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首页> 外文期刊>International Journal of Geographical Information Science >A Voronoi-based method for land-use optimization using semidefinite programming and gradient descent algorithm
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A Voronoi-based method for land-use optimization using semidefinite programming and gradient descent algorithm

机译：基于Voronoi的土地利用优化方法使用SEMIDEFINITE编程和梯度下降算法

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摘要

The land-use optimization involves divisions of land into subregions to obtain spatial configuration of compact subregions and desired connections among them. Computational geometry-based algorithms, such as Voronoi diagram, are known to be efficient and suitable for iterative design processes to achieve land-use optimization. However, such algorithms assume that generating point positions are given as inputs, while we usually do not know the positions in advance. In this study, we propose a method to automatically calculate the suitable point positions. The method uses (1) semidefinite programming to approximate locations while maintaining relative positions among locations; and (2) gradient descent to iteratively update locations subject to area constraints. We apply the proposed framework to a practical case at Chiang Mai University and compare its performance with a benchmark, the differential genetic algorithm. The results show that the proposed method is 28 times faster than the differential genetic algorithm, while the resulting land allocation error is slightly larger than that of the benchmark but still acceptable. Additionally, the output does not contain disconnected areas, as found in all evolutionary computations, and the compactness is almost equal to the maximum possible value.
机译：土地利用优化涉及土地分为次区域，以获得紧凑次区域的空间配置和其中所需的连接。已知计算几何基于基于voronoi图的算法是有效的，适用于实现土地利用优化的迭代设计过程。然而，这种算法假设产生点位置被给出为输入，而我们通常不会提前了解该位置。在本研究中，我们提出了一种自动计算合适点位置的方法。该方法使用（1）半纤维编程到近似位置，同时保持位置之间的相对位置; （2）梯度下降到迭代更新以区域约束的位置。我们将拟议的框架应用于清迈大学的实际案例，并将其性能与基准，差分遗传算法进行比较。结果表明，该方法比差分遗传算法快28倍，而结果的陆地分配误差略大于基准，但仍然可以接受。另外，输出不包含断开区域，如所有进化计算中所发现的，并且紧凑性几乎等于可能的值。

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