paigeweber13 / traveling-salesman-ilp

Applying integer linear programming to the traveling salesman problem.

Traveling Salesman ILP

Applying integer linear programming to the traveling salesman problem

Warning: VERY WIP. The only real code is in src/main-tsp-ilp.cpp. Everything else is files for unit tests and libraries and such that I figured I'd need but didn't get far enough in the project to use

Dependencies:

• catch: only needed for tests (runnable with make test). Installable on ubuntu with sudo apt install catch
• boost: installable on ubuntu with sudo apt install libboost-all-dev
  • specifically, only the Matrix datatype is used, so you can include that alone if you'd rather not install everything

Running:

Running Implementation that uses the C/C++ Callable Library

Install dependencies, then run make run in the root directory of this project

Problems:

• doesn't currently find a feasible solution and I'm not sure why. On paper I can make a feasible solution so it must be something with how I've programmed it.

Questions:

• How do the such that statements map to the parts of the matrix?
• so the matrix is a list of linear equations, right? So I guess the sum of all $x_{ij}$ would be to list every $x_{ij}$ and then say the constraint is equal to 2?
  • so only list the edges that don't have that k could be given a constant of infinity

Help from Erik

l_ij is a coefficient in one constraint x_ij are the variables

• need one variable for every edge

2nd constraint

• will need a row for every k
• constraint isn't exactly right, should be sum ik and sum kj the sum of x_e for an incident edge is 2.