- freely available
ISPRS International Journal of Geo-Information 2017, 6(9), 271; https://doi.org/10.3390/ijgi6090271
2. Related Work
3. Cartographic Selection from a GA Perspective
3.1. GA Summary
- Encoding: transforming solutions of a problem into gene representations.
- Initialization: generating a set of chromosomes that represent optional solutions to the problem.
- Selection: selecting individuals from the current population as parents for reproduction, based on their fitness values.
- Crossover: producing children by recombining the genes of two parents.
- Mutation: randomly selecting genes in an individual and replacing them by their allele to ensure diversity.
- Termination criterion: stopping the algorithm when the algorithm converges or when the number of iterations reaches a pre-specified value.
- Definition and expression of the solution to the problem, namely how to design the genes of an individual in the GA.
- Choice of appropriate genetic operators, such as selection, crossover, mutation, etc., to evolve the population of solutions.
- Definition of a fitness function to evaluate the quality of the solution with respect to a practical problem.
3.2. Selection Constraints
3.3. An Improved GA
3.3.2. Crossover and Mutation by Considering Conflicting Blocks
3.3.3. Objective Function and Fitness Function
4. Implementation of the Proposed Method
4.1. Extraction of Selection Units
4.2. Building Enlargement
- Rule 1.
- If the graphic length and graphic width of a building are less than 0.7 mm and 0.5 mm, respectively, then replace the building with a predefined symbol of the appropriate size and orientation.
- Rule 2.
- If the graphic length of a building is larger than 0.7 mm, but its graphic width is less than 0.5 mm, then expand its symbol width to 0.5 mm. Similarly, if the graphic width of a building is larger than 0.5 mm, but its graphic length is less than 0.7 mm, then expand its symbol length to 0.7 mm.
- Rule 3.
- If the graphic length and graphic width of a building are larger than 0.7 mm and 0.5 mm, respectively, then represent them with their original outline.
4.3. Local Displacement
- A C-type building is one that is located at a road corner and overlaps at least one of the roads.
- An E-type building is one that is located on one side of the road and only overlaps one of the roads.
4.4. Conflict Detection among Buildings
4.5. Enrichment of Geometric Attributes
- A type I building is determined by simple area calculation and comparison to the minimum size threshold. According to the National Administration of Surveying , buildings with an area of more than 0.35 mm2 are considered to be of this type.
- A type II building is identified on the basis of detecting the proximity relationship among buildings and roads. Before performing the GA on a selection unit, a proximity graph is constructed using the method proposed by Liu et al. . It is then possible to obtain information as to whether a building is adjacent to a road and how close it is. Utilizing the information, a building that is adjacent to two or more roads and whose proximity distance to each road is less than a certain threshold (e.g., 15 m) can be defined as a type II building.
- To identify a type III building, the boundary of a settlement should be defined first. A boundary deriving method proposed by Yan and Weibel  is adopted after converting the building group to a point cluster. The buildings that overlap the generated boundary are called the boundary buildings. A type III building can be derived from these boundary buildings by performing a line reduction algorithm on the boundary line. The Douglas–Peucker algorithm  is preferred because it keeps all the key points that make up the basic shape of a line and removes the other points. The simplified tolerance in the algorithm is set to 25 m by experiment. The buildings corresponding to the points retained on the simplified line will be type III buildings.
4.6. Selection Based on the GA
- Mark all genes as ‘free’;
- Assign the gene values corresponding with the must-be-selected buildings as 1 s and mark these genes as ‘fixed’;
- Assign the gene values corresponding with the must-be-discarded buildings as 0 s and mark these genes as ‘fixed’;
- Repeat the following steps until the number of genes assigned as 1 s reaches the target selection number or all the genes are marked as ‘fixed’;
- Randomly select a ‘free’ building B and assign its gene as 1, then mark the gene as ‘fixed’;
- Identify ‘free’ buildings from CB(B), assign the corresponding genes as 0 s and mark these genes as ‘fixed’;
4.6.2. Selection, Crossover, and Mutation
4.6.3. Iteration and the Elite Retention Strategy
5. Results and Analysis
5.1. Experimental Results
5.2.1. Local Constraints
5.2.2. Contextual Constraint of Spatial Relationships and Patterns
6. Conclusions and Future Work
Conflicts of Interest
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|Selection Unit||Scale||Initial Conflicts||Final Conflicts||Estimated Building Number||Resultant Building Number||Execution Time (s)|
|Selection Unit||Unit A||Unit B|
|Ratio of changes (%)||3.38||11.24||1.85||9.99|
|Selection Unit||Unit A||Unit B|
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