A Novel Method for Building Displacement Based on Multipopulation Genetic Algorithm
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applied sciences Article A Novel Method for Building Displacement Based on Multipopulation Genetic Algorithm Wende Li 1, Tinghua Ai 1,* , Yilang Shen 1 , Wei Yang 2 and Weilin Wang 1 1 School of Resource and Environment Sciences, Wuhan University, Wuhan 430079, China; [email protected] (W.L.); [email protected] (Y.S.); [email protected] (W.W.) 2 School of Management Science and Real Estate, Chongqing University, Chongqing 400044, China; [email protected] * Correspondence: [email protected]; Tel.: +86-139-0863-9199 Received: 10 November 2020; Accepted: 25 November 2020; Published: 26 November 2020 Abstract: Owing to map scale reduction and other cartographic generalization operations, spatial conflicts may occur between buildings and other features in automatic cartographic generalization. Displacement is an effective map generalization operation to resolve these spatial conflicts to guarantee map clarity and legibility. In this paper, a novel building displacement method based on multipopulation genetic algorithm (BDMPGA) is proposed to resolve spatial conflicts. This approach introduces multiple populations with different control parameters for simultaneous search optimization and adopts an immigration operation to connect different populations to realize coevolution. The optimal individuals of each population are selected and preserved in the elite population through manual selection operation to prevent the optimal individuals from being destroyed and lost in the evolutionary process. Meanwhile, the least preserving generation of the optimal individuals is used as the termination basis. To validate the proposed method, urban building data with a scale of 1:10,000 from Shenzhen, China are used. The experimental results indicate that the method proposed in this paper can effectively resolve spatial conflicts to obtain better results. Keywords: cartographic generalization; building displacement; conflict resolution; multipopulation genetic algorithm 1. Introduction In automatic cartographic generalization, spatial conflicts (e.g., proximity conflicts or overlap conflicts) often occur between both the same and different features (e.g., between buildings and buildings or between buildings and roads) because of map scale reduction and other cartographic generalization operations. To resolve such conflicts, several generalization operations, such as selection [1], aggregation [2,3], elimination [4], typification [5,6], and displacement [7,8], have been used. Compared with other generalization operations, the displacement operation is the most important and frequently adopted method to resolve spatial conflicts. With the development of big data and artificial intelligence, spatial conflict solutions based on displacement operation in cartographic generalization are facing new challenges (e.g., real-time displacement) [9,10]. Therefore, it is urgent to explore more effective automatic displacement approaches. Building displacement only slightly moves buildings from their original position to new position on the premise of ensuring positional accuracy, which does not significantly reduce the information content in a map [11]. In the process of displacement, several main issues should be considered. First, the displacement approach should try to resolve all possible spatial conflicts under the constraint of positional accuracy, which indicates that the maximum displacement distance of objects on a map should be limited to a specified range (e.g., 0.5 mm). Second, the displacement operation should Appl. Sci. 2020, 10, 8441; doi:10.3390/app10238441 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 8441 2 of 20 avoid generating secondary conflicts after moving some map objects. Third, the displacement should maintain the spatial positional relations between individual buildings and the arrangement patterns and distribution characteristics within building groups. However, different constraints may contradict each other, and it is not possible to find a solution that satisfies all constraints completely. Instead, a feasible solution is to find the best compromise among constraints. Therefore, the problem of building displacement can be regarded as the combinatorial optimization problem satisfying multiple cartographic constraints [12], which can be solved by the heuristic search method. The genetic algorithm (GA) [13] is a highly parallel and adaptive global optimal search algorithm based natural selection in the biological world. Because of its strong robustness and global search ability, the GA has been widely used in the cartographic generalization field, such as the geographical feature label placement problem [14], map conflation [15], feature selection [1,16], and displacement operation [17,18]. However, with the development of GA research, its shortcomings have gradually been exposed, such as premature convergence. For example, when the GA is used for the displacement of buildings to resolve spatial conflicts, the premature convergence of the GA will cause all individuals in the population to tend to be in the same state and stop evolution, resulting in the algorithm not resolving all defined spatial conflicts. Therefore, we propose a novel building displacement method based on multipopulation genetic algorithm (BDMPGA) to resolve spatial conflicts. The BDMPGA breaks through the structure of traditional GA that only relies on a single population for genetic evolution, which introduces multiple populations with different control parameters to conduct simultaneous optimization searches. The immigration operation is used to realize the information exchange among different populations to maintain the diversity of individuals in the population and obtain the optimal solution. Meanwhile, this method adopts elite retention strategy that the optimal individuals in the population are selected and preserved in the elite population through manual selection operation, and the elite population is also the basis for the termination of the algorithm. The remainder of this article is organized as follows. Section2 summarizes existing studies on the spatial conflict resolution by the displacement operation. Section3 introduces the main steps of the BDMPGA. Section4 presents the specific application of the BDMPGA in building displacement and compares it with GA and the immune genetic algorithm (IGA). Section5 describes the conclusions of this study and future work. 2. Related Work In this section, we will briefly summarize the relevant approaches of the displacement operation to resolve spatial conflicts. These approaches can be divided into two categories: sequential approaches and optimization approaches. 2.1. Sequential Approaches For sequential approaches, first, conflicting map objects are detected by analyzing the context of the map objects. Then, the displacement vector of each conflicting object is calculated. Finally, the spatial conflicts are resolved by moving each conflicting object in turn. Lichtner [19] proposed a method to calculate the displacement vector by establishing an equation system. Mackaness [20] presented a radial displacement algorithm for the point cluster displacement issue. This method adopts cluster analysis to identify conflicting groups and uses a density function to control the displacement decay to maintain the gestalt or pattern of the cluster. Ruas [21] proposed a reactive displacement algorithm for urban area buildings. This method uses constraint analysis and result evaluation to control the displacement process and combines with other map generalization operations. To resolve the conflict between roads and buildings because of an exaggeration of the road symbol, Fei [22] proposed a special hybrid raster–vector data structure. By dividing buildings into four types, conflicts can be resolved according to corresponding strategies. Basaraner [23] proposed an iterative displacement method for buildings based on generalization zones. This algorithm first creates the generalization zones by means of Voronoi tessellation and spatial analysis techniques and then uses Appl. Sci. 2020, 10, 8441 3 of 20 multiple criteria to control the displacement. Ai et al. [7,24] borrowed the idea of fields from physics discipline and established a vector field model to handle the displacement of multiple conflicts in building generalization. This approach applies the displacement force on conflicting objects and considers the displacement distance decay effect, secondary conflicts can be resolved by attractive force. Later, Zhou et al. [8] proposed a multisource force field model to resolve multiple conflicts and maintain spatial relationships of buildings. 2.2. Optimal Approaches Compared with sequential approaches, optimization approaches consider all map objects and resolve all spatial conflicts simultaneously and can be further divided into combinatorial and functional optimization approaches. 2.2.1. Combinatorial Optimization Approaches In combinatorial optimization approaches, the new locations of map objects are determined by trials, and the most commonly adopted approaches are heuristic search algorithms. Ware et al. [25] adopted simulated annealing approach and steepest gradient descent approach to resolve graphic conflicts. Through experimental comparison, the simulated annealing approach is superior with regard to the degree of conflict reduction. Afterwards, multiple generalization operators, such as displacement, size exaggeration, deletion, and size reduction, were adopted as the candidate trial positions of buildings in simulated annealing approach,