] It is evident that when this application grows spatial contiguous blocks, it takes into account the requirement of geographical spatial continuity, controls internal homogeneity through multi-dimensional attribute similarity, and ensures the accessibility of growth scale by dynamically adjusting the similarity threshold. This allows the generated spatial contiguous blocks to not only truly reflect the regional natural and land use characteristics, but also adapt to the actual needs of planning tasks at different scales.

[0049] When generating offspring individuals, this application generates two new offspring individuals by swapping the positions of the entire usage codes corresponding to the same geographical area in the two parent individuals. This not only preserves the integrity of their original structures but also achieves the block migration of high-quality spatial layout features.

[0050] It should be noted that the parent and offspring individuals described in this application are essentially planning schemes represented by a string of numerical codes. Each code corresponds to the land use of a planning unit on the map, such as 5 representing residential land, 6 representing commercial land, and 7 representing green space. The spatially contiguous blocks described in this application refer to the geographically connected areas with relatively similar internal attributes generated earlier. In chromosome coding, this spatially contiguous block is mapped to combinations of gene loci (i.e., combinations of elements within an array). The positions of these gene loci combinations in the coding string are fixed and locatable.

[0051] Specifically, when generating the first offspring individual, the system first finds the gene segment in the first parent individual that completely corresponds to the spatial contiguous block (this segment may be contiguous or non-contiguous in the array), extracts all the usage codes on this segment, and forms a complete gene fragment. Then, the system finds the gene segment in the second parent individual that is exactly the same, and directly overwrites it with the extracted gene fragment. Furthermore, this application only replaces the usage codes in this region of the second parent individual; the codes at all other positions remain unchanged. After the overwrite is completed, the first offspring individual is obtained. Similarly, when generating the second offspring individual, the system operates in reverse: it extracts all the usage codes at the corresponding positions of the spatial contiguous block from the second parent individual as another complete gene fragment, then copies this fragment and overwrites it with the gene segments at the same positions in the first parent individual. The usage codes at other positions in the first parent individual remain unchanged, thus obtaining the second offspring individual.

[0052] During this process, both overlays strictly adhere to the principles of precise alignment and local replacement, meaning that encoding swaps are performed only between positions corresponding to the same spatially contiguous block in the two parent individuals, without changing the encoding order or values ​​of any other regions. It should be noted that after each swap, the system automatically records the origin of each gene segment in each offspring individual, for example, marking a gene segment as originating from the first parent individual and another from the second parent individual. This allows for clear identification of which desirable layout features were inherited from which parent when evaluating the fitness of offspring individuals later.

[0053] In summary, the exchange method provided in this application differs from the random crossover approach in traditional genetic algorithms. Instead, it moves entire blocks as units of spatial contiguous blocks. This avoids disrupting the original coordinated spatial functional combinations and efficiently transfers high-quality local layout patterns that have been proven in practice, thereby improving the stability and practicality of the planning scheme optimization process.

[0054] Based on the above implementation method, this application also provides a method for optimizing land spatial planning schemes. Please refer to [link to relevant documentation]. Figure 4 and Figure 5The method includes: S201 uses superpixel segmentation technology to divide the planning area into several planning units with homogeneous internal attributes, and labels the geographical attributes and constraint types of each planning unit. Among them, planning units located within the ecological protection red line or permanent basic farmland boundary are labeled as rigid constraint units, and the rest are labeled as unconstrained units.

[0055] S202 generates an initial population consisting of N initial planning schemes; the number of initial planning schemes is determined based on the total number of planning units.

[0056] S203 assesses the suitability of each initial planning scheme.

[0057] S204, based on the evaluation results, adopts a combined strategy of binary tournament selection method combined with non-dominated ranking and crowding calculation to select N / 2 individuals from the current population to form a mating pool.

[0058] S205: Pair individuals in the mating pool into pairs, apply the spatial adjacency block crossover operator to each pair of parents to generate two offspring individuals, and perform mutation operations and feasibility checks on the offspring individuals.

[0059] S206: Merge the parent and offspring populations, select N individuals based on non-dominated sorting and crowding to form a new generation population, repeatedly evaluate the fitness of each planning scheme in the population, pair individuals in the mating pool to generate new offspring individuals, and perform mutation operations and feasibility verification on the offspring individuals until the preset iteration termination condition is met.

[0060] S207 extracts the Pareto optimal frontier individuals from the final population, decodes them into a spatial planning layout map, and outputs it.

[0061] In this application, an image processing technique called superpixel segmentation is used to divide the entire planning area into several small blocks of varying sizes, but with relatively consistent internal natural conditions and land use status. Each block is a planning unit, and at the same time as the segmentation, each block is given a clear geographical label and constraint identity.

[0062] It should be understood that the superpixel segmentation described in this application is not a simple grid-based image cutting, but rather an intelligent division based on real geographic information. The system first collects various basic data, including a Digital Elevation Model (DEM), land use maps, soil type maps, and vector maps of two types of legally protected boundaries: ecological protection red lines and permanent basic farmland. All of this data is unified to the 2000 National Geodetic Coordinate System, and the resolution is uniformly adjusted to a 30m x 30m grid. That is, the entire area is initially divided into small 30m square grids, each containing information such as topography, soil type, and land use type.

[0063] Specifically, before segmentation, the system extracts key geographic features from these basic data for each 30-meter grid, such as the slope, altitude, soil fertility level, current status (farmland or forest), and distance from the nearest town center. These features are aggregated to form a feature matrix representing each grid's identity. Then, based on this feature matrix, the system performs superpixel segmentation: first, an initial block size of approximately 50 meters x 50 meters is set; then, the feature similarity between adjacent grids is compared. If the overall similarity between two adjacent grids in terms of slope, soil type, etc., reaches or exceeds 0.8, they are merged into the same planning unit. This process is repeated until the entire area is segmented. Each resulting planning unit is an irregular polygon composed of several 30-meter grids, but the geographic features and current land use within the unit are generally similar, meaning the internal attributes are homogeneous.

[0064] During this process, the system also simultaneously labels each planning unit. On one hand, it records the basic geographical attributes of the unit, including the topographic relief, average slope, main existing land types, and soil types. On the other hand, it determines whether the unit falls within the legally protected area. If the planning unit spatially overlaps with the ecological protection red line vector map or the permanent basic farmland vector map, even if only partially, it is labeled as a rigidly constrained unit. Other planning units not falling within these two types of protection areas are uniformly labeled as unconstrained units. All these labeling results are stored in a dedicated unit attribute database for subsequent optimization algorithms to access.

[0065] Then, the system first determines how many planning units are divided in the planning area, and then decides how many initial planning schemes to generate based on this, thus forming a planning scheme candidate pool as the starting point for subsequent optimization algorithms; each scheme in this candidate pool has already met the basic requirements of legal constraints and superior land use indicators.

[0066] The initial population follows clear quantitative rules and strict quality control. The system first counts the total number of planning units in the entire planning area, denoted as M. Then, based on the size of M, it determines the final number of initial planning schemes to generate, i.e., the population size N. For example, if the total number of planning units does not exceed 1000, 50 initial schemes are generated; if it is between 1001 and 5000, 100 are generated; and if it exceeds 5000, 150 are generated. This design aims to ensure that the initial population covers a sufficiently diverse range of layout possibilities without wasting computational resources due to excessive size.

[0067] Specifically, each initial planning scheme is represented by a one-dimensional integer array of length M. Each position in the array corresponds to a planning unit, and the position number is exactly the same as the planning unit number. The values ​​in the array represent the land use assigned to that unit, such as 1 for ecological land, 2 for arable land, 3 for construction land, and 4 for other land use. This coding method is pre-defined. When filling in this array, the system will operate in three steps: First, the use of rigidly constrained units is directly locked. All planning units falling within the ecological protection red line area are fixedly coded as 1; all planning units falling within the permanent basic farmland area are fixedly coded as 2; the use of these units will not be changed. The second step involves randomly allocating the remaining unconstrained units based on their permitted uses according to their geographical conditions. For example, if an unconstrained unit has a slope exceeding 25 degrees or too thin a soil layer, making it unsuitable for housing or grain cultivation, the system will determine that it is only permitted for ecological use and will randomly select from code 1. Conversely, if another unit has flat terrain and fertile soil, it may be permitted to choose from 1 (ecological), 2 (arable land), or 3 (construction), and the system will randomly select one to fill in. The third step involves checking the total area of ​​all land uses in each initial plan to see if it meets the minimum and maximum control targets set by higher authorities. If a certain type of land use is too little or too much, the system will select no more than 5% of the total number of unconstrained units, readjust their use codes, and repeat the trial calculation until the plan meets all area targets.

[0068] In this process, each initial planning scheme is generated independently and verified one by one to ensure that it does not violate rigid boundaries or exceed the total land use control from the outset. It should be noted that all these operations are completed automatically by the program without human intervention, which not only ensures the legitimacy of the initial population but also lays a stable and reliable foundation for subsequent genetic optimization.

[0069] After generating N initial planning schemes, the fitness of each of the N initial planning schemes needs to be evaluated. For example, this application establishes a three-level fitness evaluation system of "constraint verification - target calculation - comprehensive scoring".

[0070] Specifically, the system will measure the actual performance of each initial planning scheme in the three core objectives of ecological protection, economic development and food security, and convert each performance into a specific score. Finally, the scores are weighted and summed into a total score, which serves as the fitness value of the scheme. This process is not a simple scoring, but rather a rigorous check to see if any red lines have been crossed before calculating the score item by item to ensure that each score corresponds to the actual spatial effect.

[0071] It's important to note that fitness assessment is not a subjective evaluation, but rather a repeatable and verifiable quantitative process. The system first interprets the plans, converting each initial planning scheme from a string of numerical codes into a realistic map layout, clearly defining the specific purpose and location of each planning unit. Then, two rounds of verification are immediately conducted: The first round is a hard constraint check, determining whether any legal bottom lines are violated. For example, are all units within the ecological protection red line truly designated as ecological land (code 1), are all units within the permanent basic farmland area designated as arable land (code 2), and is the total area of ​​all land use types within the limits set by higher authorities? If any of these criteria are not met, the scheme is directly deemed infeasible, its fitness value is set to 0, and it is excluded from subsequent scoring. If the hard constraint check is passed, the system further checks some soft constraints, such as whether urban construction land is contiguous and whether permanent basic farmland is concentrated in large areas. While these results are not immediately reset to zero, they are recorded for reference in subsequent comprehensive scoring. Among them, the connectivity of urban land use is calculated using the connectivity index, which is calculated as: connectivity index = number of connected urban units / total number of urban units; and the contiguous rate of permanent basic farmland = area of ​​contiguous farmland plots / total farmland area.

[0072] After confirming the legality and feasibility of the plan, the system calculates the ecological security objective function value, the economic development objective function value, and the food security objective function value respectively. The ecological security objective function value is F_1 = Σ(E_i × X_i1), where E_i is the ecological value index of the i-th unit and X_i1 is the indicator variable; The economic development objective function value is F_2 = Σ(D_i / C_i × X_i3), where D_i is the development potential index of the i-th unit and C_i is the distance from the i-th unit to the nearest town center; The objective function value for food security is F_3 = Σ(A_i × X_i2), where A_i is the agricultural suitability index of the i-th unit, and X_i2 and X_i3 are indicator variables.

[0073] Here, E_i is calculated based on the vegetation cover (Normalized Difference Vegetation Index, NDVI) obtained from satellite remote sensing and local biodiversity data. The higher the value, the more important the ecological function. The value ranges from 0 to 10. X_i1 is equal to 1 only when the unit is indeed set for ecological use; otherwise, it is 0. Finally, the products of all units are added together to obtain the ecological security objective function value F_1, which intuitively reflects how much high ecological value land this scheme protects. The economic development objective function value F_2 is calculated by dividing the development potential index D_i (which is derived from factors such as location and transportation convenience, and also ranges from 0 to 10) of each planning unit designated for urban construction by its actual distance C_i (in kilometers) from the nearest town center. The closer the distance and the higher the potential, the larger this ratio becomes. Then, a use label X_i3 is multiplied (which is 1 only when the unit is actually used for urban construction). Finally, the ratios of all such units are summed to obtain F_2, which reflects the extent to which the plan places construction activities in locations that are both suitable for development and close to existing towns. The third item is the food security objective function value F_3, which is calculated in a similar way to the first item: for each planning unit that is allocated for agricultural use (including permanent basic farmland and general agricultural land), multiply its agricultural suitability index A_i (this index is determined by soil fertility, irrigation water security, etc., and also takes values ​​from 0 to 10) by the use label X_i2 (1 when the unit is used for agriculture, and 0 otherwise), and then sum up the results of all units to get F_3, which reflects how much high-quality farmland this plan actually uses for grain planting or agricultural production.

[0074] In this process, the three function values ​​are calculated independently without interfering with each other, but their physical meanings are clearly corresponding: F_1 represents how much good ecology has been preserved, F_2 represents how rationally the construction was carried out, and F_3 represents how solidly the planting was carried out. It should be noted that these three scores are not simply added together, but are synthesized using a weighted TOPSIS method. That is, based on the development positioning of this planning area, different weights are assigned to each objective. For example, in ecological priority areas, F_1 ​​accounts for 40%, and F_2 and F_3 each account for 30%. After the weights are determined, the system will recalculate the three scores of each scheme according to their weights, and then standardize them by combining the score distribution of all schemes, ultimately generating a comprehensive fitness score between 0 and 100. This score is based on real geographical data and clear usage judgments for each item, ensuring that the optimization direction selected by the algorithm always closely aligns with the core objectives of national land space governance.

[0075] It is evident that the adaptability assessment mechanism provided in this application not only safeguards the bottom line but also takes into account development needs and the foundation of people's livelihood, transforming abstract planning goals into measurable, comparable, and traceable spatial performance indicators.

[0076] Subsequently, based on the evaluation results, parent individuals are selected. In this embodiment, a composite selection method of first dividing into tiers and then comparing characteristics is adopted to select half of the high-quality individuals from all current planning schemes to form a mating pool. This ensures that the selected schemes perform well overall and prevents the parent individuals from having too similar layout ideas in the three objectives of ecology, economy and food, thus reserving sufficient optimization space for subsequent cross-mutation.

[0077] It should be understood that the "high quality" described in this application does not solely rely on a single total score, but rather comprehensively considers three mutually constraining objectives: the ecological security objective function value F_1, the economic development objective function value F_2, and the food security objective function value F_3. The system first performs a non-dominated ranking: if a planning scheme is significantly better than another scheme in at least one of the three scores, and the other two are not worse, then it dominates the latter; all schemes not dominated by any other scheme are assigned to Front 1 level, which is the optimal tier; among the remaining schemes, those dominated only by Front 1 schemes but not by other schemes are assigned to Front 2 level; and so on, forming multiple frontier levels from best to worst. This classification method does not rely on a weighted total score and can truly reflect the trade-offs between multiple objectives.

[0078] Furthermore, within the same frontier level, the system also calculates the crowding degree of each planning scheme. This value is measured in a three-dimensional target space comprised of the ecological security target function value, the economic development target function value, and the food security target function value. That is, for individuals within the same frontier level, their crowding degree in the three target spaces is calculated: crowding degree = Σ (difference in target values ​​between adjacent individuals in each target dimension). A higher crowding degree indicates a more unique distribution of the individual in the target space. For each scheme, the score difference between it and the two nearest individuals in each target dimension is examined, and the sum of these three differences is its crowding degree. For example, if a scheme has a particularly high ecological score, a moderate economic score, and a low food score, and no other schemes fall into a similar position, its crowding degree is high; conversely, if a group of schemes are concentrated in the area of ​​moderate ecology, high economy, and low food, and are very close to each other, their individual crowding degrees are low. A higher crowding degree indicates that the planning logic represented by this scheme is more unique and irreplaceable.

[0079] During this process, the system executes a binary tournament selection: each time, two planning schemes are randomly selected from the current population for comparison. The scheme with a higher frontier rank (e.g., Front 1 beats Front 2) wins; if both belong to Front 1, crowding is compared, and the one with greater crowding wins. This process is repeated until half the total number of planning schemes (i.e., N / 2) are selected to form the mating pool. It should be noted that the entire selection process is completely automated, without human intervention, and each round of comparison is based solely on objectively calculated three function values ​​and spatial distribution characteristics, ensuring that the final selected parent individuals are both competitive and representative.

[0080] In summary, the composite selection strategy provided in this application effectively avoids the bias caused by traditional single-index screening, enabling the algorithm to identify truly coordinated and balanced high-quality solutions while retaining differentiated planning ideas, thus providing a reliable foundation for generating more scientific and robust spatial optimization results.

[0081] After forming the mating pool, it is necessary to generate offspring using the mating pool. This application pairs the planning schemes in the mating pool into two groups, and then performs a whole-block exchange on each parent scheme using the aforementioned spatial adjacency block cross operator generation method, generating two new schemes first. Then, two types of lightweight adjustments are made to these two new schemes: fine-tuning the use at the individual unit level and adjusting the boundaries at the area level. Finally, a unified check is performed to ensure that they still meet the legal bottom line requirements, ensuring that each generated offspring scheme is both novel and compliant.

[0082] It should be understood that the mating pool is a collection of N / 2 high-quality planning schemes with different styles selected in the previous step. These schemes are first sorted from highest to lowest frontier priority, and then randomly paired up within the same priority level. For example, if there are 10 schemes in Front 1, they are randomly paired into 5 pairs; if there are 8 schemes in Front 2, they are randomly paired into 4 pairs. The purpose of this is to allow schemes of similar quality but different approaches to learn from each other, avoiding the dilution of high-quality resources due to significant disparities in strength.

[0083] Specifically, for each pair of parent individuals, the system directly calls the spatial adjacency block crossover operator generation method described above: first, it identifies a geographically continuous spatially contiguous block with relatively homogeneous internal attributes in each parent scheme (the location and composition of this block are completely identical in both parents); then, it extracts all the usage codes corresponding to this block in the first parent and overwrites the corresponding position in the second parent to generate the first child individual; then, it extracts all the usage codes of this block in the second parent and overwrites the corresponding position in the first parent to generate the second child individual. In this way, each pair of parents stably produces two new schemes with complementary structures and interchangeable local features, generating a total of N child individuals.

[0084] During this process, the system will further perform two mutation operations on these N offspring individuals. With the first mutation probability, a non-rigidly constrained unit is randomly selected, and its usage encoding is randomly flipped within its set of allowed uses to another allowed use; With a second mutation probability higher than the first mutation probability, a spatial cluster of urban land or ecological land is randomly selected, and a sprawl operation or a shrinkage operation is performed; the sprawl operation is to expand a set number of units to the adjacent unconstrained units of the selected cluster, and the shrinkage operation is to remove a set number of units from the edge of the selected cluster.

[0085] The aforementioned mutation operation only applies to non-rigidly constrained units, that is, those units that are not within the ecological protection red line or the permanent basic farmland area. The micro-unit use reversal mutation is performed with a probability between 0.01 and 0.05 (a higher value of 0.05 is used when the current population diversity is low, and a lower value of 0.01 is used when it is high). Some units are randomly selected and their current use codes are changed to one of the other uses allowed by the unit (for example, a unit with a steep slope that only allows ecological use can only be changed to an ecological code; while a flat and fertile unit that allows ecological, arable land, and construction can be used, one of these can be randomly changed), ensuring that the adjustment always falls within a reasonable range. Macro-morphological spread or contraction variations are specifically designed for clusters of urban or ecological land that have already formed a continuous area: with a probability between 0.1 and 0.2, a spread operation is randomly performed on the cluster to occupy 1 to 2 more adjacent unconstrained units, or a contraction operation is performed to remove 1 to 2 units from the edge. Regardless of the method, it must be ensured that the cluster remains a geographically continuous whole on the map after the operation, without any breaks or enclaves.

[0086] It should be noted that the mutation operation is optional. That is, after generating two offspring individuals, if the offspring individuals perform well and the population diversity is good according to the fragmentation score, then the mutation operation is not necessary. If the population diversity of the offspring is poor or moderate according to the fragmentation score, then the mutation operation is performed.

[0087] It should be noted that after all mutations are completed, the system immediately performs hard constraint checks on each offspring individual, focusing on verifying whether the unit use within the ecological protection red line and permanent basic farmland area is still strictly locked (the former must be ecological code 1, and the latter must be arable land code 2), and whether the total area of ​​various land uses is still within the upper and lower limits of the indicators issued by the superior. If any condition is found to be violated, the offspring individual will be removed and will not enter the subsequent process. This verification does not pursue perfection, but rather maintains the minimum threshold of feasibility, leaving a reliable foundation for subsequent multiple iterations.

[0088] It is evident that this offspring generation mechanism, which prioritizes cross-fertilization, supplements it with variation, and relies on verification, is not a blind restart, but rather a directional, measured, and guaranteed process that promotes the continuous evolution of planning schemes while respecting spatial logic and legal constraints.

[0089] Furthermore, after generating offspring, it is necessary to combine the parent and offspring generations to select a new generation of population. This involves comparing the previous generation's planning schemes with the newly generated ones, and then selecting the N best-performing and most diverse schemes as the next generation population. The best-performing schemes are consistently retained. This entire process of evaluation, selection, crossover, and mutation is repeated continuously to achieve elite retention and iteration until the optimization results are sufficiently stable or a predetermined number of rounds are reached. It should be understood that the elite preservation described in this application does not simply involve passing the best solutions from the previous generation to the next generation unchanged. Instead, it employs a more robust merging and selection mechanism. The system first puts all N parent individuals from the previous generation and N newly generated child individuals together to form a temporary population containing 2N solutions. Then, these 2N solutions are re-ranked non-dominated, that is, they are again divided into different tiers such as Front 1 and Front 2 based on their performance in three aspects: ecological security objective function value, economic development objective function value, and food security objective function value. Front 1 is the optimal set of solutions that has not been comprehensively surpassed by any other solution. Based on this, the system prioritizes retaining all individuals in Front 1; if the number of solutions in Front 1 is exactly equal to N, then all of them are selected directly; if it is less than N, then the solutions are filled from Front 2 in descending order of crowding; if Front 1 itself has more than N individuals, then only the top N with the highest crowding are selected. This ensures that each generation contains at least the current best solution, and also prevents high-quality solutions from excessively crowding out slots due to internal homogenization.

[0090] After selecting the new generation of population, the system immediately initiates the next complete iteration: First, it recalculates the three objective function values ​​for each planning scheme and performs hard constraint verification to obtain a new fitness score; then, using a binary tournament combined with non-dominated sorting and crowding, it selects N / 2 individuals from the population to form a new mating pool; next, it pairs individuals in the mating pool, calls the spatial adjacency block crossover operator to generate N offspring individuals, and performs micro-unit use-flipping mutation and macro-morphological spread or contraction mutation on each offspring; finally, it performs hard constraint verification on all mutated offspring and eliminates obviously non-compliant schemes. This closed-loop process will be executed repeatedly until the set exit conditions are met.

[0091] Throughout this process, the system continuously monitors two termination signals: one is the preset maximum number of iterations, G_max, which is set according to the accuracy requirements of the planning task. For example, it is set to 200 to 300 iterations when making detailed layouts for key ecological functional areas, and 100 to 200 iterations when making preliminary scheme comparisons for general areas. The other is whether the average fitness improvement of the Front 1 edge over 50 consecutive iterations is less than a set value (0.1% to 0.3%, with the upper limit for complex areas and the lower limit for simple areas). Once it is found that there is almost no improvement over 50 consecutive iterations, it is considered that the algorithm has converged to the vicinity of a stable and high-quality solution, and the iteration is actively stopped. It should be noted that only one of these two termination conditions needs to be met to end the process, avoiding unnecessary idle cycles and ensuring that the results have both sufficient exploration depth and practical operability. For example, if the maximum number of iterations G_max is set to 200 and the set value ε is 0.1%, when iterating to the 168th generation, the average fitness improvement of the Front 1 edge over 50 consecutive iterations is 0.08% < 0.1%, which meets the termination condition, and the iteration stops.

[0092] This shows that the iterative mechanism is not blind trial and error, but rather adheres to the bottom line, respects spatial logic, preserves high-quality resources at every step, and judges when to stop in a quantifiable and verifiable way, so that the entire optimization process is scientific, robust and engineering practical.

[0093] This embodiment can be understood as follows: from the population after the final iteration, all planning schemes that have not been completely surpassed by other schemes are selected to form a set of high-quality schemes. Then, they are compared and ranked horizontally according to actual planning needs. Finally, each scheme is restored into an understandable map and equipped with various key indicator data for decision-makers to choose intuitively.

[0094] It should be understood that the Pareto optimal frontier individuals mentioned in this application are not a single "unique optimum," but rather refer to a set of schemes in the final population that are mutually exclusive in terms of the three objective functions of ecological security, economic development, and food security. For example, scheme A scores higher in ecological protection but has slightly lower food yield; scheme B has better food yield but slightly weaker ecological value; since neither is dominant, they both belong to Front 1, which is the Pareto optimal frontier. After the system terminates its iteration, it first extracts all Front 1 individuals to form a set of Pareto optimal planning schemes. Each scheme in this set represents a high-quality spatial layout possibility under different trade-offs.

[0095] Specifically, after generating this set of schemes, the system does not directly output one randomly, but further conducts a multi-dimensional evaluation: on the one hand, it verifies the implementation of hard constraints for each scheme, such as whether all areas within the ecological protection red line are ecological land, whether all areas within the permanent basic farmland are arable land, and whether the total area of ​​various types of land use is within the upper and lower limits of the indicators issued by the higher authorities; on the other hand, it calculates the degree of compliance with soft constraints, such as whether urban construction land is contiguous, whether permanent basic farmland is concentrated in large areas, and whether ecological land forms an effective network; at the same time, it records the three target function values ​​and comprehensive fitness score for each scheme. This information is then compiled into a complete scheme evaluation report. Next, the system prioritizes these schemes based on the focus of this planning task. If the region is positioned as an ecological priority area, it is ranked from highest to lowest according to the F_1 score; if it is a key urban development area, F_2 is emphasized; if it is a major grain-producing county, F_3 is highlighted. This ranking method is flexible and adjustable, and does not fixate on a single standard.

[0096] During this process, the system decodes each Pareto optimal solution after ranking them: that is, it restores the planning scheme, originally represented by a string of numerical codes, into a distribution map on the real geographic space. The map clearly marks the specific boundaries and area values ​​of each type of land use (such as ecological land, cultivated land, and urban construction land areas), as well as the key quantitative results corresponding to the scheme, including the ecological security objective function value F_1, the economic development objective function value F_2, the food security objective function value F_3, the comprehensive fitness score, and auxiliary indicators such as hard constraint satisfaction rate and soft constraint compliance rate. All these maps and data are output synchronously, which not only allows planners to see the spatial pattern at a glance, but also supports professional comparison and compliance review.

[0097] It is evident that this output mechanism does not simply provide a result in a cross-tabulation manner, but rather offers a set of high-quality options that have been thoroughly explored, are complementary to each other, and are all legally feasible. These options are presented in a way that combines spatial visualization and quantitative indicators, thus meeting the practical needs of multi-party consultation.

[0098] The optimization method for the territorial spatial planning scheme provided in this application has at least the following beneficial effects: 1. Solved the spatial fragmentation problem of traditional crossover operators: This application uses geographically continuous spatial blocks as gene exchange units, avoiding spatial regional fragmentation caused by random gene splitting, ensuring the continuity of functional areas such as ecological protection, urban construction, and farmland protection in the offspring scheme, and conforming to the spatial morphology rules of national land spatial planning (such as prohibiting urban units from being isolated by ecological units and encouraging the distribution of farmland in patches).

[0099] 2. Achieve efficient inheritance of high-quality spatial features from the parent generation: Through the overall exchange of block genes, the reasonable spatial layout of the parent generation (such as continuous ecological protection areas and well-connected urban clusters) is directly passed on to the offspring generation, avoiding the loss of high-quality spatial structures in the genetic iteration and improving the basic quality of the offspring scheme.

[0100] 3. Balancing population diversity and solution feasibility: While ensuring spatial continuity, new gene combinations are introduced by exchanging different parent space blocks to enrich population diversity. At the same time, infeasible solutions are avoided, reducing the computational cost of subsequent optimization and improving the overall optimization efficiency of the algorithm.

[0101] 4. High adaptability: It can be directly integrated into multi-objective land spatial planning optimization systems based on genetic algorithms (such as NSGA-II) without reconstructing the overall algorithm framework. The technology can be upgraded simply by replacing the crossover operator. It is suitable for land spatial planning scenarios of different scales and regions.

[0102] The following section uses a specific planning area as an example to provide a detailed description of the specific implementation method provided in this application. The total area of ​​this planning area is 2000 km², and it is necessary to balance three major goals: ecological protection (with a 50 km² ecological protection red line within the area), economic development (prioritizing the guarantee of 80 km² urban construction land indicators), and food security (400 km² permanent basic farmland indicators). The proposed method is used to optimize the scheme.

[0103] Planning Unit Preprocessing: 1. Basic Data Collection: Collect the 1:10,000 digital elevation model (DEM) of the county-level planning area, the 2024 land use status map, soil type distribution map, ecological protection red line vector data (50km²), permanent basic farmland vector data (400km²), urban built-up area boundary map, etc., using the 2000 National Geodetic Coordinate System as the unified coordinate system, and a raster resolution resampling of 30m; 2. Geographic Feature Extraction: Calculate the terrain slope and altitude based on the DEM, extract soil fertility level based on the soil type map, determine the current land use type based on the land use status map, calculate the distance from each raster to the town center based on the urban built-up area boundary map, and construct a 5-dimensional geographic feature matrix; 3. 1. Improved SLIC superpixel segmentation: The initial superpixel size is set to 50m×50m. With the geographic feature matrix as a constraint, the feature similarity of adjacent rasters is calculated (slope weight 0.3, soil fertility weight 0.3, current land type weight 0.4). Rasteres with feature similarity ≥0.8 are merged, and the 1500km² planning area is finally divided into M=3000 homogeneous planning units, each with an area of ​​0.5km². 4. Unit attribute labeling: Through spatial overlay analysis, 200 units within the ecological protection red line and 800 units within the permanent basic farmland are identified as rigidly constrained units, and the remaining 2000 are unconstrained units. An attribute database containing unit number, geographic attribute, and constraint type is established.

[0104] Population Initialization: 1. Population Size Setting: Since M=3000 (1000<M≤5000), the population size N=100; 2. Chromosome Encoding: Each planning scheme is encoded as a one-dimensional integer array of length 3000. The array index 0-2999 corresponds to 3000 planning units. The encoding rules are: 1=ecological protection, 2=permanent basic farmland, 3=urban construction, 4=general agriculture; 3. Constraint Adaptation Initialization: 200 ecological red line units are fixed as coded as 1, 800 permanent basic farmland units are coded as 2, and for 2000 unconstrained units, codes are assigned according to the permitted use set (e.g., non-constrained units with slope > 25°). The set of permitted uses for constrained units is {1}, which can only be coded as 1; the set of permitted uses for unconstrained units with a slope ≤25° and high soil fertility is {2, 4}, which can be coded as 2 or 4); 4. Pre-adjustment of quantity constraints: The land use indicators issued by the superior are 80km² for urban construction land (corresponding to 160 units), ≥50km² for ecological protection land (corresponding to ≥100 units), and ≥400km² for farmland land (corresponding to ≥800 units). The number of land use units for each scheme after the initial allocation is counted. For schemes that do not meet the indicators or exceed the indicators, the codes of ≤5% of the unconstrained units are adjusted. Finally, all 100 initial schemes meet the land use indicator requirements.

[0105] Fitness assessment: 1. Scheme decoding: The chromosome codes of 100 initial schemes are parsed into spatial planning schemes to clarify the purpose and spatial distribution of each unit. 2. Constraint Verification: All initial schemes meet the hard constraints (fixed use of red lines and farmland units, and land area meets standards); the soft constraint verification results show that the urban land connectivity index is between 65% and 75%, and the contiguous rate of permanent basic farmland is between 70% and 80%. 3. Objective Function Calculation: Calculate the F_1, F_2, and F_3 values ​​for each scheme, where E_i, Di_i, and A_i are quantified using a 1-10 scale (e.g., a unit with an ecological value index E_i=8 indicates high ecological value). For example, the initial scheme has F_1=78, F_2=65, and F_3=80. 4. Comprehensive Fitness Score: This county-level region is a region of coordinated ecological and economic development. F_1 weights are set to 0.35, F_2 weights to 0.35, and F_3 weights to 0.3. The weighted TOPSIS method is used to calculate the comprehensive fitness value. The fitness value of the example scheme is 74.2. 5. Non-Dominated Ranking and Crowding Calculation: Divide the 100 initial schemes into Fronts. Front 1 (15 individuals), Front 2 (25 individuals), Front 3 and beyond (60 individuals), calculate the crowding degree of individuals in Front 1, and select the top 10 individuals with the highest crowding degree as high-quality initial individuals.

[0106] Parent selection: A binary tournament selection method is adopted. Two groups are randomly selected from 100 initial schemes to form a competition group. A total of 50 competition groups are conducted. Individuals with higher frontier levels are selected first. If the frontier levels are the same, individuals with higher crowding are selected. Finally, 50 high-quality parents are selected to enter the mating pool, including 30 Front 1 individuals and 20 Front 2 individuals, to ensure the quality and diversity of individuals in the mating pool.

[0107] Offspring generation: (1) Parent pairing and seed selection: The 50 parents were sorted according to the front level. 15 pairs were randomly paired within the Front 1 individuals, and 10 pairs were cross-paired between the Front 1 and Front 2 individuals, for a total of 25 parent pairs. For each parent pair, one seed unit was selected from 2000 unconstrained units by uniform random sampling to ensure that the seed units were evenly distributed. (2) Generation of spatial contiguous blocks: The county-level planning area has a scale of 1500 km² (>500 km² and ≤2000 km²). The growth scale is determined to be 7%-12%. 8% is randomly selected as the growth scale for this batch, i.e. 240 units. Starting from each seed unit, adjacent units are iteratively included. Units with attribute similarity ≥0.7 are given priority. If there are not enough, units with lower similarity are included. During the growth process, rigid constraint unit boundaries are avoided. Finally, 25 geographically continuous and attribute-homogeneous spatial contiguous blocks are generated. (3) Block gene exchange: For each pair of parents, locate the gene loci corresponding to the spatial continuous block, extract the gene fragment of the first parent individual and copy it to the corresponding position of the second parent individual to generate the first offspring individual, extract the gene fragment of the second parent individual and copy it to the corresponding position of the first parent individual to generate the second offspring individual. Each pair of parents generates 2 offspring, and 25 pairs of parents generate a total of 50 offspring individuals; Exchange example: The spatial block gene fragment of the first parent individual is [1, 1, 1, ..., 1] (240 1s, ecological protection), and the corresponding spatial block gene fragment of the second parent individual is [3, 3, 3, ..., 3] (240 3s, urban construction). After the exchange, the corresponding spatial block gene fragment of the first offspring individual is [1, 1, 1, ..., 1], and the corresponding spatial block gene fragment of the second offspring individual is [3, 3, 3, ..., 3]. Genes in non-spatial block regions remain unchanged; (4) Dual-scale mutation optimization: The current population diversity is moderate. The micro-mutation probability is set to 0.03. The unconstrained units of 50 offspring individuals are randomly flipped, and the codes of 36 units are flipped. After flipping, all units meet the allowed use set. The macro-mutation probability is set to 0.15. The urban land use cluster of 12 offspring individuals is sprawled (each expands by 1-2 units), and the ecological land use cluster of 8 offspring individuals is contracted (each removes 1 unit). After mutation, hard constraint verification is performed. Two individuals that violate the land use area index are removed, and two offspring individuals are generated to obtain 50 offspring individuals. One round of offspring generation is completed. The above steps are repeated to generate 100 offspring individuals.

[0108] Elite Preservation and Iteration: 1. Population Merging: Merge the parent (100 individuals) and offspring (100 individuals) populations into a temporary population of 200 individuals; 2. Environmental Selection: Perform non-dominated sorting on the temporary population to obtain Front 1 (22 individuals), Front 2 (38 individuals), Front 3 and beyond (140 individuals); Since the number of individuals in Front 1 is 22 < 100, select 78 individuals from Front 2 according to their crowding density from highest to lowest to form a new generation population of 100 individuals; 3. Iterative Cycle: Repeat the fitness evaluation, parent selection, offspring generation, and elite preservation process for the new generation population; 4. Termination Condition Setting: Maximum number of iterations G_max = 200, threshold ε = 0.1%. When iterating to the 168th generation, the average fitness value improvement of Front 1 over 50 consecutive generations is 0.08% < 0.1%, which meets the termination condition, and the iteration stops.

[0109] Solution Output: 1. Optimal Solution Set Selection: Extract the Front 1 individuals from the 168th generation population, totaling 12, to form a Pareto optimal planning solution set; 2. Solution Evaluation: All 12 solutions meet the hard constraints, and the soft constraints are met as follows: urban land connectivity rate ≥90%, permanent basic farmland contiguous area rate ≥85%; the three objective function values ​​are improved by an average of 15% compared to the initial solution, with F_1 improving by an average of 12%, F_2 by an average of 18%, and F_3 by an average of 13%; 3. Spatial Output: Decode the 12 solutions into a spatial layout map, marking the boundaries and areas of ecological protection red lines, permanent basic farmland, and urban construction land. Output quantitative data such as fitness value, objective function value, and constraint satisfaction for each solution. Based on the county-level region's positioning of "coordinated ecological and economic development," the solutions with F_1=85, F_2=82, and F3=83 are listed as the highest priority solutions for decision-makers' reference.

[0110] Comparative experiments show that, using the spatial adjacency block crossover operator of this application, the spatial fragmentation index (fragmentation index = number of scattered plots / total number of plots) of the offspring scheme is reduced by 62% compared with the traditional single-point crossover operator, the connectivity of urban land is improved by an average of 35%, and the consolidation rate of permanent basic farmland is improved by an average of 28%. At the same time, the convergence speed of the algorithm is improved by 25%, effectively reducing the generation of invalid solutions. The optimization results not only satisfy mathematical optimality, but also have strong practical feasibility.

[0111] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0112] It will be apparent to those skilled in the art that this application is not limited to the details of the exemplary embodiments described above, and that this application can be implemented in other specific forms without departing from the spirit or essential characteristics of this application. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of this application is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within this application. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for generating a spatial adjacency block crossover operator, characterized in that, The method includes: First and second parent individuals are selected from the population of land spatial planning schemes that meet the hard constraints of planning. Both the first and second parent individuals are one-dimensional integer chromosomes with a length equal to the total number of planning units M. Each element in the chromosome corresponds to the use code of a planning unit. The planning units include rigid constraint units and non-rigid constraint units. One planning unit is randomly selected from the non-rigid constraint units as a seed unit. Starting from the seed unit, a spatially continuous block with geographically continuous and internally homogeneous properties is generated using a spatial region growth method according to a preset growth scale. The growth scale is determined based on the planning area scale. Extract all the usage codes corresponding to the spatial contiguous block in the first parent individual as the first gene fragment, copy it as a whole and cover the corresponding gene loci in the second parent individual, while keeping the other gene loci of the second parent individual unchanged, to generate the first offspring individual; Extract all the usage codes corresponding to the spatial contiguous block in the second parent individual as the second gene fragment, copy it as a whole and overwrite the corresponding gene loci in the first parent individual, while keeping the other gene loci of the first parent individual unchanged, to generate the second offspring individual.

2. The method for generating spatial adjacency block crossover operators according to claim 1, characterized in that, Starting from the seed unit, and according to a preset growth scale, the steps of generating geographically continuous and internally homogeneous spatially contiguous blocks using the spatial region growth method include: The target number of planning units contained in a spatial contiguous block is determined based on the scale of the planning area. Starting from the seed unit, adjacent units that share the same edge or angle with the current spatial block are iteratively included using the spatial region growing method until the number of planning units contained in the spatial contiguous block reaches the target number; wherein, the comprehensive attribute similarity between each adjacent unit to be included and the current spatial contiguous block is greater than a threshold.

3. The method for generating spatial adjacency block crossover operators according to claim 2, characterized in that, Starting with the seed unit, the steps of iteratively incorporating adjacent units sharing edges or angles with the current spatial block using the spatial region growing method until the number of planned units contained in the spatial contiguous block reaches the target number include: For each adjacent unit to be included, normalization is performed based on topographic slope, soil type, and current land use indicators; The similarity of each indicator was calculated using the absolute value method; The overall attribute similarity is determined based on the set weights and the similarity of each indicator; Adjacent units with a comprehensive attribute similarity greater than a threshold are included in the current spatial contiguous block until the number of planning units contained in the spatial contiguous block reaches the target number; wherein, when the number of planning units contained in the spatial contiguous block is insufficient, the threshold is reduced.

4. The method for generating spatial adjacency block crossover operators according to claim 3, characterized in that, The steps for incorporating adjacent units with a comprehensive attribute similarity greater than a threshold into the current spatial contiguous block, until the number of planning units contained in the spatial contiguous block reaches the target number, include: Incorporate adjacent units whose comprehensive attribute similarity to the units within the current spatial block is greater than or equal to the first threshold. If the number of adjacent units that meet the conditions is insufficient, adjacent units with similarity lower than the first threshold but greater than or equal to the second threshold, as well as adjacent units with similarity lower than the second threshold, are included in sequence until the number of planning units contained in the spatial contiguous block reaches the target number; wherein, the first threshold is greater than the second threshold.

5. The method for generating spatial adjacency block crossover operators according to claim 2, characterized in that, The steps for determining the target number of planning units contained in a spatially contiguous block based on the planning area scale include: When the planned area is ≤500 km², the target number is 10%-15% of the total number of planning units M; When the planned area is >500 km² and ≤2000 km², the target number is 7%-12% of the total number of planning units M; When the planned area is greater than 2000 km², the target number is 5%-10% of the total number of planning units M.

6. The method for generating spatial adjacency block crossover operators according to claim 1, characterized in that, The planning hard constraints include: planning units located within the ecological protection red line area, whose use codes are fixed for ecological protection purposes; planning units located within the permanent basic farmland boundary area, whose use codes are fixed for agricultural planting purposes; and the codes of the rigid constraint units remain unchanged during genetic operations.

7. A method for optimizing land spatial planning schemes, characterized in that, The method includes: Using superpixel segmentation technology, the planning area is divided into several planning units with homogeneous internal attributes, and the geographical attributes and constraint types of each planning unit are labeled. Among them, planning units located within the ecological protection red line or permanent basic farmland boundary are labeled as rigid constraint units, and the rest are labeled as unconstrained units. Generate an initial population consisting of N initial planning schemes; the number of initial planning schemes is determined based on the total number of planning units; The suitability of each initial planning scheme is evaluated; Based on the evaluation results, a combined strategy of binary tournament selection method and non-dominated ranking and crowding calculation was adopted to select N / 2 individuals from the current population to form a mating pool. Individuals in the mating pool are paired up, and two offspring individuals are generated by applying the spatial adjacency block crossover operator generation method as described in any one of claims 1 to 6 to each parent pair; and mutation operations and feasibility verification are performed on the offspring individuals. The parent and offspring populations are merged, and N individuals are selected based on non-dominated sorting and crowding to form a new generation population. The fitness of each planning scheme in the population is evaluated repeatedly, and individuals in the mating pool are paired to generate new offspring individuals. The offspring individuals are then subjected to mutation operations and feasibility verification until the preset iteration termination condition is met. Extract the Pareto optimal frontier individuals from the final population, decode them into a spatial planning layout map, and output it.

8. The method for optimizing territorial spatial planning schemes according to claim 7, characterized in that, The steps for generating two offspring individuals and performing mutation operations and feasibility verification on the offspring individuals include: Individuals in the mating pool are sorted from high to low according to their non-dominant ranking. Individuals of the same ranking are randomly paired to form N / 2 pairs of parent individuals. Gene recombination is performed on each pair of parent individuals according to the spatial adjacency block crossover operator generation method described in any one of claims 1 to 6, so that each pair of parent individuals generates 2 offspring individuals, and a total of N offspring individuals are generated; For all offspring individuals, perform two-scale guided mutation operations; Perform hard constraint fast verification on all offspring individuals that have completed the mutation operation, remove infeasible individuals that violate the hard constraints, and select the corresponding number of individuals from the original offspring to supplement them, or make local corrections to the removed individuals and re-include them.

9. The method for optimizing land spatial planning schemes according to claim 8, characterized in that, For all offspring individuals, the steps for dual-scale guided mutation manipulation include: With the first mutation probability, a non-rigid constraint unit is randomly selected, and its use encoding is randomly flipped within its set of allowed uses to another allowed use; With a second mutation probability higher than the first mutation probability, a spatial cluster of urban land or ecological land is randomly selected, and a sprawl operation or a shrinkage operation is performed; the sprawl operation is to expand a set number of units to the adjacent unconstrained units of the selected cluster, and the shrinkage operation is to remove a set number of units from the edge of the selected cluster.

10. The method for optimizing territorial spatial planning schemes according to claim 8, characterized in that, The steps for evaluating the fitness of each initial planning option include: Calculate the objective function values ​​for ecological security, economic development, and food security respectively; among them, The ecological security objective function value is F_1 = Σ(E_i × X_i1), where E_i is the ecological value index of the i-th unit and X_i1 is the indicator variable; The economic development objective function value is F_2 = Σ(D_i / C_i × X_i3), where D_i is the development potential index of the i-th unit and C_i is the distance from the i-th unit to the nearest town center; The objective function value for food security is F_3 = Σ(A_i × X_i2), where A_i is the agricultural suitability index of the i-th unit, and X_i2 and X_i3 are indicator variables.

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