Least Cost Path function

Overview

Calculates the least-cost path from a source to a destination. The least accumulative cost distance is calculated for each cell over a cost surface, to the nearest source. This produces an output raster that records the least-cost path, or paths, from selected locations to the closest source cells defined within the accumulative cost surface, in terms of cost distance.

Tip:

The Distance Accumulation and Optimal Path As Raster functions provide enhanced functionality or performance.

Each least-cost path is assigned a value when encountered in the scanning process. The ending pixel on the Source Raster of a cost path receives a value of 1. The first path receives a value of 3, the second 4, and so on. When multiple paths merge and follow the remaining distance back to a source on the same route, the segment where the two paths travel together is assigned a value of 2. The merged portion of the path cannot be assigned the value of one of the paths, since the merged portion belongs to both routes.

This is a global raster function.

Notes

The Source Raster must be a raster. If your source is a feature class, you'll need to convert it to a raster before you can use it as an input. The NoData values that exist in the Source Raster are not included as valid values in the function. The value 0 is considered a legitimate value in the source raster. A Source Raster can be created using the extraction tools or the Clip function.

Cell values of NoData in the Cost Raster act as barriers in the cost surface. Any cells that are assigned a value of NoData in the Cost Raster will also have a value of NoData in the output raster. The Cost Raster cannot contain a value of 0 since the algorithm is a multiplicative process. If values of 0 represent areas of low cost, change the value of 0 to a small positive value such as 0.01 using the Con function. If the value of 0 represents areas that should be excluded from the analysis, these values should be turned into NoData using the Set Null function.

If the Source Raster and the Cost Raster have different extents, the default output extent is the intersection of the two rasters. If you want a cost distance surface output of the entire extent, choose the Union of Inputs option on the Output Extent geoprocessing environment.

The Maximum Distance is specified in the same cost unit as the Cost Raster.

The characteristics of the source, or the movers from a source, can be controlled by the following parameters:

• Multiplier to Apply to Costs—The mode of travel or magnitude at the source.
• Start Cost—The starting cost before the movement begins.
• Accumulative Cost Resistance Rate—A dynamic adjustment accounting for the impact of accumulated cost; for example, simulating how much a hiker is becoming fatigued.
• Capacity—The cost a source can assimilate before reaching its limit.

If any of the source characteristics' parameters are specified using a value, that value is applied to all of the sources. If the parameters are specified through fields associated with the Source Raster, the values in the table will be uniquely applied to the corresponding sources.

If the Mask has been set in the geoprocessing environments, all masked cells will be treated as NoData values. When a mask is defined in the Raster Analysis window and the cells to be masked will mask a source, the calculations will occur on the remaining source cells. The source cells that are masked will not be considered in the computations. These cell locations will be assigned NoData in the output raster. See Analysis environments and Spatial Analyst for additional details on the geoprocessing environments that apply to this function.

Parameters

Parameter nameDescription

Source Raster

(Required)

This is a raster dataset identifying the cells or locations from which the least accumulated cost distance for every output cell location is calculated.

Destination Raster

(Required)

A raster dataset that identifies the pixels from which the least-cost path is determined to the least costly source. This input consists of pixels that have valid values, and the remaining pixels must be assigned NoData. Values of 0 are valid.

Destination Field

The field used to obtain values for the destination locations.

Cost Raster

(Required)

A raster defining the cost or impedance to move planimetrically through each cell. The value at each cell location represents the cost-per-unit distance for moving through it. Each cell location value is multiplied by the cell resolution, and also compensates for diagonal movement to obtain the total cost of passing through the cell.

The values of the Cost Raster can be integer or floating point, but they cannot be negative or zero.

Path Type

A keyword defining the manner in which the values and zones on the input destination data will be interpreted in the cost path calculations:

• Each Cell—A least-cost path is determined for each pixel with valid values on the input destination data, and saved on the output raster. Each cell of the input destination data is treated separately, and a least-cost path is determined for each from cell.
• Each Zone—A least-cost path is determined for each zone on the input destination data and saved on the output raster. The least-cost path for each zone begins at the pixel with the lowest cost distance weighting in the zone.
• Best Single—For all pixels on the input destination data, the least-cost path is derived from the pixel with the minimum of the least-cost paths to source cells.

Maximum Distance

The threshold that the accumulative cost values cannot exceed. If an accumulative cost distance exceeds this value, the output value for the cell location will be NoData. The maximum distance defines the extent for which the accumulative cost distances are calculated. The default distance is to the extent of the output raster.

Multiplier to Apply to Costs

This parameter allows for control of the mode of travel or the magnitude at a source. The greater the multiplier, the greater the cost to move through each cell.

The values must be greater than zero. The default is 1.

Start Cost

The starting cost that will be used to begin the cost calculations. This parameter allows for the specification of the fixed cost associated with a source. Instead of starting at a cost of 0, the cost algorithm will begin with the value specified.

The value must be zero or greater. The default is 0.

Accumulative Cost Resistance Rate

This parameter simulates the increase in the effort to overcome costs as the accumulative cost increases. It is used to model fatigue of the traveler. The growing accumulative cost to reach a cell is multiplied by the resistance rate and added to the cost to move into the subsequent cell.

It's a modified version of a compound interest rate formula that's used to calculate the apparent cost of moving through a cell. As the value of the resistance rate increases, it increases the cost of the cells that are visited later. The greater the resistance rate, the higher the cost to reach the next cell, which is compounded for each subsequent movement. Since the resistance rate is similar to a compound rate and generally the accumulative cost values are very large, small resistance rates are suggested, such as 0.005 or even smaller, depending on the accumulative cost values.

The value must be greater than zero. The default capacity is to the edge of the output raster.

Capacity

Defines the cost capacity for the traveler for a source. The cost calculations continue for each source until the specified capacity is reached.

The value must be greater than zero. The default capacity is to the edge of the output raster.

Travel Direction

Defines the direction of the traveler when applying the source resistance rate.

• From Source—The source resistance rate will be applied beginning at the input source and moving out to the non-source cells. This is the default.
• To Source—The source resistance rate will be applied beginning at each non-source cell and moving back to the input source.

Either specify the From Source or To Source keyword, which will be applied to all sources, or specify a field in the Source Raster that contains the keywords to identify the direction of travel for each source. That field must contain the string FROM_SOURCE or TO_SOURCE.

Environment settings

Geoprocessing environment settings for global functions are controlled at the application level. Setting processing environments in ArcGIS Pro can be done by clicking the Environments button on the Analysis tab. See Analysis environments and Spatial Analyst for additional details on environment settings.

The following environments are supported by this global function: