Modeling and optimization of least-cost corridors

Sammanfattning: Given a grid of cells, each having a value indicating its cost per unit area, a variant of the least-cost path problem is to find a corridor of a specified width connecting two termini such that its cost-weighted area is minimized. A computationally efficient method exists for finding such corridors, but as is the case with conventional raster-based least-cost paths, their incremental orientations are limited to a fixed number of (typically eight orthogonal and diagonal) directions, and therefore, regardless of the grid resolution, they tend to deviate from those conceivable on the Euclidean plane. Additionally, these methods are limited to problems found on two-dimensional grids and ignore the ever-increasing availability and necessity of three-dimensional raster based geographic data. This thesis attempts to address the problems highlighted above by designing and testing least-cost corridor algorithms. First a method is proposed for solving the two-dimensional raster-based least-cost corridor problem with reduced distortion by adapting a distortion reduction technique originally designed for least-cost paths and applying it to an efficient but distortionprone least-cost corridor algorithm. The proposed method for distortion reduction is, in theory, guaranteed to generate no less accurate solutions than the existing one in polynomial time and, in practice, expected to generate more accurate solutions, as demonstrated experimentally using synthetic and real-world data. A corridor is then modeled on a threedimensional grid of cost-weighted cubic cells or voxels as a sequence of sets of voxels, called ‘neighborhoods,’ that are arranged in a 26-hedoral form, design a heuristic method to find a sequence of such neighborhoods that sweeps the minimum cost-weighted volume, and test its performance with computer-generated random data. Results show that the method finds a low-cost, if not least-cost, corridor with a specified width in a threedimensional cost grid and has a reasonable efficiency as its complexity is O(n2) where n is the number of voxels in the input cost grid and is independent of corridor width. A major drawback is that the corridor found may self-intersect, which is often not only an undesirable quality but makes the estimation of its cost-weighted volume inaccurate.