Take in 20x random 2d coordinates and work out the shortest path for a person to visit each point.
That is the travelling salesman problem. It is a NP Hard problem meaning there is no known polynomial complexity algorithm for this. The only known ways to solve this are using exponential complexity algorithms. For TSP, brute force will be O(n!) which means you can't use brute force even if you have just 20 points to visit.
You have to solve such problems using heuristic algorithms (sub optimal). One such algorithm that is used for TSP is Held-Karp algorithm which has a complexity of O(2^n). You can read about it here : Held-Karp