An experimental analysis of least-cost path models on ordinal-scaled raster surfaces

Abstract

Selection of optimal paths or sequences of cells from a grid of cells is one of the most basic functions of raster-based geographic information systems. For this function to work, it is often assumed that the optimality of a path can be evaluated by the sum of the weighted lengths of all its segmentsweighted, i.e. by the underlying cell values. The validity of this assumption must be questioned, however, if those values are measured on a scale that does not permit arithmetic operations. Through computational experiments with randomly generated artificial landscapes, this paper compares two models, minisum and minimax path models, which aggregate the values of the cells associated with a path using the sum function and the maximum function, respectively. Results suggest that the minisum path model is effective if the path search can be translated into the conventional least-cost path problem, which aims to find a path with the minimum cost-weighted length between two terminuses on a ratio-scaled raster cost surface. On the other hand, the minimax path model is found mathematically sounder if the cost values are measured on an ordinal scale and practically useful if the problem is concerned not with the minimization of cost but with the maximization of some desirable condition such as suitability.

A method for finding least‐cost corridors in three‐dimensional raster space

“…A “cloudy” (Murekatete & Shirabe, 2020) cost grid has spatially autocorrelated and locally similar values (see Figure 5a for an example). Each such grid was created with the following procedure.…”

“…The cost grids used in the experiment were generally characterized by three parameters: size (50 A "cloudy" (Murekatete & Shirabe, 2020) cost grid has spatially autocorrelated and locally similar values (see Figure 5a for an example). Each such grid was created with the following procedure.…”

A method for finding least-cost corridors with reduced distortion in raster space

“…Each of those grids were converted into five cost surfaces by classifying its values into 5, 10, 25, 50, and 100 classes with an equal interval and assigning each set of classes equally (or as equally as possible) spaced integers ranging from 1 to 100. As a result, we had 500 cost surfaces, which were referred to as 'cloudy' (Murekatete and Shirabe 2020). As illustrated in Figure 8, those with larger numbers of classes had their values more smoothly varying.…”

An Effective Method for Computing the Least-Cost Path Using a Multi-Resolution Raster Cost Surface Model

“…Here, f (i) denotes the value of grid i on the cost surface f , and l(i, j) denotes the straight distance between grids i and j. The formula, known as "minimum-cost path" [10], is the LCP model that is compared with the method in this paper. Additionally, the optimality of the minimum-cost path can be evaluated by minimizing the maximum cost length.…”

“…Raster cells are assigned a cost value or a risk indicator, and planners can determine the optimal spatial pathway through analyzing the distribution of these values. By evaluating the cost situation along the pathway, the quality of the route can be assessed [10]. Searching for the least-cost path on a cost surface can be seen as finding the shortest path on the graph.…”