Traveling Santa Problem Solver

This is a heuristic written in Python for the Traveling Santa Problem. It is based on Concorde -- a state-of-the-art Traveling Salesman Problem (TSP) solver.

Heuristic

The Traveling Santa Problem naturally decomposes into two TSP with side constraints (an edge can be in at most one TSP). This heuristic uses Concorde's Lin-Kernighan heuristic as follows:

1. Run Lin-Kernighan heuristic on first path.

   Edge restriction: can used at most n edges from the second path.

2. Run Lin-Kernighan heuristic on second path.

   Edge restriction: can't use any edge from the first path.

Result

This heuristic (IRO on the leaderboard) found a solution with an objective value of 6,593,676, which is at 1% of the solution found by the winning team (6,526,972).

Usage

Computing k Nearest Neighbor

Since each subproblem (TSP) uses a strict subset of the edges, we need to explicitly list the allowed edges to Concorde. And we can't list all edges because there are too many (~11 billions). So I decided to include edges from the k nearest neighbor graph (K-NNG). The script k_nearest_neighbor.py generates such graph in a naive way O(n^2), but it's fully parallelizable so it shouldn't take too long if you have a few cores.

Parameters:

• number of processes
• k
• instance

Example:

python3 k_nearest_neighbor.py 24 200 santa.nodes > santa.neighbors.200

Running the Heuristic

Parameters:

• instance
• neighbors
• initial solution
• linkern path
• k
• path1 time limit
• path2 time limit

Example:

python3 heur.py \
    santa.nodes \
    santa.neighbors.200 \
    incumbent_solution \
    ~/concorde/LINKERN/linkern \
    200 \
    120 \
    300

The script run can also be used to launch multiple heur.py in parallel.

Parameters:

• number or processes

Example:

./run 24

Note: you need to adapt run to your environment before using it.

Author

Mahieu Larose mathieu@mathieularose.com

License

See LICENSE