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GA optimization technique’s in interpolation for dynamic GIS
3. Application of Genetic Algorithm for Integrating Behavioral Models and Observational Data to Class Variable Interpolation
3.1 3D Representation of an Individual (coding) In the research, two dimensional spatial and one dimensional temporal space was considered to compose a 3D spatio-temporal space as shown in Figure.1, in which horizontal surface is used to represent 2D space and vertical dimension is used to represent temporal dimension. A three dimensional array is defined to represent the individual.  Figure 1 Representation of Individual 3.2 Initialization of Population An initial population for a genetic algorithm is usually chosen at random; one random trial is made to produce each individual. All members of initial population are chosen automatically by same procedure so that the expected value of each member of initial population is same. In addition we use cubes of 1 * 1 * 1, 2*2*2 and 3*3*3 pixels as the initial unit for the initialization of population to increase the efficiency of algorithm. 3.3 Definition of Individual's Fitness 3.3.1 Spatio-temporal Behavioral Models/Rules of Class Variable Data It should be noted that any types of behavioral/structural models/rules can be used for the GA-based interpolation if they can determine the probability of every possible behavior/transition of class variables. In class variable data, the possible changes of a class at one pixel are basically defined by the probability of the changes from one class to another. One of the simplest example is a Markov chain, where only the previous class determines transitional probability. In addition the probability also can be affected by combination of classes in the neighborhood. In this study, we assume the transitional probability is determined by the combination of classes in the neighborhood. And land use data with five classes is used as test data. The spatial and temporal relations affect the transitional probability in three ways as shown in the Figure.2. The first is so-called the spatial continuity, which is based on the assumption that the same class data tends to continue in spatial dimension. Therefore, the effects of the spatial relation happen just within the same time-slice data. Second one is called temporal continuity. This is an extension of spatial continuity to temporal domain- the third aspect is expansion-contraction relation based on the assumption that some class data has high possibility to expand its area at next time-slice, while others tend to contract. The pixel’s class itself will determine the temporal change in the pixel with un-contractible class type. And class of the pixel and classes of its expandable neighborhood will determine the temporal land use change in the pixel with contractible type.  Figure 2 3D Spatial-Temporal Relation of Pixel-based Class Variable Data |