# Overview of Least Cost Path Analysis

Amanda Briney

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Least cost path analysis is a distance analysis tool within GIS that uses the least cost path or the path between two locations that costs the least to those travelling along it to determine the most cost-effective route between a source and destination. Cost can be a function of time, distance or other criteria that is defined by the user. When using least cost path analysis in GIS, the eight neighbors of a raster cell are evaluated and the generated path moves to the cells with the smallest accumulated or cost value (“Distance Analysis Using ArcGIS”). This process is repeated multiple times until the source and destination are connected. The completed path is the smallest sum of raster cell values between the two points and it has the lowest cost.

Least cost path analysis is an important GIS tool to understand because it has many different applications – all of which can help businesses, city planners and other users save time and money.

## Requirements for Least Cost Path Analysis

Prior to conducting a least cost path analysis there are there are some requirements that all users must have and understand. These are a source raster, a cost raster, cost distance measures and an algorithm for deriving the least cost path (Chang). A source raster is a raster that “defines the source to which the least-cost path from each cell is calculated” (Chang, pg. 380). This means that the source raster is the raster that defines where the least cost path is going and the source cell is the end of that path. In the source raster only the source cell has a value and all others are given a “no data” value.

The cost raster is the raster that defines the cost or other impedance (defined by the user) to move through each raster cell. A cost raster has three characteristics. The first is that the cost of each cell is the sum of the different costs while the second is that the cost can represent either the actual or the relative cost (Chang). The third characteristic is that the cost factors can be weighted depending on the importance of each factor (Chang). For example if travel time is considered a more important factor than the monetary cost, it can be it can be weighted more in the analysis.

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The cost distance measure portion of least cost path analysis is centered on the node-link raster cell representation (Chang). In this representation a node is the center of the raster cell and the link connects the node to its neighboring cells. A lateral link is also included to connect a cell to one of its four nearest neighbors and a diagonal link connects the cell to the corner neighbors (Chang). The cost distance is the cost that it takes to travel from the node to these links and the least cost path is based on these costs.

Finally, least cost path analysis requires an algorithm for deriving a least cost path. An algorithm is an important component of least cost path analysis because accumulative cost between two cells can be calculated by adding the costs of connecting the two cells but least accumulative costs are challenging because there are many different ways to connect two cells and they do not have to be immediate neighbors (Chang). Least cost paths are derived after all possible paths are evaluated, thus an algorithm makes these complex and time consuming calculations much easier.

## Creating a Least Cost Path Analysis

Once the four requirements for conducting a least cost path analysis are met it is important to consider and correctly weight the rasters making up the cost raster to create an effective least cost path analysis (“Creating the Least Cost Path.”). The cost is the factor that is being tested in these analyses and they can be a function of time, distance and/or other criteria that the user defines and deems most important. How the cost rasters are weighted depends on the project application and the desired results.

Take for example a least cost path analysis examining routes between two campgrounds. The time it takes to travel between them and the monetary cost of fuel are the two are the important costs being tested. The user needs to determine which of these is most important and weight them accordingly. Weighted distance analysis (the determination of the best path between the two campgrounds considering time and fuel usage based on terrain, etc.) is one tool that can be used to help weight the two factors (“Distance Analysis Using ArcGIS”). Once correctly weighted a least cost path analysis between the two is generated based on factors such as speed limits and terrain among others.

When creating a least cost path analysis there is a simple workflow to follow to ensure that the analysis is complete. The ESRI Virtual Campus course, “Distance Analysis Using ArcGIS,” outlines this workflow nicely. The first step in the least cost path analysis workflow is to reclassify the value ranges of the rasters to make sure that they use a common weighting scale. The next step is to combine the reclassified rasters and create a total cost surface. This step is followed by performing a cost weighted analysis to create cost the distance and cost direction rasters that are required to complete the analysis. The final step in conducting a least cost path analysis is to use the cost distance and cost direction rasters as the main inputs in the cost path tool. This tool then determines the final least cost path from the source to the destination.

## Applications/Examples of Least Cost Path Analysis

Least cost path analysis has a number of different GIS applications. It is often used in planning infrastructure such as roads, pipelines, canals, and power transmission lines as well as for recreational uses such as the development of a hiking trail system in a national park (Chang). Least cost path analysis can also be used by ecologists to monitor wildlife movements to combat environmental issues like habitat fragmentation. Economic and business geographers as well as those making tourist maps and guides can use least cost path analysis to determine the best and most cost-effective routes between places on delivery routes, national monuments or other destinations.

Whatever its use, least cost path analysis is an important tool in GIS because it has the ability to help businesses, city planners and other users save time and money.

References

Chang, Kang-tsung. (2012). Introduction to Geographic Information Systems. McGraw-Hill: New York, 6th Edition.

ESRI. (n.d.). “Creating the Least Cost Path.” ArcGIS Resources. Retrieved from: http://resources.arcgis.com/en/help/main/10.1/index.html#//009z00000021000000[S1]  (3 April 2014).

ESRI. (n.d.). “Distance Analysis Using ArcGIS.” ESRI Virtual Campus. Personal Notes. (Course Taken 2 April 2014).