Reducing the Size of Travelling Salesman Problem Instances by Fixing Edges

Summary

The Travelling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem, for which a large variety of evolutionary algorithms are known. However, with instance size the effort to find good solutions increases considerably. Here, we discuss a set of eight edge fixing heuristics to transform large TSP problems into smaller problems, which can be solved easily with existing algorithms. The edge fixing heuristics exploit properties of the TSP such as nearest neighbour relations or relative edge length. 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 requires significantly less time to be achieved.