A Voronoi-based method for land-use optimization using semidefinite programming and gradient descent algorithm

Abstract

ABSTRACT 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.