Improving an exact solver for the traveling salesman problem using partition crossover

Abstract

The best known exact solver for generating provably optimal solutions to the Traveling Salesman Problem (TSP) is the Concorde algorithm. Concorde uses a branch and bound search strategy, as well as cutting planes to reduce the search space. The first step in using Concorde is to obtain a good initial solution. A good solution can be generated using a heuristic solver outside of Concorde, or Concorde can generate its own initial solution using the Chained Lin Kernighan (LK) algorithm. In this paper, we speed up Concorde by improving the initial solutions produced by Chained LK using Partition Crossover. Partition Crossover is a powerful deterministic recombination operator that is able to tunnel between local optima. In every instance we examined, the addition of recombination resulted in an average speed-up of Concorde, and in the majority of cases, the difference in the runtime costs was statistically significant.