Shortest and least-cost pathway analysis for optimization of power-line routing
Overview
The following analysis utilizes shortest-pathway and least-cost pathway techniques to optimize routing of a power-line from a transformer to a greenhouse facility.
Background
Examples of anisotropic surfaces:
One example of an anisotropic surface would be a moving walkway. It would take virtually zero walking energy to move across the walkway in the engineered direction. Attempting to cross the walkway from the opposite direction would take significantly more energy, similar to trying to outrun a treadmill. Another example of an anisotropic surface could be a slippery grass hill. While steeper gradients require more energy to move through than lesser gradients, for this example we will assume that the potential energy present in a person at the top of the hill is accumulated without physical expenditure. To slide down the hill will require relatively little energy on the part of the person, who is simply converting the potential energy to kinetic energy in sliding down the hill. However, it will take more energy on the part of the person to climb back up the hill. For one, the grass is slippery and the lack of traction will work against the ability of the person to climb the hill. For another, the person will now be working against gravitational acceleration to climb the hill. Conversely, in the previous example gravity worked in conjunction with the person’s movements down the hill.
Basic explanation of shortest-distance and least-cost path concepts:
The shortest-path simply creates a path that follows the shortest distance between the manufacturing plant and the greenhouse facility. This line does not take into account any changes in topography or geographical conditions that may affect ease of movement across the surface. Even if there were a large mountain in the middle of the route taking the shortest path to the greenhouse facility the path would go up and over the mountain. This path would still be shorter in length than routing around the mountain, but the energy and time expended in going over the mountain would be much greater than for circumnavigating the mountain. The shortest-path may then take the most direct route to the greenhouse facility while still routing through difficult-to-cross areas. For example, the shortest-path routes directly through residential neighborhoods despite obvious associated difficulties with this choice.
The least-cost path attempts to resolve this “ease of movement” issue. In the above case the least-cost path would route around the mountain to reduce the “cost” of routing directly over the mountain. To create this path the analyst would create a “friction surface” of the terrain in between the manufacturing plant and the greenhouse. The analyst would assign different “cells” (parts of the terrain of equal areas) different values representing the ease of movement across that “cell” (“friction values”). In the case of routing the power-line to the greenhouse facility, the “costs” of moving across the different cells would be related to the difficulty or expenditure in constructing a power-line on different surfaces. In this way the least-cost path takes into account the obstacles to power-line construction across a residential neighborhood and reduces this cost by avoiding residential areas.
Results
The length of the least-cost path is 41,882 m. The length of the shortest-path route is 34,255 m. The ‘cost’ of the least-cost path is 11,450 m. The ‘cost’ of the shortest-path route is 80,487 m.