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 segments – weighted, 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.

摘要

从单元格中选择最佳路径或单元序列是基于栅格的地理信息系统最基本的功能之一。为了使该函数起作用，通常假设路径的最优性可以通过其所有段的加权长度之和来评估 - 加权，即通过基础单元格值。然而，如果这些值是在不允许算术运算的尺度上测量的，则必须质疑该假设的有效性。通过随机生成的人工景观的计算实验，本文比较了两种模型，minisum 和 minimax 路径模型，它们分别使用 sum 函数和 max 函数聚合与路径相关的单元格的值。结果表明，如果路径搜索可以转化为传统的最小成本路径问题，则最小和路径模型是有效的，该问题旨在在比例缩放的栅格成本表面上找到两个终点之间具有最小成本加权长度的路径。另一方面，如果在有序尺度上测量成本值，则极小极大路径模型在数学上更合理，并且如果问题不涉及成本的最小化，而是涉及某些理想条件（如适用性）的最大化，则该模型实际上很有用。