Given a collection of cities and the cost of travel between each pair of them, the traveling salesman problem is to find the cheapest way of visiting all of the cities and returning to starting point. The simplicity of the statement of the problem is deceptive, the traveling salesman problem is one of the most intensely studied problems in computational mathematics and yet no effective solution...

There are two major criticisms about simulated annealing as a general method for solving combinatorial optimization problems: its effectiveness when compared with other welldesigned heuristics and its excessive computation time. In this paper, we show that simulated annealing, with properly des~gned annealing schedule and move generation strategy, achieves significant speerlups for high quality...

We present a new lifting approach for strengthening arbitrary clique tree inequalities that are known to be facet defining for the symmetric traveling salesman problem in order to get stronger valid inequalities for the symmetric quadratic traveling salesman problem (SQTSP). Applying this new approach to the subtour elimination constraints (SEC) leads to two new classes of facet defining inequa...