Reducing the Size of Travelling Salesman Problem Instances by Fixing Edges

The Traveling Salesman Problem (TSP) is a well-known NPhard combinatorial optimization problem, for which a large variety of evolutionary algorithms are known. However, these heuristics fail to find solutions for large instances due to time and memory constraints. Here, we discuss a set of edge fixing heuristics to transform large TSP problems into smaller problems, which can be solved easily with existing algorithms. We argue, that after expanding a reduced tour back to the original instance, the result is nearly as good as applying the used solver to the original problem instance, but requiring significantly less time to be achieved. We claim that with these reductions, very large TSP instances can be tackled with current state-of-the-art evolutionary local search heuristics.