The Traveling Salesman Problem statement is as follows: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?

This problem is NP-hard because it is as hard as a NP-Complete problem Hamilton Cycle and doesn't have an efficient certifier (not necessarily need this to be NP-Hard though). It can not be solved within polynomial time. The reason is this: Suppose there are 19 cities in total, then I have 19 choices of which city should I travel first, 18 choices of which city should I travel second, ..., 1 choice of which city should I travel at last. In total, that is 19! possibilities, out of the 19! possibilities, I pick the one that has the shortest total distance.

If my computer can test one billion tours per second. It is going to take 19!/1,000,000,000 seconds ~ 3.85 years to finish. Therefore, it is unfeasible to enumerate all possibilities. This project proposes a partial solution using Genetic Algorithm and calls Google Maps API to visualize. You can also utilize this project to plan your travel over 100+ places with ease.

(please note that I am using my personal Google Maps API key to host the demo. So I've set up restrictions of daily usage limit. If you see Google Map does not load correctly. It means the daily limit was exceeded. The settings for the demo site are population of 128, numIterations of 10000, and mutChance of 0.2)

1. Replace apiKey attribute in config.js with your own Google Maps API Key. If you do not have one, here is the link to create one (❗❗❗ Note: Fees charged by Google may apply ❗❗❗)
2. Open index.html, type an address in the search bar and Google Maps' Autocomplete API will show you a list of addresses. click on one will add a waypoint, the first waypoint added is the origin
3. Check Return To Origin? or not, which means whether the solution should include going back to the origin
4. Click Calculate Best Route! at the bottom of index.html, enjoy!

• popSize: An integer == Population size == The total number of individual routes
• numIterations: A number > 0 == How many iterations the Genetic Algorithm should run. Generally the more iterations, the more GA converges
• mutChance: A float between 0 and 1 == Mutation chance, as explained in How Does It Work?

• This project solely calculates the distance between 2 waypoints using Haversine distance. However, this approach has 2 major disadvantages:
  • Shortest distance is not always equal to shortest time
  • Haversine distance calculates the distance of a straight line between 2 waypoints, whereas there are other factors involved in the shortest distance such as the existence/straightness of a road and/or elevation
  • All of the above 2 problems can be solved by simply querying Google Maps' Directions API, but again, Google Maps charges very high for this API. In future versions, will add support to let the user decide whether to use Google Maps' Directions API or Haversine distance for calculating distances
• Genetic Algorithm does not gurantee to generate the global optimal solution since Genetic Algorithm may converge fairly quickly. This is why we want mutChance for mutation to add a little bit of randomness here

• This project's idea originates from ITP 435-Professional C++ taught at the University of Southern California designed by Sanjay Madhav
• This is the first time I ever touched Javascript. I am a lifelong C++|Python|Java|PHP developer. So please bear with me if my Javascript coding style is a mess. Any suggestions are more than welcome!