🏈 A hybrid local search and MIP-heuristic for the traveling tournament problem.

This python package contains a simple hybrid local search and MIP-heuristic for the traveling tournament problem. In detail, it uses a modified algorithm variant of the original approach described here, which is due to M. Goerigk and S. Westphal.

The definition of the TTP is as follows: Let a set of n teams and a distance matrix D be given. Here, D[i,j] is the distance from team i to team j. One wants to find a feasible double round robin tournament of the teams satisfying the following conditions:

• the length of any home stand is at most max_k.
• the length of any road trip is at most max_k.
• the two games between any two teams do not follow immediately.
• the sum of the distances traveled by the teams is minimized.

Starting from a canonical feasible solution, the algorithm uses a greedy local search to improve the solution (Phase I). As soon as we are stuck at a local minimum, the algorithm then tries to escape the local minimum by a MIP-heuristic (Phase II). Here, it optimizes the home-away patterns and the team matchups in alternation as long as it is not possible to improve the previous solution. Then, it switches back to Phase I and repeats. It terminates if neither Phase I nor Phase II can further improve the current best solution.

The local search is written in Cython and thus guarantees a high performance. Since most of the algorithm runtime is spent in Phase II, it's possible to set a custom MIP Gap. This can reduce the runtime dramatically but will lead to worse solutions in most cases. However, there are some cases where a higher MIP Gap gives better solutions, which in turn indicates that the neighborhoods used by the local search are not fully connected.

After installing Cython and a C++ compiler with C++17 support, this package can be installed via

pip3 install git+https://github.com/jhelgert/pyTTP

import numpy as np
from pyTTP import solve, print_schedule

team_names = ["ATL", "NYM", "PHI", "MON"]
distances = np.array([[0,   745,  665,  929],
                     [745,   0,   80,  337],
                     [665,  80,    0,  380],
                     [929, 337,  380,    0]], dtype=np.int32)

objval, schedule = solve(distances, max_k=3)
print_schedule(schedule, team_names)

gives the optimal schedule

Slot    ATL     NYM     PHI     MON

 0      @MON     PHI    @NYM     ATL
 1      @NYM     ATL    @MON     PHI
 2      @PHI    @MON     ATL     NYM
 3       NYM    @ATL     MON    @PHI 
 4       MON    @PHI     NYM    @ATL 
 5       PHI     MON    @ATL    @NYM 

with objective value 8276.