I would like to know if there is any way to solve the problem, for example, the TSP, sum of subsets or knapsack problem using linear programming and not by brute force.

I ask because I make a program using linear programming and it solves them, but the execution time does not vary specifically from the input size, so I can't define O(n) yet.

For example, for the TSP with an input size n=20, depending on the cases and tested on an ordinary computer, it takes between 30 seconds and 3 minutes to solve them.

Greetings.