# Cost Path Analysis: Elements of Cost Path Analysis (Source Raster, Cost Raster, Cost Distance Measures, Algorithm) and Applications (Especially for GATE-Geospatial 2022)

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Cost path analysis is a procedure or tool for finding an optimal route between two points through continuous space that minimizes costs. “Cost” in this sense can have several connotations, including: actual monetary expenditure in construction, time and effort required to travel, and negative environmental impacts. Any path through space will accumulate these costs, and routes with high associated costs are less favorable than routes with a lower cost associated with it. Cost path algorithms are designed to efficiently find the path with the minimum total cost.

## Elements of Cost Path Analysis

Cost Path is one of a series of algorithms and tools that analyze such costs, collectively known as Cost Distance Analysis. Its most common application is for planning corridors for constructing linear infrastructure such as roads and utilities. A path analysis requires a

• Source raster
• A cost raster
• Cost distance measures
• Algorithm for deriving the least accumulative cost path Diagram Shows Source Raster, Cost Raster and Cost Distance M …

## Source Raster

A source raster defines the source cell. Only the source cell has a cell value in the source raster; all other cells are assigned no data. Similar to physical distance measure options, cost distance measures spread from the source cell. However, in the context of least-cost path analysis, one can consider the source cell as an end point of a path either the origin or the destination.

## Cost Raster

A cost raster defines the cost of moving through each cell, path analysis finds the least cost path between cells. A cost raster defines the cost or impedance to move through each cell. A cost raster has three characteristics.

• First, the cost for each cell is usually the sum of different costs. As an example, summarizes the cost for constructing a pipeline, which may include the construction and operational costs as well as the potential costs of environmental impacts.
• Second, the cost may represent the actual or relative cost. Relative costs are expressed in ranked values. For example, costs may be ranked from 1 to 5, with 5 being the highest cost value. A project such as pipeline project typically involves a wide variety of cost factors. Relative costs are therefore, a means of standardizing different cost factors for least-cost path analysis.

## Cost Distance Measures

Cost Distance Measures follows the node-link cell representation: a lateral link connects two direct neighbors, and a diagonal link connects two diagonal neighbors.

The cost distance of a lateral link is the average of the costs in the linked cells, for example, . The cost distance of a diagonal link is the average cost times 1.4142, for example,

## Algorithm for Determining Least Accumulative Cost Path

Determining an optimal cost path typically requires three steps, which in most GIS software is implemented in separate tools (because they can be used in other procedures) .

• Cost Surface: Some sample factors considered in creating a cost surface. The various types of cost are combined into one comprehensive measure that could be measured anywhere in the space (thus creating a field) , then modeled in GIS (typically with an Index model procedure) to create a raster grid known as a cost surface.
• Cost Distance: Given a source location, a new raster grid called a cost distance raster is created that calculates the accumulated cost to travel to each cell from the source. This is created by radiating out from the source, determining the cost of each cell by identifying the neighbor with the lowest accumulated cost and adding its cost to the total. Simultaneously, a separate grid, called a backlink raster encoding the direction from each cell to its lowest cost neighbor.
• Least-Cost Path: Given a destination location, this algorithm finds the corresponding cell in the backlink raster, then traces a path from the destination back to the source by following the direction of each cell to the lowest cost neighbor. The corresponding cell in the cost distance raster gives the total cost accumulated by following this optimal route.

## Applications of Path Analysis

• Least-cost path analysis is useful for planning roads, pipelines, canals, transmission lines, and trails. As examples, least-cost path analysis has been used by Rees (2004) to locate footpaths in mountainous areas, by Atkinson et al. (2005) to derive an arctic all-weather road, and by Snyder el al. (2008) to find trail location for all-terrain vehicles. Figure Shows Sum of Accumulation Cost Surfaces in Path Analy …
• Least-cost path analysis can also be applied to wildlife movements. A common application in wildlife management is corridor or connectivity study. In such studies, the source cells represent habitat concentration areas and the cost factors typically include vegetables, topography, and human activities such as roads. Analysis results can show the least costly routes for wildlife movement.
• Least-cost path analysis is important for accessibility studies such as accessibility to medical service. Accessibility is also a concept underlying studies of food deserts.

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