Traveling tournament problem

The traveling tournament problem (TTP) is an mathematical optimization problem that has been widely studied. The problem is to schedule a series of teams such that:

1. Each team plays every other team twice, once at home and once in the other's stadium.
2. No team plays the same opponent in two consecutive weeks.
3. No team plays more than three games in a row at home, or three games in a row on the road.

A matrix is provided of the travel distances between each team's home city. All teams start and end at their own home city, and the goal is to minimize the total travel distance for every team over the course of the whole season.

There have been many papers published on this subject, and there is a contest to find the best solutions for certain specific schedules.