A method for finding a least-cost corridor on an ordinal-scaled raster cost surface

Abstract

The least-cost path problem is a widely studied problems in geographic information science. In raster space, the problem is to find a path that accumulates the least amount of cost between two locations based on the assumptions that the path is a one-dimensional object (represented by a string of cells) and that the cost (per unit length) is measured on a quantitative scale. Efficient methods are available for solution of this problem when at least one of these assumptions is upheld. This is not the case when the path has a width and is a two-dimensional object called a corridor (represented by a swath of cells) and the cost (per unit area) is measured on an ordinal scale. In this paper, we propose one additional model that characterizes a least-cost corridor on an ordinal-scaled raster cost surface–or a least ordinal-scaled cost corridor for short–and show that it can be transformed into an instance of a multiobjective optimization problem known as the preferred path problem with a lexicographic preference relation and solved accordingly. The model is tested through computational experiments with artificial landscape data as well as real-world data. Results show that least ordinal-scaled cost corridors are guaranteed to contain smaller areas of higher cost than conventional least-cost corridors at the expense of more elongated and winding forms. The least ordinal-scaled cost corridor problem has computational complexity of O(n 2.5) in the worst case, resulting in a longer computational time than least-cost corridors. However, this difference is smaller in practice.