Simulated annealing with an optimal fixed temperature

Contrary to conventional belief, it turns out that in some problem instances of moderate size, fixed temperature simulated annealing algorithms based on a heuristic formula for determining the optimal temperature can be superior to algorithms based on cooling. Such a heuristic formula, however, often seems elusive. In practical cases considered we include instances of traveling salesman, quadratic assignment, and graph partitioning problems, where we obtain results that compare favorably to the ones known in the literature.