Comparison of spatial compactness evaluation methods for simple genetic algorithm based land use planning optimization problem

As one of the most important objectives for land use planning towards sustainability, the compactness could not only decrease threat to species survivability and the energy consumption, but also improve the accessibility of city and the social equity towards sustainability et al. Although there have existed several methods to evaluate compactness, the spatial autocorrelation methods have not been applied in raster based land use planning optimization problem, which is one kind of spatial optimization problem and of great complexity and generally operated by heuristic methods, such as Genetic Algorithm (GA), Simulated Annealing (SA) et al. Besides, there has not been comprehensive comparison of these methods including linear, non-linear, or spatial statics methods during the optimization process. In this research, most of these methods related are reviewed, furthermore, three of these representative methods including the non-linear neighbour method, shape index and Moran's I have been compared based on simple GA on hypothesis data. The non-linear neighbour method with the simplest principle yields the best effect and efficiency. On the other hand, Moran's I method shows another angle to evaluate the compactness although the result is not very good. Furthermore, the mono Moran's I and comprehensive Moran's I also have been compared, compared to the worse result of mono Moran's I, the comprehensive Moran's I did better while it is also worse than the neighbour methods. The effect clearly shows us one possible combination of compactness and other objectives, such as compatibility, so as to improve the efficiency of the whole land use planning optimization process.