Some Methods of Producing Approximate Solutions to Travelling Salesman Problems with Hundreds or Thousands of Cities

Many large practical combinatorial problems await methods of solution, especially those involving the scheduling of hundreds or thousands of activities. The travelling salesman problem is archetypal and has attracted much attention, yet published rigorous methods can only be applied to problems encompassing tens of cities and approximate methods appear only to have been applied to problems of up to 105 cities. None of these methods offers scope for extension to much larger problems because of rapidly increasing computing requirements.