Finding the most efficient route in a trail network

[mattkirk1]

Hello, I’m looking for help with a mapping question.

There’s a network of about 150 official trails in the Great Smoky Mountains National Park (GSMNP) totaling about 790 miles. To hike all these trails (ending at a trail head), one has to repeat some mileage. There’s a guidebook out there that provides a 1060-mile plan for completion (with hikes limited to 20-miles or less). There’s also a hiker who’s reportedly completed all the trails by hiking only 924 miles.

Here’s the question: is there a way to calculate the most efficient route for completing all unique 790 miles of trails in GSMNP using ArcGIS (or other program)?

If so, any tips to help me get started would be appreciated!

Relevant links:

Google map with all trails and trail heads:goo.gl/KV8VCv

GSMNP trail index: http://tnlandforms.us/gsmnp/trails.php

[JoeBorgione]

Efficient is subjective.  It sounds like you want to explore the  Traveling Salesman Problem.  See Travelling salesman problem - GIS Wiki | The GIS Encyclopedia 

ArcGIS Network Analyst can do it if you can get the data. 

What is the ArcGIS Network Analyst extension?—Help | ArcGIS Desktop 

About the ArcGIS Network Analyst extension tutorial—Help | ArcGIS Desktop 

[DanPatterson_Retired]

You don't happen to have the map in a GIS-able format do you?

[mattkirk1]

Here is the map (showing trails and trail heads) in arcGIS: https://arcg.is/1iHSez 

Thank you for your insight. What I mean by "efficient" is shortest distance hiked to complete all 790 unique miles of this trail network. What could complicate matters is the fact that not all trails are interconnected. The hiker can and will have drive to trail heads (pinned on the map) to access the trail network to complete the hike. I don't want the driving distance to be added to the hiking distance analysis, if that makes sense. Again, thank you for your time.

[DanPatterson_Retired]

Matt, sorry, I meant like a *.gdb or shapefile.

[mattkirk1]

I converted it (hopefully successfully) to .gdb goo.gl/jzHkji Please forgive my ignorance here. 

I will try playing around with this some this weekend myself. To clarify a bit further on parameters, I'm assuming the hiker has access to shuttles. In other words, s/he can enter/exit the trail network at any trail head to gain maximum advantage at minimizing mileage hiked.

[mattkirk1]

OK, I'm still learning, but did convert data to correct shape file format here: https://goo.gl/mGjnXq 

I will have to wait until I have subscription or access to another gis program to run a spatial analysis with this data to come to a solution. Again, I appreciate your input and thank you for the help.